To date, quantum anomalous Hall effects have been observed at band fillings ν = 1 and ν = 3 in various graphene heterostructures, where ν = An corresponds to the number of electrons per unit cell area A with n the carrier density. Although orbital magnetism is generally expected theoretically in twisted bilayer graphene, no direct experimental probes of magnetism have been reported because of the relative scarcity of magnetic samples, their small size, and the low expected magnetization density they are predicted to have.We perform spatially resolved magnetometry to image the submicron magnetic structure of the same sample presented in the previous chapter and in Ref. , which consists of a twisted graphene bilayer aligned to one of the hexagonal boron nitride encapsulating layers. Figure 5.1B shows a schematic representation of our experimental setup. We use a superconducting quantum interference device fabricated on the tip of a quartz tube from cryogenically deposited indium with a magnetic field sensitivity of approximately 15 nT/Hz1/2 at select outof-plane magnetic fields of less than 50 mT. The SQUID is mounted to a quartz tuning fork and rastered in a 2D plane parallel to, and at a fixed height above, the tBLG heterostructure. Here n is the nominal density inferred from a parallel plate capacitor model, with the capacitance determined from the lowfield Hall density . Images are acquiredin the same background magnetic field B = 22 mT but on opposite branches of the hysteresis loop shown in Fig. 5.1A. As demonstrated in Fig. 8.16, and explained in more detail in the appendix, raspberry container the measured BT F contains contributions from magnetic signals as well as other effects arising from electric fields or thermal gradients. To isolate the magnetic structure that gives rise to the observed hysteretic transport, we subtract data from Figs. 5.1, C and D, from each other.

The result is shown in Fig. 5.1E, which depicts the gradient magnetometry signal associated with the fully polarized orbital ferromagnet. To reconstruct the static out-of-plane magnetic field, Bz, we integrate BT F along ˆa from the lower and left boundaries of the image . We infer the total magnetization density m from the Bz data using standard Fourier domain techniques as shown in Fig. 5.1G. The algorithm used for this process is covered in depth in the associatd publication. Figures 5.1, H and I, show a comparison of BT F and m plotted along the contours indicated in Figs. 5.1, E and G. The shaded regions in Fig. 5.1I denote confidence intervals, whose absolute error bounds form the dominant systematic uncertainty in |ˆa|. Our measurements are taken close to ν = 3, equivalent to a single hole per unit cell relative to the nonmagnetic state at ν = 4 that corresponds to full filling of the lowest energy bands. We find that the magnetization density is considerably larger than 1 µB per unit cell area A ≈ 130/nm2 , where we have taken g = 2 as appropriate for graphene, in which spin orbit coupling is negligible. Without any assumptions about the nature of the broken symmetries, this state has a maximum spin magnetization of 1 µB per moir´e unit cell. Our data reject this hypothesis, finding instead a maximum magnetization density of m in the range 2 − 4 µB per moir´e unit cell corresponding to an orbital magnetization of 1.8-3.6× 10−4µB/carbon atom. We conclude that the magnetic moment associated with the Chern magnet phase in tBLG is dominated by its orbital component.In an intrinsic orbital magnet in which all moments arise from conduction electrons, the magnetization depends strongly on the density. Additional density dependence arises from the fact that contributions to the orbital magnetization from both wave-packet angular momentum and Berry curvature need not be uniformly distributed within the Brillouin zone.

Transport observations of aquantum anomalous Hall effect measure only the total Berry curvature of a completely filled band. At partial band filling, however, extrinsic contributions from scattering complicate the relationship between transport and band properties. In contrast, measuring m provides direct information about the density-dependent occupation of the Bloch states in momentum space. Although crystalline defects on the atomic scale are unlikely in tBLG thanks to the high quality of the constituent graphene and hBN layers, the thermodynamic instability of magic angle twisted bilayer graphene makes it highly susceptible to inhomogeneity at scales larger than the moir´e period, as shown in prior spatially resolved studies. For example, the twist angle between the layers as well as their registry to the underlying hBN substrate may all vary spatially, providing potential pinning sites. Moir´e disorder may thus be analogous to crystalline disorder in conventional ferromagnets, which gives rise to Barkhausen noise as it was originally described. A subtler issue raised by our data is the density dependence of magnetic pinning; as shown in Fig. 5.3, Bc does not simply track 1/m across the entire density range, in particular failing to collapse with the rise in m in the Chern magnet gap. This suggests nontrivial dependence of either the pinning potential or the magnetocrystalline anisotropy energy on the realized many body state. Understanding the pinning dynamics is critical for stabilizing magnetism in tBLG and the growing class of related orbital magnets, which includes both moir´e systems as well as more traditional crystalline systems such as rhombohedral graphite. In order to understand the microscopic mechanism behind magnetic grain boundaries in the Chern magnet phase in tBLG/hBN, we used nanoSQUID magnetometry to map the local moir´e superlattice unit cell area, and thus the local twist angle, in this device, using techniques discussed in the literature.

This technique involves applying a large magnetic field to the tBLG/hBN device and then using the chiral edge state magnetization of the Landau levels produced by the gap between the moir´e band and the dispersive bands to extract the electron density at which full filling of the moir´e superlattice band occurs . The strength of this Landau level’s magnetization can be mapped in real space , and the density at which maximum magnetization occurs can be processed into a local twist angle as a function of position . It was noted in that the moir´e superlattice twist angle distribution in tBLG is characterized by slow long length scale variations interspersed with thin wrinkles, across which the local twist angle changes rapidly. These are also present in the sample imaged here . The magnetic grain boundaries we extracted by observing the domain dynamics of the Chern magnet appear to correspond to a subset of these moir´e superlattice wrinkles. It may thus be the case that these wrinkles serve a function in moir´e superlattice magnetism analogous to that of crystalline grain boundaries in more traditional transition metal magnets, pinning magnetic domain walls to structural disorder and producing Barkhausen noise in measurements of macroscopic properties. In tBLG, a set of moir´e subbands is created through rotational misalignment of a pair of identical graphene monolayers. In twisted monolayer-bilayer graphene a set of moir´e subbands is created through rotational misalignment of a graphene monolayer and a graphene bilayer. These systems both support Chern magnets. Both systems are also members of a class of moir´e superlattices known as homobilayers; in these systems, large plastic pots for plants the 2D crystals forming the moir´e superlattice share the same lattice constant, and the moir´e superlattice appears as a result of rotational misalignment, as illustrated in Fig. 5.17A. Homobilayers have many desirable properties; the most important one is that the twist angle can easily be used as a variational parameter for minimizing the bandwidth of the moir´e subbands, producing the so-called ‘magic angle’ tBLG and tMBG systems. Homobilayers do, however, have some undesirable properties. Although local variations in electron density are negligible in these devices, the local filling factor of the moir´e superlattice varies with the moir´e unit cell area, and thus with the relative twist angle. The tBLG moir´e superlattice is shown for two different twist angles in 5.17B-C across the magic angle regime; it is clear that the unit cell area couples strongly to twist angle in this regime, illustrating the sensitivity of these devices to twist angle disorder. The relative twist angle of the two crystals in moir´e superlattice devices is never uniform. Imaging studies have clearly shown that local twist angle variations provide the dominant source of disorder in tBLG . It is hard to exaggerate the significance of this problem to the study of moir´e superlattices. Orbital magnetism at B = 0 has only been realized in a handful of tBLG devices, and quantization of the anomalous Hall resistance has only been demonstrated in a single tBLG device, in spite of years of sustained effort by several research groups. A mixture of careful device design limiting the active area of devices and the use of local probes has allowed researchers to make many important discoveries while sidestepping the twist angle disorder issue- indeed, some exotic phases are known in tBLG only from a single device, or even from individual scanning probe experiments- but if the field is ever to realize sophisticated devices incorporating these exotic electronic ground states the problem needs to be addressed.

There is another way to make a moir´e superlattice. Two different 2D crystals with different lattice constants will form a moir´e superlattice without a relative twist angle; these systems are known as heterobilayers . These systems do not have ‘magic angles’ in the same sense that tBLG and tMBG do, and as a result there is no meaningful sense in which they are flat band systems, but interactions are so strong that they form interaction-driven phases at commensurate filling of the moir´e superlattice anyway. Indeed, many of the interaction-driven insulators these systems support survive to temperatures well above 100 K. The most important way in which heterobilayers differ from homobilayers, however, is in their insensitivity to twist angle disorder. In the small angle regime, the moir´e unit cell area of a heterobilayer is almost completely independent of twist angle, as illustrated in 5.17E-F. A new intrinsic Chern magnet was discovered in one of these systems, a heterobilayer moir´e superlattice formed through alignment of MoTe2 and WSe2 monolayers. The researchers who discovered this phase measured a well-quantized QAH effect in electronic transport in several devices, demonstrating much better repeatability than was observed in tBLG. The unit cell area as a function of twist angle is plotted for three moir´e superlattices that support Chern insulators in 5.17G, with the magic angle regime highlighted for the homobilayers, demonstrating greatly diminished sensitivity of unit cell area to local twist angle in the heterobilayer AB-MoTe2/WSe2. MoTe2/WSe2 does have its own sources of disorder, but it is now clear that the insensitivity of this system to twist angle disorder has solved the replication issue for Chern magnets in moir´e superlattices. Dozens of MoTe2/WSe2 devices showing well-quantized QAH effects have now been fabricated, and these devices are all considerably larger and more uniform than the singular tBLG device that was shown to support a QAH effect, and was discussed in the previous chapters. The existence of reliable, high-yield fabrication processes for repeatably realizing uniform intrinsic Chern magnets is an important development, and this has opened the door to a wide variety of devices and measurements that would not have been feasible in tBLG/hBN.The basic physics of this electronic phase differs markedly from the systems we have so far discussed, and we will start our discussion of MoTe2/WSe2 by comparing and contrasting it with graphene moir´e superlattices. In tBLG/hBN and its cousins, valley and spin degeneracy and the absence of significant spin-orbit coupling combine to make the moir´e subbands fourfold degenerate. When inversion symmetry is broken the resulting valley subbands can have finite Chern numbers, so that when the system forms a valley ferromagnet a Chern magnet naturally appears. Spin order may be present but is not necessary to realize the Chern magnet; it need not have any meaningful relationship with the valley order, since spin-orbit coupling is absent. MoTe2/WSe2 has strong spin-orbit coupling, and as a result, the spin order is locked to the valley degree of freedom. This manifests most obviously as a reduction of the degeneracy of the moir´e subbands; these are twofold degenerate in MoTe2/WSe2 and all other TMD-based moir´e superlattices. The closest imaginable analog of the tBLG/hBN Chern magnet in this system is one in which interactions favor the formation of a valley-polarized ferromagnet, at which point the finite Chern number of the valley subbands would produce a Chern magnet.

What they do provide is a convenient way for us to produce two dimensional monocrystalline devices with exceptionally low disorder for which electron density and band structure can be conveniently accessed as independent variables. That is valuable for furthering our understanding of condensed matter phenomena, independent of whether the fabrication procedures for making these material systems can ever be scaled up enough to be viable for use in technologies. The properties of crystals differ from the properties of atoms floating in free space because the atomic orbitals of the atoms in a crystal are close enough to those of adjacent atoms for electrons to hop between atoms. The resulting hybridization of atomic orbitals produces quantum states delocalized over the entire crystal with the capacity to carry momentum. This situation is shown in schematic form in Fig. 1.9A. For quantum states delocalized over the entire crystal, position ceases to be a useful basis. Instead, under these conditions we label electronic wave functions by their momenta, kx and ky. The atomic orbitals that prior to hybridization had discrete energy spectra now have energy spectra given by discrete functions of momentum, f. We call these functions electronic bands. Electrons loaded into the electronic bands of a two dimensional crystal will occupy the quantum states with the lowest available energies, so we can specify a maximum energy at which we expect to find electrons for any given electron density. We call that energy EF , the Fermi level. We can raise the Fermi level by adding additional electrons to the crystal, as shown in Fig. 1.9B. We have already discussed how two dimensional crystals naturally allow for manipulation of the electron density, square plant pots and thus the Fermi level. We have also already discussed how the application of an out-of-plane electric field to a two dimensional crystal will change the structure of the atomic orbitals supported by that crystal.

