Anomalous Hall effect and spin Hall effect originate due to spin-orbit coupling that in the Kohn-Luttinger ${\bf k}\cdot{\bf p}$ formalism is represented by anomalous terms in the coordinate and velocity operators. Relation of these operators to the Berry curvature in the momentum space is presented for electrons in GaAs type semiconductors. For centrosymmetric semiconductors, transformational properties of Berry curvature are discussed.
We predict that a strong nonreciprocity in the resonance spectra of Dirac quantum dots can be induced by the Berry phase. The nonreciprocity arises in relatively weak magnetic fields and is manifest in anomalously large field-induced splittings of quantum dot resonances which are degenerate at $B=0$ due to time-reversal symmetry. This exotic behavior, which is governed by field-induced jumps in the Berry phase of confined electronic states, is unique to quantum dots in Dirac materials and is absent in conventional quantum dots. The effect is strong for gapless Dirac particles and can overwhelm…
We point out a practical way to induce a finite charge Hall conductivity in graphene via an off-diagonal strain. Our conclusions are based on a general analysis and supported by numerical examples. The interplay between a substrate-induced gap and the strain is discussed. We show that the substrate-induced gap itself does not break the symmetry that maps one valley onto the other, and hence does not yield a net charge Hall effect. The net charge Hall conductivity is found to be sizable and should be observable in the presence of both the gap and the strain. The sign of the Hall conductivity ca…
We consider the anomalous thermoelectric transport in gapped single and bilayer graphene where the gap may be due to broken inversion symmetry. In the presence of the gap, non-trivial Berry phase effects can be shown to mediate a transverse thermoelectric voltage in response to an applied temperature gradient even in the absence of a perpendicular magnetic field. This spontaneous, anomalous Nernst effect is nonzero for non-uniform chemical potential in the two inequivalent valleys in the graphene band structure. Conversely, the Nernst response can be used to create a valley-index polarization …
We investigate the adiabatic evolution of thermal state in non-reciprocal many-body systems coupled to their environment and subject to periodic drivings. In such systems we show that besides the dynamical phase a geometrical phase can exist and it drives the relaxation dynamic of the system. On the contrary to the dynamical phase which always pushes the system toward its equilibrium state we show that the geometric phase can speed up or reduce the speed of relaxation process. These results could have applications in the field of thermal management of complex systems.
We theoretically investigate the localization mechanism of quantum anomalous Hall Effect (QAHE) with large Chern numbers $\mathcal{C}$ in bilayer graphene and magnetic topological insulator thin films, by applying either nonmagnetic or spin-flip (magnetic) disorders. We show that, in the presence of nonmagnetic disorders, the QAHEs in both two systems become Anderson insulating as expected when the disorder strength is large enough. However, in the presence of spin-flip disorders, the localization mechanisms in these two host materials are completely distinct. For the ferromagnetic bilayer gra…
We theoretically study the phase of the reflection amplitude of an electron (massive Dirac fermion) at a lateral potential step in Bernal-stacked bilayer graphene. The phase shows anomalous jump of $π$, as the electron incidence angle (relative to the normal direction to the step) varies to pass $\pm π/4$. The jump is attributed to the Berry phase associated with the pseudospin-1/2 of the electron. This Berry-phase effect is robust against the band gap opening due to the external electric gates generating the step. We propose an interferometry setup in which collimated waves can be generated a…
We show that Weyl Fermi arcs are generically accompanied by a divergence of the surface Berry curvature scaling as $1/k^2$, where $k$ is the distance to a hot-line in the surface Brillouin zone that connects the projection of Weyl nodes with opposite chirality but which is distinct from the Fermi arc itself. Such surface Berry curvature appears whenever the bulk Weyl dispersion has a velocity tilt toward the surface of interest. This divergence is reflected in a variety of Berry curvature mediated effects that are readily accessible experimentally, and in particular leads to a surface Berry cu…
We theoretically investigate the localization mechanism of the quantum anomalous Hall effect (QAHE) in the presence of spin-flip disorders. We show that the QAHE keeps quantized at weak disorders, then enters a Berry-curvature mediated metallic phase at moderate disorders, and finally goes into the Anderson insulating phase at strong disorders. From the phase diagram, we find that at the charge neutrality point although the QAHE is most robust against disorders, the corresponding metallic phase is much easier to be localized into the Anderson insulating phase due to the \textit{interchange} of…
We examine the magnetic susceptibility of topological insulators microscopically and find that the orbital-Zeeman (OZ) cross term, the cross term between the orbital effect and the spin Zeeman effect, is directly related to the Berry curvature when the $z$-component of spin is conserved. In particular, the OZ cross term reflects the spin Chern number, which results in the quantization of the magnetic susceptibility jump at the topological phase transition. The magnitude of the jump is in units of the universal value $4|e|μ_{\rm B}/h$. The physical origin of this quantization is clarified. We a…
