Takehito Yokoyama
Transverse current due to Berry curvature in phase space is formulated based on the Boltzmann equations with the semiclassical equations of motion for an electron wave packet. It is shown that the Hall effect due to the phase space Berry curvature is absent because the contributions from "anomalous velocity" and "effective Lorentz force" are completely cancelled out.
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The Berry phase of π in graphene is derived in a pedagogical way. The ambiguity of how to calculate this value properly is clarified. Its connection with the unconventional quantum Hall effect in graphene is discussed.
We have shown that the study of topological aspects of the underlying geometry in a ferromagnetic spin system gives rise to an intrinsic Berry phase. This real space Berry phase arises due to the spin rotations of conducting electrons which can be manifested as a further contribution in anomalous Hall effect.
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.
The Berry phase origin is elaborated for the recent-discovered planar spin Hall effect which features current-induced spin polarization within the plane of the Hall deflection. We unravel a spin-repulsion vector governing the planar spin Hall effect, providing a transparent criteria for identifying intrinsic planar spin Hall materials. Finite spin-repulsion vector is found permitted in 13 crystalline point groups, revealing a big number of unexplored planar spin Hall systems. Our result can be used for the quantitative calculation of the planar spin Hall effect, facilitating further material h…
We consider Bloch electrons in the electromagnetic field and argue the relation between the Berry phase and the quantized Hall conductivity in three-dimension. The Berry phase we consider here is induced by the adiabatic change of the time-dependent vector potential. The relation has been shown in two-dimensional systems, and we generalize the relation in three-dimensional systems.
Inversion symmetry breaking and spin-orbit coupling lead to valley and spin Hall effect in MoS2. Because of the large valley separation in momentum space, the valley index is expected to be robust. In this paper, quantum Hall effect in MoS2 originated from Berry curvature is analyzed after review of symmetry structure and spin-orbit coupling Hamiltonian of MoS2. Finally an expression and rough calculation is given for valley and spin Hall effect.
Nonlinear Hall effect in isotropic k-cubed Rashba model: Berry-curvature-dipole engineering by in-plane magnetic field
该研究针对二维各向同性k立方Rashba模型开展理论分析，明确了面外磁场/净磁化是产生非零贝里曲率的必要条件，揭示了面内磁场对贝里曲率偶极子的调控作用，以及线性与二阶霍尔电导率的不同主导机制。
We have studied here the newly observed families of fractional quantum Hall states in the framework of Berry phase. It has been shown that this approach embraces in a unified way the whole spectrum of quantum Hall states with their various characteristic features. The newly observed states can be well accommodated within the primary sequence of FQH states and need not be considered as second generation FQH states as suggested by some authors.
Intrinsic nonlinear Hall effect and gate-switchable Berry curvature sliding in twisted bilayer graphene
本研究在高质量扭曲双层石墨烯中观测到Berry曲率偶极诱导的本征非线性霍尔效应，并利用位移场实现Berry曲率热点滑动及霍尔电压方向、幅度的栅极调控。
The $α$-$T_3$ model is characterized by a variable Berry phase that changes continuously from $π$ to $0$. We take advantage of this property to highlight the effects of this underlying geometrical phase on a number of physical quantities. The Hall quantization of the two limiting cases is dramatically different - a relativistic series is associated with a Berry phase of $π$ and a non-relativistic series is associated with the other limit. We study the quantization of the Hall plateaux as they continuously evolve from a relativistic to a non-relativistic regime. Additionally, we describe two ph…
Hall experiments in chiral magnets are often analyzed as the sum of an anomalous Hall effect, dominated by momentum-space Berry curvature, and a topological Hall effect, arising from the real-space Berry curvature in the presence of skyrmions, in addition to the ordinary Hall resistivity. This raises the questions of how one can incorporate, on an equal footing, the effects of the anomalous velocity and the real space winding of the magnetization, and when such a decomposition of the resistivity is justified. We provide definitive answers to these questions by including the effects of all phas…
The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi$_2$Te$_4$ thinfilms under perpendicular electric fields [Gao et al., Nature 595, 521 (2021)]. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but nonzero layer-locked hidden Berry curvature in real space. We show that compared to that of a trivial insulator, the layer Hall effect…
Hot spot of Berry curvature is usually found at Bloch band anti-crossings, where the Hall effect due to the Berry phase can be most pronounced. With small gaps there, the adiabatic limit for the existing formulations of Hall current can be exceeded in a moderate electric field. Here we present a theory of non-adiabatic Hall effect, capturing non-perturbatively the across gap electron-hole excitations by the electric field. We find a general connection between the field induced electron-hole coherence and intrinsic Hall velocity. In coherent evolution, the electron-hole coherence can manifest a…