It naturally follows that atomic orbitals so modified will produce different electronic bands, as shown in Fig. 1.9C. It is relatively straightforward to compute how electronic bands will respond to the application of a displacement field. We will be using the momentum and energy basis for the rest of this document; this basis is known as momentum space. The simplest experiment we can perform to probe the electronic properties of a two dimensional crystal in this geometry is an electronic transport experiment, in which a voltage is applied to a region of the crystal with another region grounded, so that electrical current flows through the crystal. We can check if the crystal supports any electrical transport at all, and if it does we can measure the electrical resistance of the crystal this way, in close analogy to how this is done for three dimensional crystals. Crystals will only accept and thus conduct electrons if there are available quantum states at the Fermi level; we call these crystals metals , and they can be identified in band structure diagrams by the intersection of the Fermi level with an electronic band . Crystals without empty quantum states at the Fermi level will not accept and conduct electrons , and they can be identified in band structure diagrams with crystals for which the Fermi level does not intersect with an electronic band . There exists a variety of other experiments we can perform on two dimensional crystals in order to understand their properties. Two dimensional crystals can support electronic transport in the in-plane direction if they are metals, as shown in Fig. 1.10. Capacitors can also support electronic transport in the out-of-plane direction, as long as that electronic transport occurs at finite frequency. The same structure that we use to modify the electron density and ambient out-of-plane electric field of a two dimensional crystal can also be used as a capacitive AC conductor, as illustrated in Fig. 1.11A.

The conductance will depend only on the frequency at which an AC voltage is applied and the geometry of the parallel plate capacitor. However, if a two dimensional crystal is added in series, the capacitance of the top gate to the bottom gate may be substantially modified. If the two dimensional crystal is an insulator, electric fields will penetrate it and the capacitance between the two gates will not change. However, if the two dimensional crystal is a metal it will accept electrons and cancel the applied electric field, dramatically reducing the capacitance between the top and bottom gates and neutralizing the AC current through the capacitor. This technique can be used to measure the electronic properties of specifically the bulk of a two dimensional crystal; it is the property that was both calculated and measured in Fig. 1.2C and D. These two techniques are the bread and butter of the experimental study of two dimensional crystals, because they require only the ability to create stacks of two dimensional crystals and access to tools common to the study of all other microelectronic systems. We will discuss a considerable amount of electronic transport and capacitance data as well. However, the primary focus of this thesis will be on systems for which the nanoSQUID microscope can provide important information that is inaccessible to these techniques, and so we will discuss a few such systems next. Consider the following procedure: we obtain a pair of identical two dimensional atomic crystals. We slightly rotate one relative to the other, and then place the rotated crystal on top of the other . The resulting pattern brings the top layer atoms in alignment with the bottom layer atoms periodically, but with a lattice constant that is different from and in practice often much larger than the lattice constant of the original two atomic lattices. We call the resulting lattice a ‘moir´e superlattice.’ The idea to do this with two dimensional materials is relatively new, but the notion of a moir´e pattern is much older, and it applies to many situations outside of condensed matter physics. Pairs of incommensurate lattices will always produce moir´e patterns, and there are many situations in daily life in which we are exposed to pairs of incommensurate lattices, like when we look out a window through two slightly misaligned screens, or try to take pictures of televisions or computer screens with our camera phones. Of course these ‘crystals’ differ pretty significantly from the vast majority of crystals with which we have practical experience, so we’ll have to tread carefully while working to understand their properties. To start with, if we attempt to proceed as we normally would- by assigning atomicorbitals to all of the atoms in the unit cell, computing overlap integrals, and then diagonalizing the resulting matrix to extract the hybridized eigenstates of the system- we would immediately run into problems, because the unit cell has far too many atoms for this calculation to be feasible.

There exist clever approximations that allow us to sidestep this issue, and these have been developed into very powerful tools over the past few years, but they are mostly beyond the scope of this document. I’d like to instead focus on conclusions we can draw about these systems using much simpler arguments. The physical arguments justifying the existence of electronic bands apply wherever and whenever an electron is exposed to an electric potential that is periodic, and thus has a set of discrete translation symmetries. For this reason, even though the moir´e superlattice is not an atomic crystal, we can always expect it to support electronic band structure for the same reason that we canal ways expect atomic crystals to support band structure. Two crystals with identical crystal symmetries will always produce moir´e superlattices with the same crystal symmetry, so we don’t need to worry about putting two triangular lattices together and ending up with something else.Another property we can immediately notice is that the electron density required to fill a moir´e superlattice band is not very large. This can be made clear by simply comparing the original atomic lattice to a moir´e superlattice in real space . Full depletion of a band in an atomic crystal requires removing an electron for every unit cell , plastic pots for planting and full filling of the band occurs when we have added an electron for every unit cell. We have already discussed how this is not possible for the vast majority of materials using only electrostatic gating, because the resulting charge densities are immense. Full depletion of the moir´e band, on the other hand, requires removing one electron per moir´e unit cell, and the moir´e unit cell contains many atoms . So the difference in charge density between full filling and full depletion of an electronic band in a moir´e superlattice is actually not so great , and indeed this is easily achievable with available technology. Before we go on, I want to make a few of the limitations of this argument clear. There are two things this argument does not necessarily imply: the moir´e bands we produce might not be near the Fermi level of the system at charge neutrality, and the bandwidth of the moir´e superlattice need not be small. In the first case, we won’t be apply to modify the electron density enough to reach the moir´e band, and in the latter, we won’t be able to fill the moir´e band’s highest energy levels using our electrostatic gate. We know of examples of real systems with moir´e superlattice bands that fail each of those criteria. But if these moir´e superlattice bands are near charge neutrality, and if their bandwidths are small, then we should be able to easily fill and deplete them with an electrostic gate.Finally, moir´e superlattice bands inherit any electronic degeneracies- like, for example, electron spin- that came with the original lattice. We haven’t discussed electronic degeneracies yet, and we will shortly. So if a moir´e superlattice satisfies all of these criteria, then it will provide a set of electronic bands that can be completely filled or depleted with an electronic gate. I’m sure this seems to the reader like a pretty niche system, and that’s more or less because it is. There aren’t too many material systems that need their atomic bonds aligned with a mechanical goniometer, and it’s hard to imagine ever integrating such a procedure into an industrial fabrication line. However, it’s tough to adequately express how hard it would be to replicate the properties of a moir´e superlattice band in an atomic crystal. I made an attempt to do so in the introduction to this thesis; suffice to say the control we have over the properties of these systems is more or less unprecedented within experimental condensed matter physics, and this means that we can perform experiments on electronic phases in these systems that would be difficult or impossible in atomic crystals. A variety of scanning probe microscopy techniques have been developed for examining condensed matter systems. It’s easy to justify why magnetic imaging might be interesting in gate-tuned two dimensional crystals, but magnetic properties of materials form only a small subset of the properties in which we are interested. Scanning tunneling microscopy is capable of probing the atomic-scale topography of a crystal as well as its local density of states, and a variety of scanning probe electrometry techniques exist as well, mostly based on single electron transistors. It’s worth pointing out that if you’re interested specifically in performing a scanning probe microscopy experiment on a dual-gated device, then these techniques both struggle, because the top gate both blocks tunnel current and screens out the electric fields to which a single electron transistor would be sensitive. Magnetic fields have an important advantage over electric fields: most materials have very low magnetic susceptibility, and thus magnetic fields pass unmodified through the vast majority of materials . This means that magnetic imaging is more than just one of many interesting things one can do with a dual-gated device; in these systems, magnetic imaging is a member of a very short list of usable scanning probe microscopy techniques. The simplest way in which we can use our nanoSQUID magnetometry microscope is as a DC magnetometer, probing the static magnetic field at a particular position in space .

Loss of integrity of the cuticle and epithelial cells of the integumentary and tracheal systems in T. molitor larvae due to densovirus infection may not only cause dehydration via excessive water loss, but also secondary infection by bacteria and fungi as a result of the loss of their primary defense barrier against infection. One limitation encountered in this study was the interpretation of a dark discoloration presented by densovirus-infected T. molitor larvae. Further investigation into the mechanism of this change is suggested as there remains uncertainty to whether this is in fact hemocyte granule prophenoloxidase-mediated melanization or some other possible explanation, such as the collection of debris over an unshed and desiccated cuticle. InI is the most important microscopical feature of the densovirus infection in T. molitor. InI observed on bright-field microscopy represents the DRAC observed on electron microscopy. The infection with TmDNV induces homogeneous basophilic- and eosinophilic-texturized InIs. Feulgen staining confirmed the DNA-dominant nature of the basophilic InIs, which correlates with DRACs accumulating maturing and mature virions on TEM as is shown in Figs. 6d and 7a. On the other hand, a great number of eosinophilic-texturized InIs presented with a fainter staining after the Feulgen reaction, which correlates with DRACs shown in TEM photomicrographs in Fig. 7c–f. Eosinophilic-texturized inclusions represented DRACs that ultrastructurally displayed an evolving mixture of heterogeneous viral matrix, maturing and mature virions, and ribosomes. Viral matrix observed in DARC was composed of electron-dense fibrillar small-aggregating-to-long-anastomosing streams, which evolved into a large compact mass that resembles the shape of a “rotary dial” . Similar structures were described in early studies of G. mellonella infected with densovirus. Later, H-1 parvovirus studies indicated that H-1 parvovirus–associated replication bodies, square plastic planter which are not uncommonly observed in DRAC in T. molitor , are composed of nucleolar fibrils and serve as the location of viral DNA replication. Differentiating maturing and mature virions from ribosomes in the infected nucleus on conventional plastic-embedded preparations posed a challenge.

However, the large number of virus particles recovered on direct TEM supports the observation that large quantities of round vesicles/ particles of about 18 to 24 nm in diameter found within the DRAC were in fact maturing and mature densovirus virions rather than ribosomes. The DRAC displayed a very pleomorphic morphology, which varied from accumulation of maturing and mature virions to dense virus matrix that mimicked nucleolar structures and paracrystalline arrays. This heterogeneous appearance of the DRAC is an important feature that characterizes and facilitates TmDNV diagnosis at the ultrastructural level. Initial TEM studies on the G. mellonella densovirus demonstrated that the nucleoplasm is completely replaced by virions during the first 20 hours of infection. As in other autonomous parvoviruses that depend on the S phase of the infected cells, TmDNV replication and assembly is a unique and dynamic process that demands a deeper understanding. Nonetheless, crystallization of the DRAC forming “paracrystalline arrays” was interpreted as the final stage of nuclear infection with densovirus in T. molitor. Numerous infected cells presented cytoplasmic membrane–bound vesicles containing virus particles or paracrystalline arrays. Intracytoplasmic paracrystalline arrays have been considered a distinct feature of Densovirinae infections. The origin of the structures is not well understood, but it should be considered as a process of infected nuclear breakdown, heterophagia, or autophagia. Ultrastructural changes of the nuclei and cytoplasm in TmDNV–infected epithelial cells suggest apoptosis as the mechanism of cell death, although studies on viruses of the Parvoviridae family suggest that the mechanisms of Parvoviridae-induced cell death are unique and complex, warranting further investigation. Fruit, nut, and berry crops are commonly grouped into one of three categories: temperate, subtropical, and tropical. Temperate zone crops include almond, apple, apricot, peach, grape, blueberry, and strawberry . Avocado, citrus, and guava are considered to be subtropical, while banana, cashew, and pineapple are tropical . Generally, temperate and subtropical crops can be grown in San Mateo and San Francisco Counties , but tropical crops are rarely successful.

This publication focuses on temperate and subtropical crops. Temperate zone crops generally require a period of cold temperature during the winter months for successful flower and fruit development. This cold temperature period is measured in “chill hours” . Some crops require many chill hours, while others require few. This is called the crop’s “chill requirement.” When selecting temperate zone crops, it is important to choose only those crops that have a chill requirement that will be met at your location. Subtropical crops, such as citrus, loquat, and guava, require little or no chilling. Native to warm-climate regions, these crops can be injured by cold temperatures during winter and spring months, and they require heat during the growing season for fruit maturation and flavor.Selecting climate zones and meeting chill requirements are not the only factors necessary for good fruit production. Pollination, sunlight, heat accumulation, and wind are all important considerations. For fruit development to occur, flowers have to be pollinated; that is, pollen must move from the male organs to the female organs . Pollen transfer can be facilitated by bees, beetles, flies, butterflies, moths, birds, bats, wind, and water. The pollen can come from flowers on the same tree , or from flowers of other trees of the same species . In some cases, a crop may require another tree of a specific variety for pollination. For information on pollination requirements, see the “Crop and Variety Selection Table” at the end of this publication. For further details, see “Notes on Crops and Varieties” below. Note that even in self fertile crops, cross-pollination can increase fruit set. Also, poor pollination can occur as a result of insufficient pollinator activity, such as during cool and wet weather in the spring when bees may be less active . For most crops, plentiful sunlight and warm temperatures during the growing season are needed. Factors such as fog, wind, elevation, aspect , and distance from the ocean affect sunlight level and temperature.In recent years, a variety of novel two-dimensional van der Waals magnets have been discovered, founding the active field of 2D magnetism.