A vacancy-mediated collective diffusion model is used to compute a thermally-induced (spinodal) phase separation in a typical fcc bi-metallic surface alloy at low median concentration of vacancies, focusing on the effect of the ratio, $Γ=Γ_A/Γ_B$, of the jump rates to the vacant sites of the two types of atoms. The model is formulated for the diffusion of one atomic species and vacancies, employing the kinetic transport coefficients derived by Moleko \emph{et al.} (Phil. Mag. A 59, 141 (1989)). It is demonstrated that for A$_{0.7}$B$_{0.3}$ alloy, $Γ\sim 50$ results in suppression of phase sep…
We predict that a temperature gradient can induce a magnon-mediated intrinsic torque and a transverse spin current in systems with non-trivial magnon Berry curvature. With the help of a microscopic linear response theory of nonequilibrium magnon-mediated torques and spin currents we identify the interband and intraband components that manifest in ferromagnets with Dzyaloshinskii-Moriya interactions and magnetic textures. To illustrate and assess the importance of such effects, we apply our theory to the magnon-mediated spin Nernst and torque responses in a kagome lattice ferromagnet.
Light-tunable quantum metric non-linear Hall response in Berry dipole semimetals
Centre for Nanotechnology, Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校纳米技术中心）；Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore（印度科学学院固态与结构化学单元）
Electrons in certain two-dimensional crystals possess a pseudospin degree of freedom associated with the existence of two inequivalent valleys in the Brillouin zone. If, as in monolayer MoS2, inversion symmetry is broken and time-reversal symmetry is present, equal and opposite amounts of k-space Berry curvature accumulate in each of the two valleys. This is conveniently quantified by the integral of the Berry curvature over a single valley - the valley Hall conductivity. We generalize this definition to include contributions from disorder described with the supercell approach, by mapping ("un…
We study the ac Hall response induced by passage of dc transport current in two- and three-dimensional metals with gyrotropic point groups -- the gyrotropic Hall effect -- and consider the phenomenon of current-induced optical activity in noncentrosymmetric metals as a physical application of our theory. While the effect is expected to be present in single crystals of any noncentrosymmetric metal, we expect it to be strongest in enantiomorphic Weyl semimetals. Using the semiclassical kinetic equation approach we present several mechanisms underlying the gyrotropic Hall effect. Amongst them, th…
We present magnetotransport measurements of a strongly hybridized inverted InAs/GaSb double quantum well. We find that the spin-orbit interaction leads to an appreciable spin-splitting of hole-like states, which form distinct Landau levels in a perpendicular magnetic field. The resulting quantum Hall state is governed by a periodic even and odd total filling arising due to the simultaneous occupation of electron-like and hole-like Landau levels of differing degeneracy. Furthermore, oscillatory charge transfer between all involved subbands leads to discrete phase slips in the usual sequential f…
We outline an approach to endow a plain vanilla material with topological properties by creating topological bands in stacks of manifestly nontopological atomically thin materials. The approach is illustrated with a model system comprised of graphene stacked atop hexagonal-boron-nitride. In this case, the Berry curvature of the electron Bloch bands is highly sensitive to the stacking configuration. As a result, electron topology can be controlled by crystal axes alignment, granting a practical route to designer topological materials. Berry curvature manifests itself in transport via the valley…
We consider Berry phase mediated Nernst effect in silicene. The low energy band structure of silicene consists of two valleys near the Dirac points, similar to graphene. The low energy transport properties of the quasiparticles can be described as Berry phase dependent phenomena. By contrast to graphene, silicene has strong spin-orbit interaction leading to opening of the gap in the energy spectrum and spin-splitting of the bands in each valley. If an electric field is applied perpendicular to the silicene sheet, it allows tunability of the gap. \ We show that this results in Berry-phase-suppo…
The Berry curvature (BC) - a quantity encoding the geometric properties of the electronic wavefunctions in a solid - is at the heart of different Hall-like transport phenomena, including the anomalous Hall and the non-linear Hall and Nernst effects. In non-magnetic quantum materials with acentric crystalline arrangements, local concentrations of BC are generally linked to single-particle wavefunctions that are a quantum superposition of electron and hole excitations. BC-mediated effects are consequently observed in two-dimensional systems with pairs of massive Dirac cones and three-dimensional…
We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an antiferromagnet with non-trivial magnon Berry curvature. We develop a linear response theory which gives a general condition for a Hall current to be well defined, even when the thermal Hall response is forbidden by symmetry. We apply our theory to a honeycomb lattice antiferromagnet and discuss a role of magnon edge states in a finite geometry.