We present an approach to the computation of the non-Abelian statistics of quasiholes in quantum Hall states, such as the Pfaffian state, whose wavefunctions are related to the conformal blocks of minimal model conformal field theories. We use the Coulomb gas construction of these conformal field theories to formulate a plasma analogy for the quantum Hall states. A number of properties of the Pfaffian state follow immediately, including the Berry phases which demonstrate the quasiholes' fractional charge, the abelian statistics of the two-quasihole state, and equal-time ground state correlatio…
The chirality of electronic Bloch bands is responsible for many intriguing properties of layered two-dimensional materials. We show that in bilayers of transition metal dichalcogenides (TMDCs), unlike in few-layer graphene and monolayer TMDCs, both intra-layer and inter-layer couplings give important contributions to the Berry-curvature in the $K$ and $-K$ valleys of the Brillouin zone. The inter-layer contribution leads to the stacking dependence of the Berry curvature and we point out the differences between the commonly available 3R type and 2H type bilayers. Due to the inter-layer contribu…
Tutorial: From Topology to Hall Effects -- Implications of Berry Phase Physics
本教程全面介绍Berry相位的数学框架及其与量子系统拓扑性质的联系，深入探讨量子霍尔效应等拓扑效应及拓扑绝缘体的输运性质，旨在帮助读者掌握Berry相位在拓扑量子现象中的核心作用。
Transport measurements indicate strong oscillations in the Hall-,$R_{xy}$, and the diagonal-, $R_{xx}$, resistances and exhibit Hall plateaus at the lowest temperatures, in three-dimensional Highly Oriented Pyrolytic Graphite (HOPG). At the same time, a comparative Shubnikov-de Haas-oscillations-based Berry's phase analysis indicates that graphite is unlike the GaAs/AlGaAs 2D electron system, the 3D n-GaAs epilayer, semiconducting $Hg_{0.8}Cd_{0.2}Te$, and some other systems. Finally, we observe the transport data to follow $B\times dR_{xy}/dB \approx - ΔR_{xx}$. This feature is consistent wit…
The momentum dependent splitting of spin-bands in an electronic system is known as the "Rashba effect". Systems with the "Rashba effect" possess a Dirac point in momentum space. An electron in a cyclotron orbit enclosing that Dirac point in the reciprocal space gains a "Berry phase". We report here the Shubnikov-de-Haas oscillations (SdH) at the conducting interface of EuO-KTaO$_3$ (KTO). Observed SdH oscillations suggest the presence of two Fermi surfaces. For both the Fermi surfaces, we have seen the presence of a non-trivial "Berry phase" suggesting that the surfaces enclose the "Dirac poin…
We propose the linear and nonlinear planar Hall effect (PHE) in tilted Weyl semimetals in the presence of an in-plane magnetic and electric field, where the field-induced Berry connection (FBC) plays a key role. We show that the PHE is ascribed to the quantum metric, distinct from the well-known chiral anomaly-induced PHE arising from the Berry curvature. Using a tilting vector to describe the model, we demonstrate the constrains on the linear and nonlinear PHE by the tilting directions. The linear PHE is intrinsic that is determined by the topological properties of energy bands, whereas the n…
It is well-known that a non-vanishing Hall conductivity requires time-reversal symmetry breaking. However, in this work, we demonstrate that a Hall-like transverse current can occur in second-order response to an external electric field in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the optical frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. We show that the nonlinear Hal…
There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase pi, which results in a shifted positions of Hall plateaus. Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and exhibit Berry's phase 2pi affecting their quantum dynamics. The L…
We have discussed here the polarization of quantum Hall states in the framework of the hierarchical analysis of IQHE and FQHE in terms of Berry phase. It is observed that we have fully polarized states for the filling factor $ν=1$ as well as $ν=\frac{1}{2m+1}$, $m$ being an integer. However, for $ν=p$ as well as $ν=\frac{p}{q}$, with $p>1$ and odd, $q$ odd we have partially polarized states and for $ν=\frac{p}{q}$, $p$ even, $q$ odd we have unpolarized states. It has been found that skyrmion excitations exist only for fully polarized states and for partially polarized and unpolarized states sk…
Recently, the magnetic topological insulator MnBi$_2$Te$_4$ emerged as a competitive platform to realize quantum anomalous Hall (QAH) states. We report a Berry-curvature splitting mechanism to realize the QAH effect in the disordered magnetic TI multilayers when switching from an antiferromagnetic order to a ferromagnetic order. We reveal that the splitting of spin-resolved Berry curvature, originating from the separation of the mobility edge during the magnetic switching, can give rise to a QAH insulator even \emph{without} closing the band gap. We present a global phase diagram, and also pro…