Among these prospective compounds, binary chromium tellurides Cr1–δTe are attractive owing to their rich magnetic properties, as well as inherent chemical and structural compatibility when forming heterostructures with other topological systems, such as tetradymite-type topological insulators or chalcogenide-based Dirac/ Weyl semimetals. Furthermore, the broken time-reversal symmetry and spin-orbit coupling offer unique opportunities for the interplay between spin configurations and reciprocal-space topology. In this regard, ferromagnetic Cr2Te3 with strong perpendicular magnetic anisotropy is an intriguing platform to host non-trivial topological physics, particularly for the high-quality thin films grown by molecular beam epitaxy. The intrinsic AHE is topological in nature and a hallmark of itinerant ferromagnets, which has also been observed in more exotic systems even without a net magnetization, such as spin liquids, antiferromagnets, and Weyl semimetals. When SOC coexists with long-range magnetic order, square plastic plant pot the Berry curvature can be significantly influenced near avoided band crossings, rendering the system an incredibly rich playground combining topology and magnetism. Here, we report the unique magnetotransport signatures of highquality quasi-2D Cr2Te3 MBE-grown thin films governed by non-trivial band topologies. Via synergetic structural, magnetic, and transport measurements, together with first-principles simulations, we have uncovered novel Berry-curvature-induced magnetism featuring an extraordinary sign reversal of the AHE as we modulate the temperature and the strain for the thin films containing 3–24 unit cells on Al2O3 or SrTiO3 substrates. Moreover, a hump-shaped Hall feature emerges, most likely due to the presence of multiple magnetic layers/domains under different levels of interfacial strain. This work identifies pristine ferromagnetic Cr2Te3 thin films as a fascinating platform for further engineering topological effects, given their nontrivial Berry curvature physics.The crystalline structure of Cr2Te3 thin films is described first, followed by the development of strain at the substrate/film interface by the epitaxy. Bulk Cr2Te3 crystalizes in a three-dimensional lattice with space group P31c ðD2 3d,No:163Þ, as shown in Fig. 1a–c, where each unit cell contains four vertically stacked hexagonal layers of Cr. There are three symmetrically unique sites for Cr, labeled Cr1, Cr2, and Cr3, respectively: The Cr1 atoms are sparsely arranged in a weakly antiferromagnetic sublattice, while the Cr2/Cr3 atoms form ferromagnetic layers similar to those in CrTe2. Since the Cr1 sites are often only partially filled , Cr2Te3 behaves essentially as a quasi-2D magnet. This quasi-2D nature of Cr2Te3 allows for high-quality, layer-by-layer epitaxial growth of c-oriented films on a variety of substrates. The hexagonal c axis is the easy magnetic axis, leading to PMA for the films. The sixfold in-plane symmetry is seen in the honeycombs visualized by atomic resolution scanning tunneling microscopy and scanning transmission electron microscopy high-angle annular dark-field imaging, as well as in the reflection high-energy electron diffraction and X-ray diffraction patterns.

The sharp substrate/film interface is confirmed by the cross-sectional HAADF and the corresponding integrated differential phase contrast images. The intrinsic random distribution of Cr atoms on the Cr1 sites is resolved in the enlarged view of the atoms in Fig. 1k–m, shown overlaid with red circles, while the overall chemical composition of the thin film is uniform within the resolution of energy dispersive X-ray spectroscopy . Figure 1f illustrates the basic sample architecture, where the strain in the Cr2Te3 thin films is governed by the interface with the substrate.Upon reducing the thickness t, films grown on Al2O3 can develop an IP compressive strain up to −0.15%, as determined by XRD and summarized in Fig. 1d. A higher strain level can be sustained using SrTiO3 substrates. Such control of strain is well suited for exploring interface-sensitive properties in Cr2Te3 thin films.The magnetic properties of Cr2Te3 thin films with selected thicknesses were assessed using vibrating sample magnetometry . Figure 2a shows the temperature dependence of the magnetization M for a t = 24 u.c. film on Al2O3 substrate with an out-of-plane applied magnetic field μ0H = 0.1 T. Under the field-cool condition, M rises below the Curie temperature TC ~ 180 K, reaching M ~2.50 μB per Cr at 2 K in the 0.1 T field. The zero-FC scan, on the other hand, deviates from the FC curve below the blocking temperature Tb, signaling the freezing out of domains in a random direction in the absence of an aligning field. As illustrated in Fig. 2b, Cr2Te3 favors PMA with coercive field μ0Hc = 0.76 T and saturation magnetization Ms ~2.83 μB per Cr at 2 K for t = 24 u.c., whereas the IP measurements have weaker ferromagnetic hysteresis loops. The low-T zero-field kink feature in the OOP M becomes more prominent with reduced thickness . The multistep hysteresis attests to the presence of varied layer-dependent magnetic anisotropies, despite the overall chemical and phase homogeneity of the films34. This is consistent with the interfacial strain-driven magnetic profiles revealed by the depth-sensitive polarized neutron reflectometry as described below. The PNR experiments, responsive to the IP magnetization, were carried out at chosen T and H on samples with t = 24 and 6 u.c. to uncover the impact of interfacial strain and the details of the stepwise hysteresis loops due to the interplay between anisotropy and the Zeeman energies in an applied external magnetic field. The PNR spin asymmetry ratio SA = /, measured as a function of the wave vector transfer Q = 4πsin/λ with R+ and R− being the reflectivity for the neutron spin parallel or antiparallel to the external field, evidently confirms the magnetization . By simultaneously refining PNR and X-ray reflectivity data, the depth profiles of nuclear and magnetic scattering length densities at μ0H = 1 T, 0.8 T and 0.05 T for t = 24 u.c. were obtained and are shown in Fig. 2c. The uniform MSLD profile at the IP saturation field μ0H = 1 T attests to the high quality of the magnetic Cr2Te3 film with well-defined interfaces of 0.5 nm roughness. Remarkably, at reduced IP field μ0H = 0.8 T and 0.05 T, M develops a non-uniform depth-dependent profile with two distinct regions, possessing a lower IP magnetization value close to the substrate. Given that the NSLD depth profile of the Cr2Te3 layer is uniform and no changes are detected in the structure and chemical composition of the film, we attribute the reduced IP magnetization approaching the substrate to a canting of the magnetization vector towards the OOP direction .

Those differences could be explained by the diploid phasing of the Cabernet Sauvignon genome assembly and that multiple ISNT transcripts might correspond to a single gene locus. Nonetheless, similar relative amounts of Biological Process GO terms were found among the differentially expressed genes, confirming that the transcriptome obtained using Iso-Seq captured the transcriptional reprogramming underlying the main physiological and biochemical changes during grape berry development. In addition, gene expression analysis revealed that some private isoforms are significantly modulated during berry development, indicating that in addition to identifying the private gene space, the ISNT reference makes it possible to observe its expression. In conclusion, this study demonstrates that Iso-Seq data can be used to create and refine a comprehensive reference transcriptome that represents most genes expressed in a tissue undergoing extensive transcriptional reprogramming during development. In grapes, this approach can aid developing transcriptome references and is particularly valuable given diverse cultivars with private transcripts and accessions that are genetically distant from available genome references, like the non-vinifera Vitis species used as rootstocks or for breeding. The pipeline described here can be useful in efforts to reconstruct the gene space in plant species with large and complex genomes still unresolved.While San Joaquin Valley vineyards are currently fertilized with boron through the soil and foliage , some growers have expressed interest in applying boron via drip irrigation or “fertigation.” Fertigation is a relatively simple, cost-effective and efficient way to apply nutrients. However, irrigation water with more than 1 part per million boron can lead to vine toxicity, so the safety of boron fertigation is also a concern. Our research evaluates the safety and efficacy of boron fertigation in grapevines using drip irrigation. Boron is unique among the micronutrients due to the narrow range between deficiency and toxicity in soil and plant tissues. For grapevines, 25 liter plant pot this range is 0.15 ppm to 1 ppm in saturated soil extracts, and 30 ppm to 80 ppm in leaf tissue.

The goal of boron fertilization of grapevines is to keep tissue levels within this narrow range, since both deficiency and toxicity can have serious negative effects on vine growth and production. Fertilization amounts must be precise to avoid toxicity while providing adequate boron to satisfy grapevine requirements . On the east side of the San Joaquin Valley, boron deficiency of grapevines occurs on soils formed from igneous rocks of the Sierra Nevada. This parent material is low in total boron, which is crystallized in borosilicate minerals that are highly resistant to weathering. Boron deficiency is often associated with sandy soils and vineyard areas with excessive leaching, such as in low spots or near leaky irrigation valves. Vine symptoms of boron deficiency are more widespread and pronounced following high rainfall years, when greater amounts of soluble boron are leached from the root zone. In addition, snow melt water has very low levels of boron, and vineyards irrigated primarily with this water have a greater risk of deficiency. Boron is required for the germination and growth of pollen during flowering, and vines that are deficient in this micronutrient will have clusters that set numerous shot berries, small berries with a distinctive pumpkin shape. When boron deficiency is severe, vines produce almost no crop. Foliar symptoms appear in the spring: shoots have shortened, swollen internodes and their tips sometimes die, and leaves have irregular, yellowish mottling between the veins. Grapevines are also sensitive to too much boron. Toxicity is common on the west side of the San Joaquin Valley, where most soils are derived from marine sedimentary and meta sedimentary parent material that is rich in easily weathered boron minerals. Symptoms of boron toxicity include leaves that are cupped downward in the spring and that develop brown spots adjacent to the leaf margin in middle or late summer, intensifying and leading to necrosis as boron accumulates. Yields are reduced, the result of diminished vine vigor and canopy development. When foliar boron sprays are applied in excess in the spring, juvenile leaves become cupped within 2 weeks; however, vines quickly recover and yields are usually unaffected. Toxicity also occurs when boron fertilizer is applied in excess, regardless of the soil type, and this can lead to yield loss. Over-fertilization is the sole reason for boron toxicity on the east side of the San Joaquin Valley, so it is critical to establish how much boron fertilizer can be applied safely and effectively.

Our research investigated the uptake of boron by grapevines when fertilizer was applied with a drip-irrigation system.Research was conducted from 1998 to 2001 in a mature ‘Thompson Seedless’ raisin vineyard near Woodlake in Tulare County. The vineyard was planted in Cajon sandy loam on a recent alluvial fan associated with the Kaweah River. This soil is derived from granitic parent materials, and the surface soil is highly micaceous with a slight to moderate amount of lime. The underlying soil has a coarse, sandy texture. At the onset of this study, the vineyard’s boron status was in the questionable range for deficiency. The vine’s leaf petioles and blades contained about 30 ppm boron. While the foliage had no symptoms of boron deficiency, in the past the grower had observed sticking caps and pumpkin-shaped shot berries, which are indicative of boron deficiency. During the course of the research, the vineyard was drip-irrigated from April through October. The vineyard canopy covered 60% of the land surface during summer months and about 20 inches of water was applied during the season. Boron treatments consisted of applying fertilizer in varying amounts 3 weeks prior to bloom on May 18, 1998, and then again 3 weeks prior to bloom the following year, on May 3, 1999. Growers who fertigate grapevines with a drip system generally inject material into the irrigation water over a 45-to- 60-minute period at the beginning of an irrigation set. We simulated fertigation by applying Solubor, a soluble boron product , to a shovel-sized hole beneath drippers during the first hour of the irrigation set. By doing this, precise amounts of boron could be applied to each plot and plot size could be reduced. This technique has been used successfully in previous research with other nutrients . The experiment was designed as a randomized complete block with five treatments, five blocks and five vine plots . To evaluate the rate of boron uptake and accumulation in tissue with consecutive years of fertilization, grape tissue samples were collected in 1998 and 1999 at bloom and then again about 6 weeks later during veraison. Veraison is the stage of development where berries begin to soften and/or color. To evaluate carryover, leaf tissue samples were also collected at this Tulare County site at both bloom and veraison in 2001, 2 years after the fertilization was discontinued. In each case, 100 petioles and 50 blades were sampled per plot from the center three vines. Petioles and blades were taken opposite inflorescences during bloom, and recently matured leaves were sampled at veraison. Samples were oven-dried, ground in a Wiley mill and sent to the UC Davis DANR Analytical Laboratory for analysis of total boron. Statistical analysis was by ANOVA using least significance difference to separate treatment means. A second experiment was conducted in 1998 in Fresno County near Selma, in a mature Thompson Seedless raisin vineyard planted on Pollaski sandy loam and drip-irrigated.