We argue that the static non-linear Hall conductivity can always be represented as a vector in two-dimensions and as a pseudo-tensor 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 \cite{Sodemann_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 non-linear Hall tensor that have the same scaling in impuri…
We develop a semiclassical theory of nonlinear transport and the photogalvanic effect in non-centrosymmetric media. We show that terms in semiclassical kinetic equations for electron motion which are associated with the Berry curvature and side jumps give rise to a dc current quadratic in the amplitude of the ac electric field. We demonstrate that the circular photogalvanic effect is governed by these terms in contrast to the linear photogalvanic effect and nonlinear I-V characteristics which are governed mainly by the skew scattering mechanism. In addition, the Berry curvature contribution to…
A recent scientific debate has arisen: Which processes underlie the actual ground of the valley Hall effect (VHE) in two-dimensional materials? The original VHE emerges in samples with ballistic transport of electrons due to the anomalous velocity terms resulting from the Berry phase effect. In disordered samples though, alternative mechanisms associated with electron scattering off impurities have been suggested: (i) asymmetric electron scattering, called skew scattering, and (ii) a shift of the electron wave packet in real space, called a side jump. It has been claimed that the side jump not…
Exciton Valley Hall effect is the spatial separation of the valley-tagged excitons in the presence of a drag force. Usually, the effect is associated with the anomalous velocity acquired by the particles due to the Berry curvature of the Bloch bands. Here we show that the anomalous velocity plays no role in the exciton valley Hall effect, which is governed by the side-jump and skew scattering mechanisms. We develop microscopic theory of the exciton valley Hall effect in the presence of synthetic electric field and phonon drag and calculate all relevant contributions to the valley Hall current …
We compute the intrinsic contributions to the Berry-phase mediated anomalous Hall and Nernst effects in electron- and hole-doped semiconductors in the presence of an in-plane magnetic field as well as Rashba and Dresselhaus spin orbit couplings. For both systems we find that the regime of chemical potential which supports the topological superconducting state in the presence of superconducting proximity effect can be characterized by plateaus in the topological Hall and Nernst coefficients flanked by well-defined peaks marking the emergence of the topological regime. The plateaus arise from a …
The band structure of many semiconducting monolayer transition metal dichalcogenides (TMDs) possesses two degenerate valleys, with equal and opposite Berry curvature. It has been predicted that, when illuminated with circularly polarized light, interband transitions generate an unbalanced non-equilibrium population of electrons and holes in these valleys, resulting in a finite Hall voltage at zero magnetic field when a current flows through the system. This is the so-called valley Hall effect that has recently been observed experimentally. Here, we show that this effect is mediated by photo-ge…
Two-dimensional magnetic insulators can be promising hosts for topological magnons. In this study, we show that ABC-stacked honeycomb lattice multilayers with alternating Dzyaloshinskii-Moriya interaction (DMI) reveal a rich topological magnon phase diagram. Based on our bandstructure and Berry curvature calculations, we demonstrate jumps in the thermal Hall behavior that corroborate with topological phase transitions triggered by adjusting the DMI and interlayer coupling. We connect the phase diagram of generic multilayers to a bilayer and a trilayer system. We find an even-odd effect amongst…
In the study of the anomalous Hall effect, the scaling relations between the anomalous Hall and longitudinal resistivities play the central role. The scaling parameters by definition are fixed as the scaling variable (longitudinal resistivity) changes. Contrary to this paradigm, we unveil that the electron-phonon scattering can result in apparent temperature-dependence of scaling parameters when the longitudinal resistivity is tuned through temperature. An experimental approach is proposed to observe this hitherto unexpected temperature-dependence. We further show that this phenomenon also exi…
The anomalous Hall effect in ferromagnetic metals is classified into two based on the mechanism. The first one is the intrinsic Hall effect due to the Berry curvature in momentum space; this is a Hall effect that solely arises from the band structure of solids. On the other hand, another contribution to the Hall effect, so-called extrinsic mechanism, comes from impurity scatterings such as skew scattering and side jump; for the extrinsic mechanism, the spin-orbit interaction of the impurity ions is often required. These two mechanisms are often discussed separately; the intrinsic Hall effect i…