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…
The quantum oscillation is an important probe for the detection of a topological insulator(TI) surface states by means of electrical transport since the Shubnikov-de Haas oscillations allow to extract the Berry Phase which is the key test to detect the topological surface states. Here we have extracted the non trivial Berry Phase of 1$\%$ Sn doped strong TI $Sb_2Te_2Se$. We observed oscillation in Hall resistance as well and showed that this does not arise neither from the dominance of the SdH on Hall data nor this is the precursor of quantum Hall effect, rather this happens due to the pinning…
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…
The temperature and magnetic field dependences of the anomalous Hall effect (AHE) are studied in Mn delta-doped semiconductor heterostructures with a two-dimensional hole gas in a quantum well interacting with the Mn layer. The analysis of experimental data reveals four distinct temperature ranges differing in the behavior of AHE. The Mn layer induces an inhomogeneity of the hole gas leading to an interplay between the hopping and drift conductivities. It is shown that at sufficiently low temperatures, hopping conductivity favors the mechanisms of AHE related to the geometric (Berry-Pancharatn…
Photovoltaic Hall effect -- the Hall effect induced by intense, circularly-polarized light in the absence of static magnetic fields -- has been proposed in Phys. Rev. B 79, 081406R (2009) for graphene where a massless Dirac dispersion is realized. The photovoltaic Berry curvature (a nonequilibrium extension of the standard Berry curvature) is the key quantity to understand this effect, which appears in the Kubo formula extended to Hall transport in the presence of strong AC field backgrounds. Here we elaborate the properties of the photovoltaic curvature such as the frequency and field strengt…
Nonlinear anomalous transverse responses induced by Berry curvature quadrupole in systems with broken time-reversal symmetry
本文基于半经典玻尔兹曼形式，计算了破坏时间反演对称性系统中Berry曲率四极矩诱导的非线性反常热霍尔与能斯特系数，预测了与温度梯度三次方成正比的响应，并指出该效应在已有实验系统中必然存在。
Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the Nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Dr…
We analytically show that a gap is induced around the Dirac point in the electronic spectrum of a previously metallic nanotube, in the presence of electric and magnetic fields perpendicular to the tube axis. For realistic values of the fields, a gap of at least a few meV can appear. Despite the quasi-one dimensional nature of the system, the gapped state is associated with a non-zero topological invariant and supports a Hall effect. This is revealed when the flux through the tube is varied by one flux quantum, which leads to exactly one electron per spin being transported between the ends of t…
Electric field induced Berry curvature dipole and non-linear anomalous Hall effects in higher wave symmetric unconventional magnets
该研究针对高波对称非常规磁体，揭示外电场可通过耦合量子度规诱导贝里曲率偶极子，产生非线性及三阶反常霍尔效应，可用于探测量子度规并区分序参量对称性。
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…
Carrier dynamics acquire a new character in the presence of Bloch-band Berry curvature, which naturally arises in gapped Dirac materials (GDMs). Here we argue that photoresponse in GDMs with small band gaps is dramatically enhanced by Berry curvature. This manifests in a giant and saturable Hall photoconductivity when illuminated by circularly polarized light. Unlike Hall motion arising from a Lorentz force in a magnetic field, which impedes longitudinal carrier motion, Hall photoconductivity arising from Berry curvature can boost longitudinal carrier transport. In GDMs, this results in a heli…
Nonlinear Layer Hall Effect and Detection of the Hidden Berry Curvature Dipole in $\mathcal{PT}$-Symmetric Antiferromagnetic Insulators
本研究预测了PT对称层状反铁磁体中的非线性层霍尔效应，明确其与线性效应的对称性差异，区分了隐藏贝里曲率偶极子和量子度量偶极子诱导的霍尔电流特征，为探测隐藏贝里曲率偶极子量子几何提供了实验可行的新框架。
The intrinsic spin Hall conductivity and the anomalous Hall conductivity of ferromagnetic L1$_0$-CoPt are studied using first principle calculations of the spin Berry and Berry curvatures, respectively. We find that the Berry curvature and the spin Berry curvature exhibit different symmetry with respect to that of the band structure. The Berry curvature preserves the $C_{4v}$ crystal rotation symmetry along the c-axis whereas the symmetry of the spin Berry curvature reduces to $C_{2v}$. Contributions to the Berry curvature and the spin Berry curvature are classified by the spin character of ba…
Berry phase and Berry curvature play a key role in the development of topology in physics and do contribute to the transport properties in solid state systems. In this paper, we report the finding of novel nonzero Hall effect in topological material ZrTe5 flakes when in-plane magnetic field is parallel and perpendicular to the current. Surprisingly, both symmetric and antisymmetric components with respect to magnetic field are detected in the in-plane Hall resistivity. Further theoretical analysis suggests that the magnetotransport properties originate from the anomalous velocity induced by Be…