The soil was formed in place from the weathering of softly to moderately consolidated granitic sediments. The particle size distribution of the surface soil is 63% sand, 25% silt and 12% clay. At the onset of the experiment, boron tissue levels were in the adequate range, 40 ppm. In both experiments, drip irrigations during the season were based on a schedule using historical evapotranspiration and developed for raisin vineyards in the San Joaquin Valley . The irrigation source was high-quality pump water with a boron concentration less than 0.1 ppm. The experimental design and methods were identical in both vineyards, except that the 1/16-poundper-acre boron treatment was omitted in the second vineyard. The Fresno County trial was discontinued after tissue samples were taken at bloom and veraison in 1998.At both the Tulare and Fresno county sites, black plastic plant pots boron uptake was rapid when fertilizer was applied in the spring. In both vineyards, applying boron at 2/3 or 1 pound per acre increased the boron concentration in blades by bloom, 3 weeks after application. Boron increased further in blades by veraison . In the Tulare County vineyard, boron in bloom tissue increased from a questionable deficiency range to adequate; at the Fresno location, boron in bloom tissue increased from 40 ppm to 54 ppm, a dramatic increase considering boron fertilizer was applied just 3 weeks prior. This indicates that boron uptake is rapid. None of the fertigation treatments resulted in either symptoms of boron toxicity or deficiency. Applying boron at 1/3 pound per acre or less did not significantly increase boron tissue levels by bloom or veraison at either site the first year. Fertigation over consecutive years was evaluated at the Tulare County location. Boron in grapevine tissue continued to increase with consecutive years of application. At the higher fertilizer rate , boron levels in blades increased from 35 ppm in control vines to about 60 ppm. We speculate that continuing with annual applications of 1 pound boron per acre would result in toxicity within 4 to 5 years. The 1/3-pound-per-acre rate significantly elevated boron in blades by veraison of the second year to adequate levels . There were no visual signs of toxicity in any of the fertilizer treatments, even when boron was applied at 2 pounds per acre in a single application. Boron levels in tissue remained unchanged 2 years after fertilization was discontinued at the Tulare County location . This indicates substantial treatment longevity with fertigation of a drip-irrigated vineyard. Rainfall during this experiment was below normal, which helped minimize leaching. Also, well-managed drip irrigation minimizes leaching. Under drip irrigation, salts tend to accumulate near the soil surface and 2 to 3 feet away from the drip line, with minimal water and salt movement below the root zone when irrigations are accurately scheduled . Boron concentrated more in the blades than in the petioles in response to fertilization. At the onset of the Tulare County experiment, boron concentrations in petioles and blades were similar at 31 ppm and 34 ppm, respectively. Fertilizing with 1 pound boron per acre for 2 consecutive years resulted in a 25% increase of boron in petioles but a 76% increase in blades . All fertilizer treatments increased boron in blades more than in petioles, indicating that blades should be sampled when monitoring the vines’ boron status following fertilization. Potential boron toxicity values at the time of sampling during the bloom period are 80 ppm for petioles and 120 ppm for blades, and in mid- to late summer are 100 ppm for petioles and 300 ppm for blades.Annual boron fertigation at 1/3 pound per acre elevated grapevine tissue levels from questionable to the adequate range within 2 years . In addition, tissue boron levels remained unchanged 2 years after fertilization was discontinued. This is probably because leaching was reduced by two factors: below-normal rainfall and accurately scheduled drip irrigations. After fertilization, boron was concentrated more in blades than in petioles, indicating that blades are the best choice for monitoring toxicity. Blade samples should be monitored on a routine basis and fertilizer amounts should be adjusted accordingly to avoid boron toxicity or deficiency. The results of this research can be applied to other drip-irrigated vineyards in the San Joaquin Valley under similar conditions: rapidly drained soils, high quality irrigation water, and low boron content in soil, water and vine tissue. In other regions of the state where winter rainfall is much higher, there would presumably be more leaching of boron fertilizer during winter months and less carryover time after fertilization is discontinued. In contrast, less leaching and greater carryover of boron would be expected in areas of less rainfall or on soils with finer texture and higher water-holding capacity. These variables underscore the importance of monitoring boron in tissue when developing a long-term fertilization program.The study of crop domestication has long been used as a proxy for studying evolutionary processes, such as the genetic effects of bottlenecks and the detection of selection to identify agronomically important loci .

To further explore links between management and soil fertility, we used the results from the PCA to formalize a gradient in management across all farms, and then used this gradient as the basis for comparison between Field A and Field B across all indicators for soil fertility. Using the ggplot and tidy verse packages , we displayed the difference in values between Field A and Field B for each indicator for soil fertility sampled at each farm using bar plots. We also included error bars to show the range of uncertainty in these indicators for soil fertility. Lastly, we further compared Field A and Field B for each farm using radar plots. To generate the radar plots, we first scaled each soil indicator from 0 to 1. Using Jenks natural breaks optimization, we then grouped each farm based on low, medium, and high N-based fertilizer application, as this soil management metric was the strongest coefficient loading from the first principal component . Using the fmsb package in R , we used an averaging approach for each level of N-based fertilizer application to create three radar plots that each compared Field A and Field B across the eight indicators for soil fertility. Farmers provided an overview of their farm operation, including farm size , the total number of crops each farm planted per growing season at the whole farm level, the types of crops planted in their field during the initial field visit , the type and amount of nitrogen-based fertilizer they applied on farm, and key aspects of soil health in their own words . Farm sizes ranged from 15 to 800 acres, with about one third of farms in the 15 – 50-acre range, drainage pot another third in the 100 – 450-acre range, and roughly a final third in the 500 – 800 acre-range. Farmers grew primarily summer crops, including tomato, a variety of cucurbits, strawberry, herbs, nightshades, root vegetables, and sunflower/safflower for oil.

Farmers reported applying a range of external N-based organic fertilizers, including fish emulsion, Wiserg , pelleted chicken manure, and seabird guano, at varying rates . On the low end, farmers applied <1 kg-N/acre, and on the high end, farmers applied 90 – 180 kg-N/acre per season. About a third of farmers applied 2 – 25 kg-N/acre of N-based fertilizer. Farmer responses for describing key aspects of soil health were relatively similar and overlapped considerably in content and language . Specifically, farmers usually emphasized the importance of maintaining soil life and/or soil biology, promoting diversity, limiting soil compaction and minimizing disturbance to soil, and maintaining good soil structure and moisture. Several farmers also touched on the importance of using crops as indicators for monitoring soil health and the importance of limiting pests and disease. Discussion of the importance of promoting soil life, soil biology, and microbial and fungal activity had the highest count among farmers with ten mentions across the 13 farmers interviewed. Next to this topic, minimizing tillage and soil disturbance was the second most discussed with six of 13 farmers highlighting this key aspect of soil health. In addition to discussing soil health more broadly, farmers also provided in-depth responses to a series of questions related to soil fertility—such as key nutrients of interest on their farm, details about their fertility program, and the usefulness of soil tests in their farm operation— summarized in Table 2. When asked to elaborate on the extent to which they considered key nutrients, a handful of farmers readily listed several nutrients, including nitrogen, phosphorous, potassium , and other general macronutrients as well as one micronutrient .

Among these farmers that responded with a list of key nutrients, some talked about having their nutrients “lined up” as part of their fertility program. This approach involved keeping nutrients “in balance,” such as for example, monitoring pH to ensure magnesium levels did not impact calcium availability to plants. These farmers also emphasized that though nitrogen represented a key nutrient and was important to consider in their farm operation, tracking soil nitrogen levels was less important than other aspects of soil management, such as promoting soil biological processes, maintaining adequate soil moisture and aeration, or planting cover crops regularly. As one farmer put it, “if you add nutrients to the soil, and the biology is not right, the plants will not be able to absorb it.” Or, as another farmer emphasized, “It’s not about adding more [nitrogen]… I try to cover crop more too.” A third farmer emphasized, that “I don’t use any fertilizers because I honestly don’t believe in adding retroactively to fix a plant from the top down.” This same farmer relied on planting a cover crop once per year in each field, and discing that cover crop into the ground to ensure his crops were provided with adequate nitrogen for the following two seasons. While most farmers readily listed key nutrients, several farmers shifted conversation away from focusing on nutrients. These farmers generally found that this interview question missed the mark with regards to soil fertility. One farmer responded, “I’m not really a nutrient guy.” This same farmer added that he considered [soil fertility] a soil biology issue as much as a chemistry issue.” The general sentiment among these farmers emphasized that soil fertility was not about measuring and “lining up” nutrients, but about taking a more holistic approach. This approach focused on facilitating conditions in the soil and on-farm that promoted a soil-plant-microbe environment ideal for crop health and vigor. For example, the same farmer quoted above mentioned the importance of establishing and maintaining crop root systems, emphasizing that “if the root systems of a crop are not well established, that’s not something I can overcome just by dumping more nitrogen on the plants.” Another farmer similarly emphasized that they simply created the conditions for plants to “thrive,” and “have pretty much just stepped back and let our system do what it does; specifically, we feed our chickens whey-soaked wheat berries and then we rotate our chickens on the field prior to planting.

And we cover crop.” A third farmer also maintained that their base fertility program—a combination of planting a cover crop two seasons per year, an ICLS chicken rotation program, minimal liquid N-based fertilizer addition, and occasionally compost application—all worked together to “synergize with biology in the soil.” This synergy in the soil created by management practices—rather than focusing on nutrient levels—guided this farmer’s approach to building and assessing soil fertility on-farm. Another farmer called this approach “place-based” farming. This particular farmer elaborated on this concept, saying “I think the best style of farming is one where you come up with a routine [meaning like a fertility program] that uses resources you have: cover crops, waste materials beneficial to crops, animals” in order to build organic matter, which “seems to buffer some of the problems” that this farmer encountered on their farm. Similar to other farmers, this farmer asserted that adding more nitrogen-based fertilizer did not lead to better soil fertility or increase yields, drainage planter pot in their direct experience. Regardless of whether farmers listed key nutrients, a majority of farmers voiced that nitrogen was not a big concern for them on their farm. This sentiment was shared among most farmers in part because they felt the amount of nitrogen additions from fertilizers they added were insignificant compared to nitrogen additions by conventional farms. Farmers also emphasized that the amount of nitrogen they were adding was not enough to cause environmental harm; relatedly, a few farmers noted the absurdity and added economic burden of the recent nitrogen management plan requirements—specifically among organic farms with very low N-based fertilizer application. The majority of farmers also expressed that their use of cover crops and the small amount of N-based fertilizer additions as part of their soil fertility program ensured on-farm nitrogen demands were met for their crops. Across all farmers interviewed, cover cropping served as the baseline and heart of each fertility program, and was considered more effective than additional N-based fertilizers at maintaining and building soil fertility. Farmers used a range of cover crop species and often applied a mix of cover crops, including vetches and other legumes like red clover and cowpea , grains and cereals like oats . Farmers cited several reasons for the effectiveness of cover cropping, such as increased organic matter content, more established root systems, greater microbial activity, better aeration and crumble in their soils, greater number of earthworms and arthropods, improved drainage in their soils, and more bio-available N. Whereas farmers agreed that “more is not better” with regards to N-based fertilizers, farmers did agree that allocating more fields for planting cover crops over the course of the year was beneficial in terms of soil fertility. However, as one farmer pointed out, while cover crops provide the best basis for an effective soil fertility program, this approach is not always economically viable or physically possible. Several farmers expressed concern because they often must allocate more fields to cover crops than cash crops in any given season, which means that their farm operation requires more land to be able to produce the same amount of vegetables than if they had all their fields in cash crops.

Farmers also shared that in some circumstances, such as in early spring, they are not able to realize the full potential of a winter cover crop if they are forced to mow the cover crop early to plant cash crops and ensure the harvest timeline of a high-value summer vegetable crop. The cover crop approach to soil fertility takes “persistence,” as one farmer emphasized; another farmer similarly pointed out that the benefits of cover cropping “are not always realized in the crop year. You’re in it [organic agriculture] for the long haul, there is no quick fix.” Indeed, farmers who choose to regularly plant cover crops to build soil fertility, rather than just add N-based fertilizers, reported that they came up against issues of land tenure and access to land, market pressures, and long-term economic sustainability. To build on conversations about soil fertility, farmers also provided responses to interview questions that asked them to elaborate on the usefulness of available soil tests to gauge soil fertility more broadly—and then more specifically, the usefulness of soil tests in informing their soil fertility program and/or management approaches on-farm. Overall, only three of 13 farmers reported regularly using and relying on soil tests to inform their soil fertility program or aspects of their farm operation. These farmers offered very short responses and did not elaborate. For example, one farmer shared that they “test twice a year in general,” and that they “rely on the results of the soil tests to tweak [their] fertility program.” Another farmer said briefly, “We use soil tests… we utilize them to decide what to do to try to improve the soil.” A third farmer admitted that though he “used to do a soil test every year, literally used to spend hundreds of dollars per year on soil tests,” he found that the results of soil tests did not change year-to-year and were, as he put it, very “stable.” This particular farmer no longer regularly uses or relies on soil testing for their farm operation. The remaining ten farmers confirmed that they had previously submitted a soil test, usually once and most often to a local commercial lab in the region. These farmers expressed a range of sentiments when asked about the usefulness of soil tests, including disappointment, distrust, or both, particularly in the capacity of soil tests to inform soil fertility on their farm. Some farmers said directly, “I just don’t trust soil tests,” or “frankly, I don’t believe a lot in soil testing because it’s too standardized,” while other farmers initially stated they had used “limited” or “infrequent” soil tests, and then later admitted that they did not use or rely on soil tests on their farm operation. These farmers tended to focus on the limitations of soil tests that they encountered for their particular farm application. Limitations of soil tests discussed by farmers varied.

