In general, if a surface has no rotational symmetry about the surface normal, such a photo current is allowed. Finally, we estimate the current on the surface of Bi2Se3 using an effective model for the SSs. This model captures the deviations from linearity of the SS dispersion due to the threefold rotational symmetry of the surface of Bi2Se3. These deviations have been observed in photo emission experiments on Bi2Te3. Similar deviations are expected for Bi2Se3 , though they cannot be seen in the slightly smaller momentum range compared to Bi2Te3 over which data is currently available.With a magnetic field of 10T and assuming a scattering time of 10ps, we find that a current density of ∼ 100nA/mm can be obtained due to the CPGE with a 1 Watt laser. This value can be easily measured by current experimental techniques. Conversely, the scattering time, crucial for transport processes, for Bi2Se3 SSs can be determined by measuring the current. In comparison, circular photo galvanic currents of a few nanoamperes per Watt of laser power have been measured in quantum wells of the semiconductors GaAs, SiGe and HgTe/CdHgTe. A connection between the optical response of a system and the Berry curvature of its bands has been previously noted at the low frequencies, where a semiclassical mechanism involving the anomalous velocity of electrons in a single band explains it. Here, flower display buckets we show it for inter band transitions where no quasiclassical approximation is applicable. Instead, we calculate the quadratic response function directly.
A connection is still present which points to a deeper relation between the response functions and the Berry curvature. This chapter is organized as follows. In Sec. 6.2, we state the symmetry conditions under which a CPGE may occur. We present our results, both general as well as for Bi2Se3 in particular, in Sec. 6.3.1 and describe the microscopic mechanism in Sec. 6.3.2. The calculation is described briefly in Sec. 6.3.3 and in detail in Sec. 6.3.4. In Sec. 6.4, we give our results for the optical injection of dc spin and in Sec. 6.5 we briefly discuss the situation where the rotational symmetry of the surface is broken by shining the light off-normally.There has been a surge of recent activity studying Dirac excitations in two dimensional media, most famously graphene and the surface states of topological insulators, discussed in the previous chapter. A natural question is whether there are analogs in three dimensions, with a vanishing density of states at the chemical potential and linearly dispersing excitations. It has long been known that touchings between a pair of non-degenerate bands are stable in three dimensions, and typically have linear dispersion. Near these, electronic excitations are described by an analog of the Weyl equation of particle physics, which describes twocomponent chiral fermions. Hence these states have been dubbed Weyl semimetals. This is in contrast with two dimensions: graphene’s nodes can be gapped by different intranode perturbations that break inversion or time reversal symmetry. The enhanced protection in three dimensions is due to a topological property of the nodes – they are sources of Chern flux in the Brillouin zone . This momentum space topology is associated with several physical phenomena.
In particular, it was recently realized that unusual surface states will result as a consequence of the band topology. These take the form of Fermi arcs that connect the projections of the nodes onto the surface BZ. Such topological properties are sharply defined as long as one can distinguish band touching associated with opposite Chern flux. The presence of translation symmetry, and hence conserved crystal momenta, is sufficient to protect these defining properties since the nodes are separated in the BZ. In principle one needs perfect crystalline order to define these phases; in practice, smooth disorder that only weakly mixes nodes is expected to have little effect. Other manifestations of the band topology include an anomalous Hall effect that is tied to the momentum space displacement between nodes, and magneto-resistance arising from Adler-Bell-Jackiw anomaly of Weyl fermions. Note that the band topology of WSMs is very different from the band topology of gapped phases discussed in the previous chapters. The latter, unlike the former, does not require translational invariance and hence is robust against the appropriate symmetry-conserving disorder. Agricultural intensification simplifies ecosystems through management practices such as increases in agrochemical use, decreases in habitat complexity, and decreases in crop and vegetation diversity. Agricultural intensification alters functional biodiversity;in particular, reductions in habitat complexity impact the arthropod community composition, decrease arthropod diversity and reduce pest control services. Notably, biological pest control is likely the ecosystem service most affected by biodiversity loss at the local scale. In coffee agroecosystems, management intensification alters habitat complexity by impacting vegetation connectivity and structure. The management intensification gradient ranges in coffee systems from the least intensive traditional shaded “rustic system”, in which coffee grows under a diverse closed canopy of native forest, to the most intensive “sun monoculture”, which refers to rows of open unshaded coffee monoculture, that require high inputs of agrochemicals. On the shaded end of the intensification gradient, shade coffee habitats are naturally vegetatively complex, with diverse and dense shade canopies and vines and weeds that form connections between the shade trees and the coffee plants.