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…
Fully nonequilibrium Hall response from Berry curvature
该研究针对时间反演对称、反演对称破缺的拓扑系统，提出贝里曲率诱导的完全非平衡霍尔响应，揭示其非微扰电场下不由贝里曲率偶极矩主导的特性及普适性，为强关联拓扑半金属研究提供新视角。
Negative longitudinal magnetoresistance, in the presence of an external magnetic field parallel to the direction of an applied current, has recently been experimentally verified in Weyl semimetals and topological insulators in the bulk conduction limit. The appearance of negative longitudinal magnetoresistance in topological semimetals is understood as an effect of chiral anomaly, whereas it is not well-defined in topological insulators. Another intriguing phenomenon, planar Hall effect - appearance of a transverse voltage in the plane of applied co-planar electric and magnetic fields not perf…
Planar Hall Effect in Quasi-Two-Dimensional Materials
针对二维系统中常规平面霍尔效应被禁戒的问题，提出源于隐藏Berry曲率和轨道磁矩分量的二维平面霍尔效应（2DPHE），以门控双层石墨烯为例揭示其对能带几何与Lifshitz转变的敏感性，为创新应用提供新途径。
Local phase-space Berry curvature and Hall transport in textured twisted bilayer graphene
本文针对扭转双层石墨烯，分析其纹理化微狄拉克锥的局域相空间贝里曲率，明确几何响应峰值的局域填充值，建立局域解析框架以区分TBG相关的各类要素。
We show that the spin quantum Hall effect in the vortex state of two-dimensional rotating superfluid He3 can be described as an adiabatic spin transport of Bloch quasiparticles. We show that the spin Hall conductivity is written by the Berry phase as well as the Chern number. The results have similarity to the adiabatic pumping of Bloch electrons and the spontaneous polarization in crystalline dielectrics.
The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K and K' valleys, having Berry curvatures with opposite signs, and thus vanishing anomalous Hall effect in this system. Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe2 through applying uniaxial strain to break C3v symmetry. As a result, although the Berry curvature itself is still …
Recently, the topological flat bands and spin Hall effect have been experimentally observed in the AB-stacked MoTe$_2$/WSe$_2$ heterostructures. In this work, we systematically study the Berry curvature effects in moiré transition metal dichalcogenide (TMD) heterobilayers. We point out that the moiré potential of the remote conduction bands would induce a sizable periodic pseudo-magnetic field (PMF) on the valence band. This periodic PMF creates net Berry curvature flux in each valley of the moiré Brillouin zone. The combination of the effect of the Berry curvature and the spin-valley locking …
The topological properties of a material's electronic structure are encoded in its Berry curvature, a quantity which is intimately related to the transverse electrical conductivity. In transition metal dichalcogenides with broken inversion symmetry, the nonzero Berry curvature results in a valley Hall effect. In this paper we identify a previously unrecognized consequence of Berry curvature in these materials: an electric field-induced change in the electrons' charge density orientation. We use first principles calculations to show that measurements of the electric field-induced change in the …
It is shown that the deviation of fractional quantum Hall edge fluid from power law correlation functions with universal exponent $α=1/ν$ as observed in recent experiment may be explained when analyzed from the viewpoint of chiral anomaly and Berry phase. It is observed that at the edge anomaly vanishes and this induces a nonlocal effect in the construction of the electron creation operator in terms of the edge boson fields. This nonlocality is responsible for the deviation of the power law exponent from $α=1/ν$ of the edge fluid. There are gapless edge excitations described by chiral boson fi…
Higher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles
本研究揭示贝里曲率多极矩可诱导高阶非线性反常霍尔效应，通过对称性分析与计算验证了其在反铁磁体、拓扑绝缘体等材料中的主导阶响应，并提出了多种候选材料体系。
Parent Berry curvature and the ideal anomalous Hall crystal
研究均匀Berry曲率母带中电子模型，发现高曲率下强排斥作用形成反常霍尔晶体，为理解多层石墨烯量子反常霍尔效应提供统一视角。
Piezotronics is an emerging field, which exploits strain to control the transport properties in condensed matters. At present, piezotronics research majorly focuses on insulators with tunable electric dipole by strain. Metals are excluded in this type of applications due to the absence of electric dipole. The recently discovered Berry curvature dipole can exist in metals, thus introduces the possibility of the piezotronics phenomena in them. In this paper, we predict that strain can switch the Berry curvature dipole, and lead the nonlinear Hall effect in the two-dimensional (2D) 1$H$-MX$_2$ (M…
In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects, so are their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is p…
The intrinsic anomalous Hall effect in metallic ferromagnets is shown to be controlled by Berry phases accumulated by adiabatic motion of quasiparticles on the Fermi surface, and is purely a Fermi-liquid property, not a ``bulk'' Fermi sea property like Landau diamagnetism, as has been previously supposed. Berry phases are a new topological ingredient that must be added to Landau Fermi-liquid theory in the presence of broken inversion or time-reversal symmetry.