Across all farmers interviewed, including both first- and second-generation farmers, farmers stressed the steep learning curves associated with learning to farm alternatively and/or organically. While these farmers represent a case study for building a successful, organic farm within one generations, the results of this study beg the question: What advancements in farm management and soil management could be possible with multiple generations of farmer knowledge transfer on the same land? Rather than re-learning the ins and outs of farming every generation or two, as new farmers arrive on new land, farmers could have the opportunity to build on existing knowledge from a direct line of farmers before them, and in this way, potentially contribute to breakthroughs in alternative farming. In this sense, moving forward agriculture in the US has a lot to learn from agroecological farming approaches with a deep multi-generational history . To this end, in most interviews—particularly among older farmers—there was a deep concern over the future of their farm operation beyond their lifetime. Many farmers lamented that no one is slated to take over their farm operation and that all the knowledge they had accumulated would not pass on. There exists a need to fill this gap in knowledge transfer between shifting generations of farmers in order to safeguard farmer knowledge and promote adaptations in alternative agriculture into the future.Most studies often speak to the scalability of approach or generalizability of the information presented. While aspects of this study are generalizable particularly to similar farming systems in California such as the Central Coast region, the farmer knowledge presented in this study is not generalizable and not scalable to other regions in the US. To access farmer knowledge, pots with drainage holes relationship building with individual farmers leading up to interviews as well as the in-depth interviews themselves require considerable time and energy.

While surveys often provide a way to overcome time and budget constraints to learn about farmer knowledge, this study shows that to achieve specificity and depth in analysis of farmer knowledge requires an interactive approach that includes—at a minimum—relationship building, multiple field visits, and in-depth, multi-hour interviews. Accessing farmer knowledge necessitates locally interactive research; this knowledge may not be immediately generalizable or scalable without further locally interactive assessment in other farming regions. Local knowledge among farmers in US alternative agriculture has often been dismissed or overlooked by the scientific community, policymakers, and agricultural industry experts alike; however, this study makes the case for inclusion of farmer knowledge in these arenas. In-depth interviews established that farmers provide an important role in translating theoretical aspects of agricultural knowledge into practice. It is for this reason that farmer knowledge must be understood in the context of working farms and the local landscapes they inhabit. As one of the first systematic assessments of farmer knowledge of soil management in the US, this research contributes key insights to design future studies on farmer knowledge and farmer knowledge of soil. Specifically, this study suggests that research embedded in local farming communities provides one of the most direct ways to learn about the substance of farmer knowledge; working with the local UCCE advisor in combination with community referrals provided avenues to build rapport and relationships with individual farmers—relationships that were essential to effective research of farmer knowledge. Farmer knowledge of soil management for maintaining healthy soils and productive, resilient agriculture represents an integral knowledge base in need of further scientific research. This study provides a place-based case study as a starting point for documenting this extensive body of knowledge among farmers.

It is our hope that this research will inspire future studies on farmer knowledge in other contexts so that research in alternative agriculture can widen its frame to encompass a more complete understanding of farming systems and management motivations—from theory to practice. A fundamental challenge in agriculture is to limit the environmental impacts of nitrogen losses while still supplying adequate nitrogen to crops and achieving a farm’s expected yields . To balance among such environmental, ecological, and agronomic demands, it is essential to establish actual availability of nitrogen to crops . A holistic, functional understanding of plant N availability is particularly imperative in organic agriculture, as in this farming context, synthetic fertilizers are not applied and instead, production of inorganic N—the dominant form of N available to crops—depends on internal soil processes . In organic agricultural systems, farmers may seasonally apply cover crops or integrate livestock as alternative sources of nitrogen to crops—in addition to or in place of using organic fertilizers. In applying these alternative sources of nitrogen to soil, organic farmers rely on the activity of soil microbes to transform organic N into inorganic forms of N that are more readily available for crop uptake . Currently, the predominant way crop available N is measured in organic agricultural systems tends to examine pools of inorganic N in soil . Inorganic N, or more specifically ammonium and nitrate , represents the predominant forms of N taken up by crop species in ecosystems where N is relatively available, such as in non-organic agricultural systems that apply inorganic fertilizers . However, in organic systems, crop available N is largely controlled by complex soil processes not adequately captured by simply measuring pools of ammonium and nitrate. First, because nitrogen made available to crops is controlled by soil microbes—wherein crops only have access to inorganic forms of N after microbial N transformations occur to first meet microbial N demand—pinpointing the flow of N moving through inorganic N pools as a result of these microbial N transformations is necessary to accurately measure actual N availability to crops . Second, extensive recycling of N among components of the plant-soil-microbe system complicates relying solely on measurements of inorganic N pools, which do not reflect these dynamics .

As an example, one previous study in organic vegetable systems showed examples where inorganic N pool sizes in the soil were measured to be low, yet there existed high production and consumption rates of inorganic N . This outcome highlighted that if the turnover of inorganic N is high—for instance, high rates of soil ammonium production exist in the soil with simultaneously high rates of immobilization by soil microbes and high rates of uptake by plants—measured pools of inorganic N may still be low . This study also showed that conversely, there may also exist situations when inorganic N pools are low and rates of ammonium and nitrate production are also low, in which case N availability would limit crop production. In organic systems especially, higher carbon availability as a result of organic management can increase these microbially mediated gross N flows, thereby increasing N cycling and turnover of inorganic N . Thus, we hypothesize that measuring total production of ammonium from organic N, or gross N mineralization, and subsequent total production of nitrate from ammonium, or gross N nitrification, may provide a more complete characterization of crop available N in the context of organic systems . Though the application of such diverse management practices on organic farms is known to affect rates of N cycling in soil , drainage pot measuring N flow rates as a proxy for crop available N is currently uncommon on working organic farms. The current historical emphasis on measuring inorganic pools of N in organic agriculture was originally imported from non-organic farming, wherein the Sprengel-Liebig Law of the Minimum was a widely accepted agronomic principle . In practice, this Law of the Minimum placed particular importance on using artificial fertilizers to overcome so-called “limiting” nutrients—namely, inorganic forms of N. Because inorganic N is relatively straightforward to measure, focus on quantifying pools of inorganic N has since become common practice among agronomists and agricultural researchers . However, the continued acceptance of the Law of the Minimum in organic agriculture underscores the gap in a functional understanding of organic agricultural systems, in particular the role of soil microbes in mediating N cycling. To understand crop available N more holistically, there is a need to measure actual flow rates of soil N—in addition to—static pools of inorganic N . Soil indicators that adequately capture N availability to crops are therefore necessary to move beyond the legacy of the Law of the Minimum in organic agriculture. Unpacking the soil processes that mediate flows of N may ultimately provide a more accurate characterization of soil N cycling and in turn, N availability to crops. Unfortunately, gross N mineralization and nitrification rates are very difficult to measure in practice, particularly on working organic farms . While net N flows are easier to measure in comparison to gross N flows and can provide a useful measure of N cycling dynamics as a complement to measurements of inorganic N pools, net N flows still pose serious limitations— namely that net rates cannot detect plant-soil-microbe interactions and therefore are not adequate as metrics for determining crop available N . In particular, relying on net N flows as a measure of N availability does not account for the ability of plants to compete for inorganic N, and assumes plants take up inorganic N only after microbial N demands are satisfied .

It is also possible that measuring soil organic matter pools could help indicate N availability because SOM supports microbial abundance and activity, and because SOM is also the source of substrates for N mineralization . Several studies have proposed measuring soil organic matter levels to complement measuring inorganic N pools, understand soil N cycling, and infer N availability . Assessing the total quantity of organic carbon and nitrogen within soil organic matter represents one established method for measuring levels of soil organic matter, and is more readily measurable than gross N rates. Additional indicators for quantifying “labile” pools of organic matter, such as POXC and soil protein, have also become more widely studied in recent years, and applied on organic farms as well . When used in combination with more established soil indicators that measure organic C and N pools , this suite of indicators may potentially provide added insight to understanding crop available N . Importantly, applied together these four indicators for soil organic matter levels may also more readily and accurately serve as a proxy for soil quality—generally defined as a soil’s ability to perform essential ecological functions key to sustaining a farm operation . Despite the availability of these soil indicators, very few studies have systematically examined the way in which SOM levels on working farms compare to N cycling processes, and specifically how SOM levels compare to microbially mediated gross N rates. Further, it is still unclear to what degree the interactions between soil edaphic characteristics and soil management influence N cycling and N availability to crops . For instance, soil texture may play a mediating role in N cycling, where soils high in clay content may limit substrate availability as well as access to oxygen, which in turn, may restrict the efficiency of N cycling . In this sense, it is important to understand the role that soil edaphic characteristics play in order to identify the underlying baseline limits imposed by the soil itself. Equally important to consider is the role of soil management in mediating N cycling. Compared to controlled experiments, soil management regimes on working farms can be more complex and nonlinear in nature due to multiple interacting practices applied over the span of several years, and even multiple decades. To date, a handful of studies conducted on working farms have examined tradeoffs among different management systems , though few such studies examine the cumulative effects of multiple management practices across a gradient of working organic farms. However, understanding the cumulative effects of management practices is key to link soil management to N cycling on working farms . Likewise, it is important to examine the ways in which local soil edaphic characteristics may limit farmers’ ability to improve soil quality through management practices. Though underutilized in this context, the development of farm typologies presents a useful approach to quantitatively integrate the heterogeneity in management on working organic farms . Broadly, typologies allow for the categorization of different types of organic agriculture and provide a way to synthesize the complexity of agricultural systems . Previous studies that make use of farm typologies found that differences in total soil N across farms are largely defined by levels of soil organic matter.

Blue elderberries were determined to be ripe when the berries in a cyme were deep purple, with or without the white bloom, and had no green berries present. Ripe elderberries were harvested by hand from all four quadrants of the elderberry shrub, totaling approximately 3 kg of elderberries. The berries were placed in clear plastic bags, stored on ice, and transported to the laboratory. A subsample was separated for moisture analysis, while the rest was de-stemmed and stored at -20 °C until analyzed. HPLC grade methanol , acetonitrile , phosphoric acid, ethanol, hydrochloric acid, and sodium hydroxide were purchased from Fisher Scientific . Ascorbic acid was purchased from Acros Organics . Formic acid, gallic acid, sucrose, chlorogenic acid, rutin, and catechin, and Folin-Ciocalteu reagent were purchased from Sigma Aldrich . Cyanidin-3-glucoside was purchased from Extrasynthese . Ultra-pure water was obtained from a Milli-Q water system . From each shrub, about 250 g of frozen berries were thawed in a glass container overnight at 4 °C. The following day, the thawed berries were mashed for 4 min by hand using a plastic pestle, then homogenized , and centrifuged at 3,000 rpm for 7 min. The supernatant was strained, collected, and weighed. A 15 mL aliquot of sample extract was stored in a 15 mL plastic tube at -20 °C for total monomeric anthocyanin analysis. The remaining supernatant was used to determine soluble solids, pH, and titratable acidity . One pooled sample was analyzed from each shrub and analyzed in duplicate analytical repetitions. A refractometer was used to determine soluble solids. It was calibrated with standard solutions of 5°, 10°, vertical gardening in greenhouse and 15° Brix made with sucrose and water. A 150 µL aliquot of elderberry juice was placed on the prism and read using the automatic setting. The pH was determined using a SevenMulti pH meter .