This vegetation connectivity is an important aspect of habitat complexity that impacts species interactions at the local scale. However, while progressing along the management intensification gradient, reductions in habitat complexity, driven by decreases in shade trees, increases in herbicide use, and the clearing of vegetation between coffee plants, reduce vegetation connectivity and alter species interactions within ecological communities and the ecosystem services that they provide. Connectivity is one physical component of habitats that has a profound impact on arboreal insects and ant community structure . In the absence of connectivity, trees are insular habitats with crown isolation that inhibits the movement of some taxa. Connectivity in the form of lianas and nylon ropes shape the local community structure of arboreal ants, with higher ant species richness often occurring in trees that are connected artificially or vegetatively as compared with trees without these physical connections, and higher ant species coexistence occurring in trees with higher levels of naturally occurring canopy connectivity. These results also reflect the nature of ants as highly efficient foragers, known to use branches and lianas as “opportunist walkways” that provide the quickest foraging routes by allowing for faster traveling speeds through avoiding obstacles on the ground, even if these routes are not necessarily the shortest distance. The variation in texture of natural walkways, characterized as “surface roughness”, further impacts both arboreal and ground ant running speeds and foraging efficiency. Physical connections between trees are thus important structures that facilitate not only arboreal ant mobility but also their foraging success, resource recruitment efficiency, and ant-provided ecosystem services, including pest removal. Ants play an important role in the control of the coffee berry borer , flower bucket the most damaging insect pest of coffee. In particular, the aggressive arboreal ant Azteca sericeasur nests in shade trees, forages on coffee shrubs, and is a keystone predator that controls the CBB. Like many arboreal ants, A. sericeasur prefers walking on branches and vegetation to avoid traveling on the ground. Given the role of A. sericeasur as a biological control agent, understanding how connectivity at the local scale impacts these ants has potential implications for coffee agroecosystem management. In Chiapas, Mexico, Jiménez-Soto et al. found that artificially increasing connectivity between A. sericeasur nests and coffee plants by tying jute string between ant nest trees and coffee plants increased the capacity for A. sericeasur to remove the CBB by throwing them off the coffee plants. These results suggest that naturally occurring vegetation connectivity might have a similar effect as that of artificial string connectivity on A. sericeasur activity and their associated pest removal services. Our study tests and expands on this hypothesis by examining the impact of both artificial connectivity and naturally occurring vegetation connectivity on A. sericeasur activity, its ability to recruit to resources, and its removal of the CBB with a manipulative experiment.
Specifically, we tested the following hypotheses: We predicted that the coffee plants with vegetation or artificial connections to the ant nest tree have higher A. sericeasur activity than that of the isolated control plants; A. sericeasur ants recruit to resources more efficiently oncoffee plants with vegetation or artificial connections to the nest tree; coffee plants with vegetation or artificial connections to the nest tree have greater CBB removal rates by A. sericeasur ants; and A. sericeasur activity, resource recruitment rates, and CBB removal rates decrease with increased distance from A. sericeasur nests.This study was conducted in the Soconusco region of Chiapas, Mexico at Finca Irlanda, a shaded, 300-hectare commercial polyculture coffee plantation. The plantation is located in the Sierra Madre de Chiapas Mountains at an elevation of 1100 m.a.s.l. The average canopy cover throughout the farm is 75 percent and the majority of the plantation shade trees are of the genus Inga. The climate is semi-tropical, with the rainy season occurring between May and October. Vegetation management at Finca Irlanda frequently includes “chaporreo”, in which farmworkers periodically use machetes to clear the weeds and epiphytes that grow between coffee plants. This management practice facilitates farmworker movement between coffee plants and reduces competition between weeds and coffee plants, but in the process inadvertently eliminates vegetation connections between the coffee plants and A. sericeasur nest trees.We collected data between June and August in the summer of 2022. Within the 300 hectares of Finca Irlanda, we selected 17 trees with active A. sericeasur nests as study sites. Each site was located at least 10 m away from any other active A. sericeasur nests to prevent overlapping ant activity, following the methodology used by Jimenez-Soto et al.. We chose six coffee plants within a 5 m radius of each A. sericeasur nesting tree for a total of 102 coffee study plants. At each nesting tree site, we selected two coffee plants for the natural vegetation connectivity treatment, two for the artificial connectivity treatment, and two as isolated control plants . For the vegetation connectivity treatment, we selected two coffee plants with existing vegetation connections. The vegetation connections were either coffee branches directly touching the A. sericeasur nest tree or coffee branches touching a secondary plant, such as a vine or epiphyte that was touching the nest tree. We selected two coffee plants for the artificial connectivity treatment, in which we tied jute strings between the point of the nest tree trunk with the most active ant foraging trail and the central trunk of each coffee plant. We ensured that there were no existing vegetation connections on these plants and that the string was the only point of connection between each coffee plant and the nest tree. For the control treatment, we selected two isolated coffee plants with no connections between the coffee plants and the nest tree. We measured the distance between the central trunk of each study coffee plant and the ant nest tree.At each site, we quantified the ant activity on the coffee plants by counting the number of A. sericeasur that passed a central point on the central trunk of each coffee plant during 1 min . The observations took place between 7:30 AM and 2 PM before the afternoon rainy period. The observations were stopped if it began to rain, as rain significantly reduces ant activity. After setting up the strings, we returned to each site between 7 and 13 days after the initial setup and re-measured ant activity on the coffee plants.To assess the impact of artificial and vegetation connectivity on prey removal by A. sericeasur, we placed five dead adult female CBB on white index cards on the central trunk of each coffee plant . We monitored A. sericeasur interactions on the cards for one hour, ensuring that only A. sericeasur were responsible for removing CBB, and counted the number of CBB removed. Because it has already been well-documented that A. sericeasur remove live CBB from coffee plants, we used dead prey to avoid the possibility of live CBB escaping during a longer observation period. The CBB were collected from infested coffee berries in the field, then frozen for up to 5 days before use.