We argue that static nonlinear Hall conductivity can always be represented as a vector in two dimensions and as a pseudotensor in three dimensions independent of its microscopic origin. In a ...single-band model with a constant relaxation rate, this vector or tensor is proportional to the Berry curvature dipole I. Sodemann and L. Fu, Phys. Rev. Lett 115, 216806 (2015). Here, we develop a quantum Boltzmann formalism to second order in electric fields. We find that in addition to the Berry curvature dipole term, there exist additional disorder-mediated corrections to the nonlinear Hall tensor that have the same scaling in the impurity scattering rate. These can be thought of as the nonlinear counterparts to the side-jump and skew-scattering corrections to the Hall conductivity in the linear regime. We illustrate our formalism by computing the different contributions to the nonlinear Hall conductivity of two-dimensional tilted Dirac fermions.
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In condensed matter physics, the term "chiral anomaly" implies the violation of the separate number conservation laws of Weyl fermions of different chiralities in the presence of parallel electric ...and magnetic fields. One effect of the chiral anomaly in the recently discovered Dirac and Weyl semimetals is a positive longitudinal magnetoconductance. Here we show that chiral anomaly and nontrivial Berry curvature effects engender another striking effect in Weyl semimetals, the planar Hall effect (PHE). Remarkably, the PHE manifests itself when the applied current, magnetic field, and the induced transverse "Hall" voltage all lie in the same plane, precisely in a configuration in which the conventional Hall effect vanishes. In this work we treat the PHE quasiclassically, and predict specific experimental signatures for type-I and type-II Weyl semimetals that can be directly checked in experiments.
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The appearance of negative longitudinal magnetoresistance (LMR) in topological semimetals such as Weyl and Dirac semimetals is understood as an effect of chiral anomaly, whereas such an anomaly is ...not well-defined in topological insulators. Nevertheless, it has been shown recently in both theory and experiments that nontrivial Berry phase effects can give rise to negative LMR in topological insulators even in the absence of chiral anomaly. In this paper, we present a quasi-classical theory of another intriguing phenomenon in topological insulators - also ascribed to chiral anomaly in Weyl and Dirac semimetals- the so-called planar Hall effect (PHE). PHE implies the appearance of a transverse voltage in the plane of applied non-parallel electric and magnetic fields, in a configuration in which the conventional Hall effect vanishes. Starting from Boltzmann transport equations we derive the expressions for PHE and LMR in topological insulators in the bulk conduction limit, and show the important role played by orbital magnetic moment. Our theoretical results for magnetoconductance with non-parallel electric and magnetic fields predict detailed experimental signatures in topological insulators - specifically of planar Hall effect - that can be observed in experiments.
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Attention is critical to perception, serving to select behaviorally relevant information for privileged processing. To understand the neural mechanisms of attention, we must discern how attentional ...modulation varies by cell type and across cortical layers. Here, we test whether attention acts non-selectively across cortical layers or whether it engages the laminar circuit in specific and selective ways. We find layer- and cell-class-specific differences in several different forms of attentional modulation in area V4. Broad-spiking neurons in the superficial layers exhibit attention-mediated increases in firing rate and decreases in variability. Spike count correlations are highest in the input layer and attention serves to reduce these correlations. Superficial and input layer neurons exhibit attention-dependent decreases in low-frequency (<10 Hz) coherence, but deep layer neurons exhibit increases in coherence in the beta and gamma frequency ranges. Our study provides a template for attention-mediated laminar information processing that might be applicable across sensory modalities.
•Attention engages the V4 laminar circuit in selective ways•Superficial broad-spiking cells show increased rate and reliability with attention•Low-frequency coherence decreases with attention in superficial and input layers•Correlations in V4 are highest in the input layer
Attention is a critical component of perception. Here, Nandy et al. examine the laminar organization of attentional modulation in sensory cortex. They find layer- and cell-class-specific differences in the laminar cortical circuit in area V4.
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We propose a way to observe the chiral magnetic effect in noncentrosymmetric Weyl semimetals under the action of a strong electric field, via the nonlinear part of their I-V characteristic that is ...odd in the external magnetic field, or odd-in-magnetic field voltages in electrically open circuits. This effect relies on valley-selective heating in such materials, which, in general, leads to nonequilibrium valley population imbalances. In the presence of an external magnetic field, such a valley-imbalanced Weyl semimetal will, in general, develop an electric current along the direction of the magnetic field-the chiral magnetic effect. We also discuss a specific experimental setup to observe the chiral magnetic effect of hot electrons.
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The Fine Structure of Shape Tuning in Area V4 Nandy, Anirvan S.; Sharpee, Tatyana O.; Reynolds, John H. ...