It was calibrated before each use using buffers at pH 4.0, 7.0, and 10.0. To determine TA, 10 mL of elderberry juice was diluted to 100 ml with nanopure water and mixed. This dilute juice was titrated to pH 8.2 using 0.1 N NaOH. The volume of 0.1 N NaOH used to achieve the desired pH was used to calculate the mg citric acid per 100 g fresh weight . For each of these analyses, duplicates were run on each juice. Elderberries were extracted by combining 5 g frozen berries with 25 mL MeOH:formic acid in a conical tube. The contents were homogenized, placed in a shaker without water at speed 7.5 for 20 min, then centrifuged at 3,000 rpm for 7 min. The supernatant was transferred to a 15 mL plastic tube and stored at -80 °C for no more than two weeks prior to analysis. Duplicate extracts were made from each shrub. TPC was determined using the Folin-Ciocalteu method. First, elderberry phenolic extract was diluted 1:4 with water. Each extract was analyzed in duplicate and averaged. In 10 mL glass tubes, 6 mL water was combined with 100 µL sample and 500 µL Folin-Ciocalteu reagent. After mixing and incubating for 8 min at room temperature, 1.5 mL 20% aqueous sodium carbonate was added. The tubes were mixed, covered with foil to avoid light exposure, placed in a water bath at 40 °C for 40 min, then cooled at room temperature for 15 min. The samples were read by a UV visible spectrophotometer at 765 nm and quantified using an external standard curve prepared with gallic acid . TPC is expressed as mg gallic acid equivalents per 100 g FW. Five grams of frozen berries were mixed with 25 mL of in a conical tube, which was then homogenized for 1 min at 7,000 rpm . The mixture was stored at 4 °C overnight, then in the morning, centrifuged at 4,000 rpm for 7 min. The supernatant was used directly for analysis. Three pooled samples were made for each hedgerow, each consisting of even amounts of berries from three distinct shrubs. Eachpooled sample was extracted once to give 3 biological replicates, and each extract was run in duplicate . The concentration of phenolic compounds in blue elderberry followed the method by Giardello et al. with some modifications.

Briefly, samples were analyzed via reversed-phase liquid chromatography on an Agilent 1200 with a diode array detector and fluorescence detector . The column used was a PLRP-S 100A 3 µm 150 x 4.6 mm at 35 °C, and the injection volume was 10.0 µl. Mobile phase A was water with 1.5 % phosphoric acid, while mobile phase B was 80%/20% acetonitrile/ mobile phase A. The gradient used was 0 min 6% B, 73 to 83 min 31% B, 90 to 105 min 6% B. The DAD was used to monitor hydroxybenzoic acids at 280 nm, hydroxycinnamic acids at 320 nm, flavonols at 360 nm, and anthocyanins at 520 nm. The FLD was used to monitor flavan-3-ols, with excitation at 230 nm and emission at 321 nm. External calibration curves were prepared using chlorogenic acid for phenolic acids, rutin for flavonols, and cyanidin-3-glucoside for anthocyanins , at the following concentrations: 200, 150, 100, 75, 50, 25, 10, 5, and 2.5 mg/L. Catechin was used to quantify flavan-3-ols and standards were run at 150, 100, 75, 50, 25, 10, 5, 2.5, and 1 mg/L. Compounds were identified based on retention time and spectral comparisons with standards. Information about the linear equations and lower limits of detection and quantitation can be found in Table S1 in the supplementary material. The LLOD was calculated as 3.3 times the standard deviation of the y-intercept of the curve divided the slope, while the LLOQ was calculated as 10 times those values.Several peaks appeared in the HPLC chromatograms that could not be identified using the above parameters. Chromatographic eluents of these peaks were collected individually and dried under vacuum. These extracts were reconstituted with mobile phase A, and 5 µL were injected into the HPLC- QTOF-MS/MS for accurate mass analysis . A Poroshell 120 EC-C18 column was used at 35 °C. Mobile phase A was 1% formic acid in distilled water, and mobile phase B was 1% formic acid in acetonitrile. The gradient used was 0 min 3% B, 30 min 50% B, 31-32 min 95% B, 33-38 min 3% B. The mass spectrometer was used in negative mode, and the mass range for MS was 100 to 1000 m/z while the range for MS/MS was 20-700 m/z. Collision energies at 10, 20, and 40 V were applied. The drying gas was set to a flow of 12 L/min at 250 °C, while the sheath gas was set to 11 L/min at 350 °C. The nebulizer was set to 40 psig, the capillary voltage was 3500 V, the nozzle was set to 500 V, and the fragmentor was set to 100 V. Data was analyzed using Agilent MassHunter Workstation Qualitative Analysis 10.0 .

Tentative identification was achieved by comparing the mass to charge ratio of the precursor and fragment ions to online libraries of compounds as well as using formula generation for the peaks in the spectra. The composition of blue elderberries is presented for the first time, which is key to understanding how this subspecies of Sambucus nigra compares to commercialized elderberry subspecies, S. nigra ssp. nigra and S. nigra ssp. canadensis. These data help to establish the blue elderberry grown in hedgerows in California as a viable source of berries and bioactive compounds. Data for the compositional assays is presented for the 2018 and 2019 harvest years as the average of all shrubs sampled in Table 2. The average moisture for the blue elderberries was 79.5 ± 1.5% in 2018 and 79.5 ± 1.6% in 2019, which is very similar to the levels found in wild elderberries in Spain 95. The average soluble solids found in blue elderberry ranged from 11.94 ± 2.08 to 14.95 ± 1.02 g per 100 g FW in 2018 and from 12.64 ± 1.86 to 17.09 ± 1.60 g per 100 g FW in 2019. These values are slightly higher than the soluble solids found in S. nigra ssp. cerulea grown in Slovenia29 and American elderberries grown in Ohio52. Compared to European and American elderberries evaluated in other studies, blue elderberries have similar levels of soluble solids 8,18,29,49,50,95. In the present study, the overall average content of soluble solids was significantly different between years, greenhouse vertical farming as blue elderberries harvested in 2019 had significantly higher average soluble solids than the elderberries harvested in 2018 . The pH in the blue elderberry ranged from 3.44 to 3.86 in 2018 and from 3.46 to 3.79 in 2019, with no significant difference found between harvest years. These values are slightly lower than the values found in European elderberry, which ranged from 3.9 ± 0.06 to 4.1 ± 0.04 with an average pH of 3.9 ± 0.2, and American elderberry, which ranged from 3.9 ± 0.04 to 4.5 ± 0.03 with an average pH of 4.2 ± 0.2 49 Another evaluation of pH in American elderberries had a range of 4.5 ± 0.08 to 4.9 ±0.12, higher than those found in the blue elderberry.52 The higher sugar and lower pH levels in blue elderberry could potentially impact taste and performance in food and beverages as compared with the European and American species. The average titratable acidity in blue elderberries ranged from 0.45 ± 0.08 to 0.77 ± 0.03 g citric acid per 100 g FW in 2018 and from 0.54 ± 0.06 to 0.77 ± 0.11 g citric acid per 100 g FW in 2019 with no significant difference found between harvest years. These values are lower than the total acids found by Mikulic-Petkovsek et al. 29 in S. nigra ssp. cerulea , but they are similar to the levels found in European elderberry 8,18,49,50 . Anthocyanins are a class of phenolics that contribute red, purple, and blue hues to fruits and vegetables, act as attractants for pollinators, and are potent antioxidants. European and American elderberries are well-known for containing high levels of anthocyanins 8,18,49. The anthocyanin content of elderberries strongly correlates to the antioxidant potential of the fruit, which may confer health-promoting properties 50,89, which is one reason why elderberries are used in supplements and value-added products. Elderberry is also used as a source of natural food colorants due to the levels of anthocyanins35. Understanding the levels of anthocyanins in the blue elderberry grown in hedgerows is critical towards establishing this native fruit as an additional and more sustainable elderberry. The average TMA measured in blue elderberry ranged from 34.2 ± 9.7 to 113.4 ± 18.2 mg CGE per 100 g FW in 2018 and from 43.1 ± 11.5 to 121.5 ± 11.5 mg CGE per 100 g FW in 2019 . TMA was variable between hedgerows in both years of harvest, with relative standard deviation values between 16% and 30%, yet there was not a significant difference in the overall average TMA between 2018 and 2019 . Furthermore, most hedgerows were not significantly different from the other hedgerows harvested that year despite significant differences in TMA values found between farms in both years . Regarding the age of the elderberry shrub, hedgerows 2 and 14 had two of the three highest concentrations of TMA in 2019 . This suggests that blue elderberries can be harvested from plants as young as two years without a significant loss of TMA concentrations. TMA values for the blue elderberries are lower than those found in other elderberry subspecies. In European elderberries, TMA levels range from 170 ± 12 to 343 ± 11 with an average of 239 ± 94 mg CGE per 100 g FW 49. A study of American elderberry grown in Ohio showed a range from 354 ± 59 to 595 ± 26 mg CGE per 100 g FW.52 In the present study, bare root prerooted cuttings of American elderberries were planted, along with blue elderberries, on Farm 1 in 2018, and three shrubs were harvested in 2019. These American elderberries had an average TMA value of 263 ± 5.4 mg CGE per 100 g FW, which is more similar to what has been observed in other studies on this subspecies. This suggests it is a subspecies difference contributing to the lower anthocyanin concentration in the blue elderberry and not the difference in growing conditions.

These inequivalent valleys at K and K0 lead to the valley Hall effect which, unlike the ordinary Hall effect, produces not only charge but also spin imbalance at the edges. The valley Hall effect has been understood in terms of the Berry curvature; the symmetries in 1 ML 2H-MX2 cause a sign change in the Berry curvature as one goes from one valley to an inequivalent valley in the BZ. This allows us to understand the valley Hall effect in terms of pseudospins, and provides possibilities to control the pseudo-spins by an external field. On the other hand, the Berry curvature is expected to vanish in the bulk because the bulk TMDCs have an inversion symmetry. However, one can imagine that the valley Hall in each layer could be nonvanishing—only the sum vanishes. This may naturally introduce the concept of “hidden Berry curvature,” a nonvanishing Berry curvature localized in each layer. Existence of hidden Berry curvature implies that the topology could be determined by local field; the local symmetry determines the physics. While experimental verification of a hidden Berry phase in the Bloch state is highly desired, standard measurements such as quantum oscillation cannot reveal a hidden Berry phase because these measurements represent an averaged quantity, with hidden quantity invisible. However, if we use an external field or surface sensitive technique such as angle resolved photo emission, then the direct measurement of such a hidden Berry curvature may be possible. In fact, the surface sensitivity of ARPES has recently been utilized in the measurement of hidden spin polarization. Then, the question is if Berry curvature can be measured by means of ARPES. In this regard, we note a recent proposal, based on a tight-binding model calculation on a simple cubic lattice with s and p orbitals, grow bucket that the nonAbelian Berry curvature is approximately proportional to the local orbital angular momentum in the Bloch state.

We use a similar approach and derived the relationship between OAM and the Berry curvature by using a three band, tight-binding model for in WSe2. We find that there is a linear relationship between OAM and the Berry curvature . Even though circular dichroism ARPES is not a direct measure of the OAM in the initial state in genera, it has been shown that CD-ARPES bears information on the OA. This fact can provide us a way to observe the existence of hidden Berry curvature by using CD-ARPES. In actual measurements, an important challenge lies in the fact that CD-ARPES has contributions other than the one from OAM. The most notable contribution comes from the geometrical effect, which is caused by a mirror symmetry breaking in the experimental geometry. Therefore, how we separate the Berry curvature and geometrical contributions holds the key to successful observation of the hidden Berry curvature. We exploit the unique valley configurations of TMDCs in the BZ to successfully disentangle the two contributions. The observed hidden Berry curvature has opposite signs at K and K0 as theoretically predicted. Moreover, we find the hidden Berry curvature exists over a wide range in the BZ. These features are consistently explained within the first principles calculations and tight binding description. ARPES measurements were performed at the beam line 4.0.3 of the Advanced Light Source at the Lawrence Berkeley National Laboratory. Data were taken with left and right-circularly polarized 94 eV light, with the circular polarization of the light better than 80%. The energy resolution was better than 20 meV with a momentum resolution of 0.004 Å−1 . Bulk 2H-WSe2 single crystals were purchased from HQ graphene and were cleaved in situ at 100 K in a vacuum better than 5 × 10−11 Torr. All the data were taken at 100 K. Figure 1 shows the crystal structure of 2H-WSe2 for which the inversion symmetry is broken for a ML.