The spontaneous Hall effect is usually governed by three conventional mechanisms, such as the Berry curvature, skew scattering and side jump, which widely exist in ferromagnetic or antiferromagnetic materials. However, in this work, based on first principle calculations, we predict a giant crystal Hall effect (CHE) in the antiferromagnetic $γ$-FeMn, which can not be understood by the previous three conventional mechanisms and the Hall angle therein can be as large as 18.4% at low temperature. Furthermore, with Boltzmann transport equation and a tight-binding model, we conclude that, the asymme…
We report the magnetic and electronic transport properties of the inversion and time-reversal symmetry breaking Weyl semimetal NdAlGe. This material is analogous to NdAlSi, whose helical magnetism presents a rare example of a Weyl-mediated collective phenomenon, but with a larger spin-orbit coupling. Our neutron diffraction experiments revealed that NdAlGe, similar to NdAlSi, supports an incommensurate Ising spin density wave ($T_{\text{inc}}=6.8$ K) with a small helical spin canting of 3$^\circ$ and a long-wavelength of $\sim$ 35 nm, which transitions to a commensurate ferrimagnetic state bel…
Gate-tunable large second-order and third-order nonlinear Hall effect in topological insulator BiSbTeSe2
National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Jiangsu Physical Science Research Center, and School of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室、先进微结构协同创新中心、江苏省物理科学研究中心和物理学院）；Institute of Atom Manufacturing, Nanjing University（南京大学原子制造研究所）；Jiangsu Provincial Key Laboratory of Atomic Level Manufacturing, Nanjing Institute of Atomic Scale Manufacturing（江苏省原子级制造重点实验室、南京原子尺度制造研究所）；School of Physics and Electronic Information, Jiangsu Second Normal University（江苏第二师范学院物理与电子信息学院）
We report on the observation of the acoustic spin Hall effect that facilitates lattice motion induced spin current via spin orbit interaction (SOI). Under excitation of surface acoustic wave (SAW), we find a spin current flows orthogonal to the propagation direction of a surface acoustic wave (SAW) in non-magnetic metals. The acoustic spin Hall effect manifests itself in a field-dependent acoustic voltage in non-magnetic metal (NM)/ferromagnetic metal (FM) bilayers. The acoustic voltage takes a maximum when the NM layer thickness is close to its spin diffusion length, vanishes for NM layers wi…
As nanoelectronics approaches the nanometer scale, a massive effort is underway to identify the next scalable logic technology beyond Complementary Metal Oxide Semiconductor (CMOS) computing. Such computing technology needs to improve switching energy & delay at reduced dimensions, allow improved interconnects and provide a complete logic/memory family. However, a viable beyond-CMOS logic technology has remained elusive. Here, we propose a scalable spintronic logic device which operates via spin-orbit transduction combined with magneto-electric switching. The proposed Magneto-Electric Spin Orb…
We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field is kept up to quadratic order, and both cases of small and large frequencies corresponding to intra- and interband transitions are considered. In particular, this formulation is suitable for the study of nonlinear Hall effect and photogalvanic phenomena. The role of impurity scattering is carefully addressed. Specifically, in addition to previously studied …
The anomalous Hall effect (AHE) is studied on the surface of a 3D magnetic topological insulator. By applying a modified semi-classical framework, all three contributions to the AHE, the intrinsic Berry phase curvature effect, the side-jump effect and the skew scattering effects are systematically treated, and analytical expressions for the conductivities are obtained in terms of the Fermi level, the spatial orientation of the surface magnetization and the concentration of magnetic and non-magnetic impurities. We demonstrate that the AHE can change sign by altering the orientation of the surfa…
Much has been learned about the topological transport in real materials. We investigate the interplay between magnetism and topology in the magneto-transport of PrRhC$_2$. The four-fold degeneracy reduces to two-fold followed by non-degenerate Weyl nodes when the orientation of the magnetic quantization axis is changed from easy axis to body-diagonal through face-diagonal. This engenders chirality imbalance between positive and negative chirality Weyl nodes around the Fermi energy. We observe a significant enhancement in the chiral anomaly mediated response such as planar Hall conductivity and…
An applied electric current through a space-inversion asymmetric magnet induces spin-orbit torques (SOTs) on the magnetic moments, which holds much promise for future memory devices. We discuss general Green's function expressions suitable to compute the linear-response SOT in disordered ferromagnets. The SOT can be decomposed into an even and an odd component with respect to magnetization reversal, where in the limit of vanishing disorder the even SOT is given by the constant Berry curvature of the occupied states, while the odd part exhibits a divergence with respect to disorder strength. Wi…