Neuron (Cambridge, Mass.),
06/2013, Volume:
78, Issue:
6
Journal Article
Peer reviewed
Open access
Previous studies have shown that neurons in area V4 are involved in the processing of shapes of intermediate complexity and are sensitive to curvature. These studies also suggest that curvature-tuned ...neurons are position invariant. We sought to examine the mechanisms that endow V4 neurons with these properties. Consistent with previous studies, we found that response rank order to the most- and least-preferred stimuli was preserved throughout the receptive field. However, a fine-grained analysis of shape tuning revealed a surprising result: V4 neurons tuned to highly curved shapes exhibit very limited translation invariance. At a fine spatial scale, these neurons exhibit local variation in orientation. In contrast, neurons that prefer straight contours exhibit spatially invariant orientation-tuning and homogenous fine-scale orientation maps. Both of these patterns are consistent with a simple orientation-pooling model, with tuning for straight or curved shapes resulting, respectively, from pooling of homogenous or heterogeneous orientation signals inherited from early visual areas.
•Organization of V4 receptive fields using dual-scale reverse correlation•Curvature-tuned cells show limited spatial invariance and heterogenous fine-scale maps•Straight-tuned cells exhibit spatial invariance and homogenous fine-scale maps•Simple local pooling of fine-scale orientation signals explains contour tuning
Nandy et al. investigate the detailed microstructure of receptive fields in macaque V4, an area important for shape perception. They find a trade-off between tuning complexity and translation invariance and describe a simple model to account for this trade-off.
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•The change in forest cover was predicted using logistic regression model (LRM).•Explanatory variables (EV) associated with forest conversion process were analyzed.•Distance from forest edge, roads, ...settlements and slope position classes were the EV.•Highest regression coefficient (β=−26.892) was observed for distance from forest edge.•The LRM modeled forest conversion by predicting forest cover with high accuracy (ROC=87%).
Forest cover conversion and depletion are of global concern due to their role in global warming. The present study attempted to study the forest cover dynamics and prediction modeling in Bhanupratappur Forest Division of Kanker district in Chhattisgarh province of India. The study aims to examine and analyze the various explanatory variables associated with forest conversion process and predict forest cover change using logistic regression model (LRM). The forest cover for the periods 1990 and 2000, derived from Landsat TM satellite imagery, was used to predict the forest cover for 2010. The predictive performance of the model was assessed by comparing the model-predicted forest cover with the actual forest cover for 2010. To explain the effects of anthropogenic pressure on forest, this study considered three distance variables viz., distance from forest edge, roads and settlements, and slope position classes as explanatory variables of forest change. The highest regression coefficient (β=−26.892) was noticed in case of distance from forest edge, which signifies the higher probability of forest change in areas that are closer to the forest edges. The analysis showed that forest cover has undergone continuous change between 1990 and 2010, leading to the loss of 107.2km2 of forest area. The LRM successfully predicted the forest cover for the period 2010 with reasonably high accuracy (ROC=87%).
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It has recently been realized that the first-order moment of the Berry curvature, namely, the Berry curvature dipole (BCD), can give rise to nonlinear current in a wide variety of time-reversal ...invariant and non-centrosymmetric materials. While the BCD in two-dimensional Dirac systems is known to be finite only in the presence of either substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones or higher order warping of the Fermi surface, we argue that the low-energy Dirac quasiparticles arising from the merging of a pair of Dirac points without any tilt or warping of the Fermi surface can lead to a nonzero BCD. Remarkably, in such systems, the BCD is found to be independent of Dirac velocity as opposed to the Dirac dispersion with a tilt or warping effects. We further show that the proposed systems can naturally host helicity-dependent photocurrent due to their linear momentum-dependent Berry curvatures. Finally, we discuss an important byproduct of this work, i.e., nonlinear anomalous Nernst effect as a second-order thermal response.
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The manifestation of chiral anomaly in Weyl semimetals typically relies on the observation of longitudinal magnetoconductance (LMC) along with the planar Hall effect, with a specific magnetic field ...and angle dependence. Here we solve the Boltzmann equation in the semiclassical regime for a prototype of a Weyl semimetal, allowing for both intravalley and intervalley scattering, along with including effects from the orbital magnetic moment (OMM), in a geometry where the electric and magnetic fields are not necessarily parallel to each other. We construct the phase diagram in the relevant parameter space that describes the shift from positive to negative LMC in the presence of OMM and sufficiently strong intervalley scattering, as has been recently pointed out for only parallel electric and magnetic fields. On the other hand, we find that the chiral anomaly contribution to the planar Hall effect always remains positive (unlike the LMC) irrespective of the inclusion or exclusion of OMM, or the strength of the intervalley scattering. Our predictions can be directly tested in experiments, and may be employed as new diagnostic procedures to verify chiral anomaly in Weyl systems.
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Attention selectively enhances neural responses to low contrast stimuli in visual area V4, a critical hub that sends projections both up and down the visual hierarchy. Veridical encoding of contrast ...information is a key computation in early visual areas, while later stages encoding higher level features benefit from improved sensitivity to low contrast. How area V4 meets these distinct information processing demands in the attentive state is unknown. We found that attentional modulation in V4 is cortical layer and cell-class specific. Putative excitatory neurons in the superficial layers show enhanced boosting of low contrast information, while those of deep layers exhibit contrast-independent scaling. Computational modeling suggested the extent of spatial integration of inhibitory neurons as the mechanism behind such laminar differences. Considering that superficial neurons are known to project to higher areas and deep layers to early visual areas, our findings suggest that the interactions between attention and contrast in V4 are compartmentalized, in alignment with the demands of the visual processing hierarchy.
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