In the bulk form of 2H-WSe2, the layers are stacked in a way that inversion symmetry is recovered. In the actual experiment, the contribution from the top layer to the ARPES signal is more than that from the sublayer, as illustrated by the dimmed color of the sublayer. Figure 1 schematically sketches the electronic structure with the hexagonal BZ of WSe2. The low energy electronic structures of 2H-WSe2 ML was found to be described by the massive Dirac-Fermion model, with hole bands at K and K0 points. These hole states at K and K0 points have local atomic OAM of 2ℏ and −2ℏ, respectively, which works as the valley index. The bands are then spin split due to the coupling between the spin and OAM. In the bulk, layers are stacked in a way that K of a layer is at the same momentum position as the K0 of next layer. Consequently, spin and valley symmetries are restored due to the recovered inversion symmetry and any valley sensitive signal should vanish. On the other hand, the in-plane nature of the primary orbital character of the Bloch states around the K and K0 points and the graphenelike phase cancellation as well as the strong spin orbital coupling strongly suppress the interlayer hopping along the c axis and make them quasi-two dimensional . In that case, the valley physics as well as the spin-split nature maybe retained within each layer as illustrated in Fig. 1 by the top- and sub-layer spin-split bands . In that case, one may be able to measure the hidden Berry curvature by using ARPES because it preferentially probes the top layer due to its surface sensitivity as, once again, illustrated by the dimmed color of the sub-layer. Since the signal is preferentially from the top layer, the situation becomes as if ARPES data are taken from the topmost layer of WSe2, for which the inversion symmetry is broken. As mentioned earlier, it was argued that OAM is directly related to the Berry curvature, which indeed has opposite signs at the K and K0 points as OAM does. Then, the hidden Berry curvature may be measured by using CDARPES, which was shown to be sensitive to OAM.

However, CD-ARPES has aforementioned geometrical contribution due to the broken mirror symmetry in the experimental geometry. In order to resolve the issue, we exploit the unique character of the electronic structures of TMDCs. The key idea is that, while the contribution from the geometrical effect is an odd function of k about the mirror plane, we can make the OAM contribution an even function. In that case, the two contributions can be easily isolated from each other. To make the OAM contribution an even function, we use the experimental geometry illustrated in Fig. 1. The experimental mirror plane, which is normal to the sample surface and contains the incident light wave vector, is precisely aligned to cross both K and K0 points. In such experimental condition, the Berry curvature is mirror symmetric about the experimental mirror plane and so is its contribution to the CD-ARPES. Then, the CD-ARPES is taken along the momentum perpendicular to the mirror plane , i.e., from K to K and K0 to K0 as shown in Fig. 1 by green dash-dot and brown dashed lines, respectively. We point out that we kept the same light incident angle for K-K and K0 -K0 cuts [note the color pair for the cut and light incidence in Fig. 1to prevent any contribution other than those from Berry curvature and experimental chirality. Figures 1–1 show data along the K0 -K0 cut. The dispersion is very symmetric with the minimum binding energy at the K0 point as expected. However, dutch bucket for tomatoes the intensity varies rather peculiarly; there appears to be no symmetry in the CD intensity in Fig. 1. The K-K cut in Figs. 1–1 shows a similar behavior. While the dispersion is symmetric , the CD intensity in Fig. 1 at a glance does not seem to show a symmetric behavior. However, upon a close look of the CD data in Figs. 1 and 1, one finds that the two are remarkably similar; the two are almost exact mirror images of each other if the colors are swapped in one of the images. This is already an indication that the CD data reflect certain aspects of the electronic structure that are opposite at the K and K0 points, most likely the hidden Berry curvature of bulk 2H-WSe2.In the calculation, the parameters are adjusted until the dispersion fits the experimental one and previous TB result. Then, the Berry curvature of the upper band is calculated based on the TKNN formula and its map is plotted in Fig. 3. The momentum dependent local OAM is obtained by density functional theory calculation. The resulting Lz map is depicted in Fig. 3. The in-plane components of the Berry curvature and OAM are also calculated but are found to be negligible over the whole BZ and thus are not presented. One can immediately note that the three plots of experimentally obtained IS NCD, Berry curvature from TB analysis, and local Lz from DFT calculation show remarkably similar behavior; their signs are determined by the valley indices and change only across the Γ − M line. In addition, all of them retain significant values quite far away from the K and K0 points. Our observation shows that IS NCD can be considered as a measure of the OAM and Berry curvature. We also find that IS taken with different photon energies shows no qualitative difference .

These observations support the notion that IS reflects an intrinsic property of the state, that is, OAM. For a more quantitative comparison, we plot IS NCD, Berry curvature and OAM along the high symmetry lines . Once again, IS NCD, Berry curvature and OAM show very similar behavior. As the Bloch states at the Γ and M points possess inversion symmetry, IS NCD, and Berry curvature as well as OAM are all zero. One particular aspect worth noting is their behavior near the Γ point. They are approximately zero near the Γ point but suddenly increase about a third of the way to the K or K0 point. Orbital projected band structure from TB calculation shows that this is when the orbital character of the wave function switches from out-of-plane dz2 and pz orbitals to in-plane dxy, dx2−y2 , px, and py orbitals. This behavior can be understood from the fact that the local OAM is formed by in-plane orbitals. These results strongly suggest that IS NCD is indeed representative of the Berry curvature and that the Berry curvature is closely related to the local OAM, at least for TMDCs. Characteristics of electron wave functions in the momentum space often play very important roles in macroscopic properties of solids. For example, topological nature of an insulator is determined by the characteristics of electron wave function at high symmetric points in the momentum space. The Berry curvature which is also embedded in the nature of the electron wave function in the momentum space determines the Berry phase and thus macroscopic properties such as spin and valley Hall effects. Through our work, we demonstrated a way to map out the Berry curvature distribution over the Brillouin zone and provide a direct probe of the topological character of strongly spin-orbit-coupled materials. This stands in contrast with transport measurement of spin and charge which reflect the global momentum-space average of the Berry curvature. In this regards, CD-ARPES can be a useful experimental tool to investigate certain aspects of the phase in electron wave functions if one can disentangle different contributions in the CD-ARPES. This work was supported by Research Resettlement Fund for the new faculty of Seoul National University and the research program of Institute for Basic Science . S. R. P. acknowledges support from the National Research Foundation of Korea . The Advanced Light Source is supported by the Office of Basic Energy Sciences of the U.S. DOE under Contract No. DE-AC02-05CH11231.In the momentum space of atomically thin transition metal dichalcogenides , a pair of degenerate exciton states are present at the K and K’-valleys, producing a valley degree of freedom that is analogous to the electron spin12–14. The electrons in the K and K’-valleys acquire a finite Berry phase when they traverse in a loop around the band extrema, with the phase equal in magnitude but opposite in sign at the K and K’-valleys, as required by the time-reversal symmetry.

As an effect of this bill alone, the California Energy Commission estimates that the state will need to triple its electricity power capacity in the renewable sector to achieve this goal. In 2022, the California Air Resources Board passed a plan mandating that all new cars sold in California be electric starting in 2035. The combination of these two laws creates a desperate need for increased electricity production capacity fueled by renewable energy. As more of the California economy ’electrifies’, the need for clean energy sources will only increase. The timelines of SGMA, SB 100 and the CARB mandate align well with one another to form an ideal environment for farmers to transition from traditional crop production to energy production. Policymakers could leverage these alignments to incentivize solar energy infrastructure investment and lessen farmer losses from water scarcity. The aim of this paper is to identify agricultural land parcels in the San Joaquin Valley that would provide both private and social benefit from switching to solar energy generation. This paper analyzes crop choice from both a private farmer’s and a social planner’s perspective and will rank land parcels based on the estimated total benefits generated by permanently transitioning agricultural land to energy production. I will analyze usable farmland in the San Joaquin Valley that has been fallow for at least one recent growing season and use computed water application and revenues per acre for different crops to find relative sensitivities to water price shocks induced by continued water scarcity and regulation. A wide range of crops are grown in the region, nft growing system and crop choice drives most of the variation in revenue and water cost per acre. I will compare traditional crop revenues with projected solar energy revenues to determine if a land use transition would be privately profitable. Current water application to the land parcel and total acreage will determine the water savings and added solar generation capacity .

Growers in California have experienced increasingly varied precipitation and, consequently, surface water availability since the 1980s . 75% of California’s rain and snow occurs in the top third of the state, far from where the bulk of the agricultural activity occurs . In response to this reality, multiple water projects were created by the state to move water from where water is relatively plentiful in the north to the parched southern population hubs and central agricultural regions. Moving this water expends energy, and those requesting water delivery bear the cost. The price of water varies heavily by region due to variation of relative water availability, and is a large part of farmers’ variable costs of producing an acre of crop. The amount of precipitation is hugely important in farmer cropping decisions, and land allocation choices vary based on the relative wetness or dryness of the growing year. In figures 2 and 3, crop cover and fallow land in the SJV for growing years 2010 & 2014 are shown by hydrologic region. 2010 represents a year with relatively typical precipitation, and 2014 was a drought year in the midst of historic drought conditions lasting from 2012- 2016 . In each figure, I display the crop cover choices and fallow land from two years relatively close to one another, but with very different surface water availability. Panels and show fallow land in each of the hydrologic regions that make up the San Joaquin Valley. Comparing these figures, there is a pronounced increase in fallow land from the ’wet’ year to the ’dry’ year . Differences in crop mix for farmers are to be tied to the precipitation conditions they grew under. Comparing panels and of figure 2, the marked decrease in double cropping activity in the central portion of the San Joaquin River in 2014 is apparent. In the same panels in figure 3, deciduous tree fruits and nuts are nearly wiped out by the dry conditions, and the acreage of cotton planted decreases as well. Surface water availability plays a massive role in farmers’ land use and crop mix decisions. Relevant literature in the agricultural economics field study farmers’ adaptation decisions when facing water scarcity. Hagerty finds that in the short-term, California farmers operating irrigated land choose to fallow some or all of their usable land when confronted with water scarcity.

This finding is supported visually by the increase in the fallow land acreage from 2010 to 2014, as shown in figures 2 and 3. Water is more costly in years with decreased precipitation for two reasons: less surface water is available and groundwater levels are lower, which means that water is more expensive to pump. Hagerty estimates that a 10% decrease in annual surface water level predicts a 3.6% decrease in farm revenues for the growing season due to inability to grow high-value annual crops that are generally more water intensive than the more stable perennial crops. Further, when facing long-term water scarcity, Hagerty finds that California-based farmers adapt by permanently removing fallow land from cultivation. This retired agricultural land becomes grassland, which can be used to graze cattle, or is left untouched. This kind of unirrigated rangeland has a mean revenue of $11, where the mean revenue of the least water intensive crop category is $622 with mean water needs of 1.31 acre-feet per acre . Although grain has the smallest mean water needs per acre, the volume of water needed to cultivate any crops successfully is a massive cost to farmers. Delivery of water alone averages around $250 per acre-foot in the San Joaquin Valley, and water right permits can cost over $30,000 to obtain . Farmers who have no choice but to stop irrigating some or all of their land are suffering huge losses as compared to those that are able to shift land toward less water intensive crops. These losses are even greater when compared to the average revenue per acre of utility-scale solar production. Annually, renting land to solar energy generators could earn between $1,000 – $1,500 per acre of farmland . This value is larger than returns from cultivating most annual crops , and some perennial orchard crops . In addition to crop choice, political factors like access to water rights impact a farmer’s decision to fallow a piece of land. Smith finds that growers with lower priority water access are more likely to fallow their land, whereas farmers with better access tend to make water conservation choices that are less costly. Growers who have higher priority water rights are more likely to make smaller adjustments to planting decisions when water supply is constrained, like planting earlier or planting varietals that develop quickly.

This means there are also distributional impacts of water scarcity, and farmers who may be historically excluded or limited in their water access will be hurt more by the continued scarcity in the coming decades. Taken together, the agricultural water scarcity literature suggests that agricultural land in the San Joaquin Valley that is currently oscillating between active and fallow will be taken offline in years to come, with potentially devastating consequences for farmers’ economic well-being. If farmers were able to shield themselves from climate-related income risk with solar energy generation, they may be more able to tolerate increasing water costs caused by SGMA-induced scarcity and increased drought frequency.Although rooftop solar PV panels are easily installable in neighborhoods across California and the American Southwest, there are unique challenges and benefits associated with scaling up solar energy generation to the farm level. Electricity transmission lines are a major limiting factor in building out utility-scale solar energy, vertical hydroponic nft system and current infrastructure is concentrated in residential distributed generation areas and areas with existing large-scale solar generation . However, to its benefit, utility-scale farming may not be plagued by the solar rebound effect that is present for residential solar generation. The household solar rebound effect is the ratio of the increase in total electricity consumption to the amount of energy generated from a household’s solar panel system . Various studies investigate the percent solar rebound effect in the US and abroad, with estimates ranging from 12% to as much as 50% for an individual household’s rebound effect . The increase in electricity usage driven by adoption of residential solar PV diminishes the positive externalities that solar adoption provides. Oliver argues that SRE is avoided when bringing utility-scale solar generating sites because the very drivers that cause the phenomenon on an individual household level do not exist. Utility-scale solar decouples households’ electricity consumption decisions from the generation itself, which avoids the need for additional policies to induce adoption. This makes utility-scale solar relatively more energy efficient than distributed generation or rooftop solar tends to be due to the solar rebound effect. Utility-scale solar generation is commonly defined as solar projects with more than 5MW of generation capacity . For utility-scale solar energy generation, there are two dominant technologies farmers could choose to use on their farms: primary photovoltaic or concentrated solar power . CSP uses mirrors to amplify solar radiation, making it a more efficient, but more expensive, system. Typical fixed solar PV panels are less energy efficient, but a much more accessible and widely adopted tech- nology. There is substantially more information on energy generation using fixed solar PV, both in economic literature and in practical experience from users of the technology. In this analysis, I will assume all farmers who switch to solar energy generation will use a fixed PV system, and all costs associated with installing the system are equal across farmers. I will assume additionally that all adopting farmers have the same electricity generating capacity per acre of land, and thus equal revenues from using an acre of land for solar. This requires that all PV systems installed by farmers have the same energy conversion efficiency. In reality, solar panel systems can have a variety of features that increase sunlight exposure, like rotating in accordance with the optimal sun angle . I will assume all farmers choosing to produce solar energy will use ground-mounted PV panels with equal energy conversion rates and equal installation costs. Equal electricity generating capacity across farmers also requires that all farm plots receive equal amounts of usable solar radiation per acre. Figure 5 shows statistics for two different measures of solar radiation: direct normal irradiance and global horizontal irradiance . Both are used in determining solar PV generating capacity, though GHI is most commonly used to calculate fixed solar panel generating potential . Average daily GHI in the U.S. is shown in the map in figure 4. Visually, it is clear that the majority of solar resources are concentrated in the Southwest. Analyzing average daily DNI and GHI values, I find that the SJV has substantially more energy-generating potential than the rest of the Americas and California, with less variation. What little variation there is has a relatively small impact on energy generating ability, and thus revenues per year. Using the resource ranking system from NREL , all land in the SJV falls into the top four of the ten categorizations of solar potential based on GHI values. Thus, the San Joaquin Valley has ample solar resources to support utility-level generation. Currently in the valley, some land is already used for utility-scale solar generation. The PPIC estimates that the existing 3GW of capacity in the SJV takes up 15,000 – 25,000 acres of land, with projects averaging a density between 5-8MW per acre . By comparison, there were over 170,000 fallow acres of land in the same area in 2023 alone . Because of the existence of these solar projects, there is already some infrastructure to support the distribution of the energy currently generated in SJV. In order to feed utility-scale amounts of electricity into the California energy system, solar farms must be connected to high-voltage transmission lines, which are defined as those able to handle 69 kV or more . Figure 6 shows the various existing transmission lines over the active agricultural land in the SJV. Although Ayres et al. estimate that more high-voltage transmission lines will need to be built to handle incoming solar projects, the existing infrastructure can be built upon, and is near much of the active agricultural land. As a result, some land is already being used for energy generation, and energy transmission lines have been installed across the valley to distribute the harvested solar. Above, figure 6 shows transmission lines that are able to carry utility-generated electricity.

Importantly, rather than resting on an inverse farm size – productivity relationship, policy that seeks to impact both equity and efficiency should focus on ensuring that smallholders have access to the productivity gains experienced by their larger counterparts. Thus, policies that help build human capital, facilitate adoption of new technologies, and enhance access to markets via a reduction in transactions costs will continue to be indispensable for reducing rural poverty in developing countries.The regularity with which an inverse relationship between farm size and land productivity is observed led to many theoretical explanations for the phenomenon. Early explanations centered around multiple market failures , asymmetric information , and risk aversion among farmers . A second set of explanations emphasized empirical issues such as systematic measurement error in farm size and/or output and omitted variables . Empirical studies have typically found that existing theory fails to fully explain the observed inverse relationship, generating a body of mixed and at times contradictory evidence. Chapter 1 illustrates how the choice of productivity measure can alter the relationship observed and how it can obscure a changing relationship between farm size and total factor productivity, the more relevant productivity measure. A dynamic relationship was found between farm size and total factor productivity in the rapidly modernizing agricultural regions of Brazil, contributing to an emerging literature that documents changing farm size – productivity relationships as agricultural sectors modernize and develop . This is consistent with Helfand et al. , hydroponic bucket whose findings suggest that both the larger commercial farms and smaller family farms in Brazil have advantages in harnessing technical change and achieving rapid gains in productivity.

In this paper the hypothesis of a dynamic farm size – productivity relationship is extended to the context of Mexico, identifying the relationship in a panel of family farms from the Mexican Family Life Survey and testing for changes over the sample period of 2002-2009. Mexico is an interesting case for assessing changes in the farm size – productivity relationship because of its long history of land reform and the recent agricultural policy reform associated with the North American Free Trade Agreement in the 1990s. These policies are a prime example of the Washington Consensus, liberalizing markets for land, agricultural inputs, and agricultural output in Mexico with the objective of spurning the modernization, competitiveness, and productivity of the agricultural sector and the broader economy. An environment with such market reforms, if successful, is expected to diminish the multiple market failure explanation of the inverse relationship between farm size and productivity, and any observed inverse relationship might weaken accordingly. We test for changes in the farm size – productivity relationship and, contrary to expectations, find that an inverse relationship exists and has remained strong in the wake of Mexico’s market reforms. We explore the relationship further by estimating a stochastic production frontier, an approach often applied in developed economy agriculture but infrequently applied in developing economy contexts. While frontier productivity growth has increased rapidly for larger farms, eliminating the inverse relationship at the frontier, the average relationship has remained unchanged due to more rapidly increasing technical inefficiency amongst the larger farms in the sample. This finding highlights the need for, and echoes calls for, policies that support family farms’ transitions towards modern agriculture and adaptation to market liberalization in Mexico.

The proceeding section discusses agricultural policy in Mexico, providing context for the empirical analysis. This is followed by an introduction of the empirical methodology, a description of the data, and the presentation of empirical results. Policy recommendations for Mexican agriculture and research implications conclude.The institutional structure of Mexican agriculture continues to reflect agricultural policies implemented after the Mexican Revolution of the early 20th century. Land policy of the 1934 Agrarian Code established the ejidos – tracts of communally held land with individual plots farmed by designated households – as a principle tool for redistributing land and property rights to peasants. Agrarian communities, a distinct form of land tenure located predominantly in the South where farmers had pre-existing claims to agricultural land, were similarly formed although to a lesser extent. A dual system of agricultural tenure emerged, with ejido farmers on the one hand and private landowners on the other. Within both the ejido and private farm sectors there exists both the larger, commercially oriented farms and the smaller predominantly subsistence farms. It is in this context that Berry and Cline first studied the farm size – productivity relationship in Mexico. Drawing from the Mexican Agricultural Census of 1940 and of 1960, they compared land productivity of small and large private farms. They found land productivity of small farms to be 6.5 times larger than that of larger farms in 1940, but just 3.5 times as large by 1960. More importantly, when output per unit of land and capital was measured, a more comprehensive measure of productivity, small farms were 1.7 times more productive than large farms in 1940 but just 0.8 times as productive in 1960. This early evidence illustrates that an inverse relationship between farm size and land productivity is neither necessary nor sufficient for an inverse relationship between farm size and more comprehensive productivity measures, similar to the findings of chapter 1 in the context of Brazil.

Berry and Cline hypothesized that the changing productivity ratios reflected a shift from livestock to crops on large farms, facilitated by government investment in infrastructure, provision of credit, and other supportive policies. As the birthplace of the Green Revolution, Mexican agriculture experienced productivity growth throughout this period, notably becoming net exporters of important staples such as wheat and maize. A weakening of the IR between farm size and land productivity accompanied this period of agricultural modernization and development, as did a reversal of the IR between farm size and output per unit of capital and labor. More recent research using farm-level panel data from the Mexico National Rural Household Survey , a household survey statistically representative of 80% of rural Mexico, showed evidence of an inverse relationship between farm size and productivity in 2003 and 2008 . By estimating an average production function and a stochastic production frontier, they find an inverse relationship between farm size and land productivity, farm size and average TFP, and farm size and TFP along the production frontier. They conclude that the observed farm size – TFP relationship was driven, in part, by larger farms being further from the frontier . Mexican agriculture in the early 20th century is an interesting setting for studying the farm size – productivity relationship because of the policy changes and market reforms associated with The North American Free Trade Agreement going into effect in 1994. As part of an economy-wide reduction in tariffs, agricultural tariffs were gradually eliminated over a 14-year span ending in 2008. The liberalization of agricultural trade exposed the Mexican agricultural sector to increased competition and imports from Northern neighbors. As a result, a flood of cheap imports has led to a decline in the price of staple crops for many Mexican farmers . For Mexican agriculture, NAFTA was part of a broader program of reform and market liberalization. One important change was the Program for the Certification of Ejido Rights and Titling of Urban Plots , which included reform of the ejido system of land tenure. Following a constitutional amendment, Procede facilitated the new option for ejidos to privatize individual parcels that could then be mortgaged, rented, or sold. Further, agricultural rights to ejido parcels ceased being contingent upon actual agricultural production, strengthening property rights for the ejido sector. Importantly for the private sector, stackable planters the practice of expropriating large private holding for the formation of ejidos was ended. By securing property rights and integrating ejidos into the market, these changes were expected to increase opportunities throughout the rural farm sector. A World Bank evaluation of the ejido reforms found that, while Procede had been widely successful in securing property rights, often in the form of certificates of agricultural rights, the program had not led to widespread land transfers and ejido farms remained credit constrained at the turn of the century. A second set of policy changes affected the manner in which government supported agricultural input and output markets. Policy shifted away from heavily subsidizing inputs and providing price supports for output towards a system of direct transfers for those impacted by increased international competition. In general, producers of staple products have suffered due to increased competition with relatively cheap imports whereas exports of high-valued horticultural products have benefited . The Program for Direct Assistance in Agriculture , primarily an income support program, offered per hectare payments to any farms with a history of producing any of nine key staples prior to 1993 that were actively farming one of those crops. An important change to the program in 1995 allowed participation of any farm producing any legal crop that had previously qualified for the program.

Further changes to the program in 2001 included higher per-hectare payments for farms under 5 hectares and a shift of the timing of payments to the start of the planting season. Alongside Procampo is Alianza para el Campo, a suite of programs designed to increase agricultural productivity primarily through investment in infrastructure and extension assistance. As government programs withdrew, farms became increasingly reliant upon markets for access to key agricultural inputs such as fertilizer, pesticides, and seed and for access to credit. Although government credit programs have scaled back, well functioning credit markets have not appeared in rural Mexico and access to credit markets is not widespread, inhibiting access to key inputs and modern technology. As in other developing country contexts, market concentration in both input markets and post harvest processing and marketing has hurt the profitability of family farms and generated economies of scale in transacting with the agricultural supply chain. We hypothesize that the farm size – TFP relationship is likely to be changing over time in the wake of Mexico’s NAFTA-era reforms, much as it appears to have done in Mexico during the Green Revolution and in Brazil’s modernizing agricultural regions . This hypothesis rests upon the assumptions that market imperfections contribute to any pre-existing IR in Mexican agriculture and Mexico’s NAFTA-era market liberalization has improved the efficiency of agricultural input and output markets. Beyond the farm size – productivity relationship, agricultural productivity is important to Mexico for both rural economic development and poverty reduction. According to data from the World Bank,2 agricultural output made up 3.6% of Mexico’s GDP but employed 13-14% of the workforce in 2015. Further, approximately62% of Mexico’s rural population is impoverished when using the national poverty line, suggesting that agricultural productivity has a potentially important role in Mexico’s rural economic development and efforts to reduce poverty. There are similar implications for trends in migration, as increasing agricultural productivity on family farms facilitates the ability to generate adequate livelihoods and effectively support families, reducing an important push factor in migration decisions.As discussed in chapter 1, land productivity is a partial measure of productivity and does not account for the use of inputs other than land. Where other inputs are used in production, failing to account for the use of those resources potentially introduces bias into estimates of the relationship between farm size and productivity if the intensity of input use varies with farm size. Controlling for all inputs in agricultural production can be accomplished with estimation of a production function, uncovering TFP, the comprehensive and preferable measure of productivity. We use two complementary approaches to explore the relationship between farm size and TFP with a panel of Mexican farms. First, we use an average production function to estimate average TFP and its relationship with farm size. Second, we use a stochastic production frontier to estimate both TFP along the technological frontier and technical inefficiency, identified as deviations from the frontier. The frontier analysis identifies any relationship between farm size and frontier TFP and any relationship between farm size and technical inefficiency. As is standard in the literature , we view TFP change as a combination of changes in the technological frontier and changes in the deviations from the frontier.