Anomalous skew-scattering nonlinear Hall effect and chiral photocurrents in {\it PT}-symmetric antiferromagnets
本研究针对PT对称反铁磁金属中单一机制霍尔效应消失的问题，发现了贝里曲率与斜散射协同产生的反常斜散射非线性霍尔效应，其具有螺旋度依赖的光电流特性，为反铁磁序探测提供了新工具。
We consider the Nernst and Hall effects in fluctuation regime of chiral superconductors above transition temperatures, that are raised not by conventional Lorentz force, but by asymmetric scattering due to fluctuations of the Berry phase of the Bogoliubov-de Gennes Hamiltonian. It is found that these effects can be more significant than conventional ones for cleaner samples, exhibiting qualitatively distinct behaviors. The results provide systematic and comprehensive understanding for recent experimental observations of the Nernst effect in a clean URu$_2$Si$_2$ sample, which is suggested to b…
The spin Hall effect is investigated in a high mobility two dimensional electron system with the spin-orbital coupling of both the Rashba and the Dresselhaus types. A spin current perpendicular to the electric field is generated by either the Rashba or the Dresselhaus coupling. The spin Hall conductance is independent of the stength of the coupling, but its sign is determined by the relative ratio of the two couplings. The direction of spin current is controllable by tuning the magnitude of the surface electric field perpendicular to the two dimensional plane via adjusting the Rashba coupling.…
Recently, a type of Hall effect due to an unusual layer-locked Berry curvature called the layer Hall effect (LHE) has been reported in the even-layered two-dimensional antiferromagnetic (AFM) MnBi2Te4 [A. Gao et.al, Nature 595, 521 (2021)]. In this work, we report that the quantization of LHE, which we call the quantum anomalous layer Hall effect (QALHE), can be realized in MnBi2Te4. The QALHE originates from kicking a layer-locked Berry-curvature monopole out of the Fermi sea by a vertielectric cal field. Remarkably, we demonstrate that the electric-field reversal can switch the sign of the q…
We study the quantum nonlinear planar Hall effect in bilayer graphene under a steady in-plane magnetic field. When time-reversal symmetry is broken by the magnetic field, a charge current occurs in the second-order response to an external electric field, as a result of the Berry curvature dipole in momentum space. We have shown that a nonlinear planar Hall effect originating from the anomalous velocity is deduced by an orbital effect of an in-plane magnetic field on electrons in bilayer graphene in the complete absence of spin-orbit coupling. Taking into account the symmetry analysis, we deriv…
Various nonlinear characteristics of solid states, such as the circular photogalvanic effect of time-reversal symmetric insulators, the quantized photogalvanic effect of Weyl semimetals, and the nonlinear Hall effect of time-reversal symmetric metals, have been associated with the Berry curvature dipole (BCD). Here, we explore the question of whether the Berry curvature dipole and multipoles of time-reversal symmetric insulators can be traced in the nonlinear optical responses. We performed real-time time-dependent density functional theory calculations and examined the second harmonic generat…
One big achievement in modern condensed matter physics is the recognition of the importance of various band geometric quantities in physical effects. As prominent examples, Berry curvature and the Berry curvature dipole are connected to the linear and the second-order Hall effects, respectively. Here, we show that the Berry connection polarizability (BCP) tensor, as another intrinsic band geometric quantity, plays a key role in the third-order Hall effect. Based on the extended semiclassical formalism, we develop a theory for the third-order charge transport and derive explicit formulas for th…
Magnetotransport such as the giant magnetoresistance and Hall effect lies at the heart of fundamental physics and technologies. Recently, some experiments have clearly demonstrated linear magnetotransport (LMT) proportional to magnetic field but the underlying physical mechanism is still unclear. In this work, we show that Berry curvature effect is a new mechanism dominating the LMT. The Berry-curvature-induced LMT widely exists in 66 out of 122 magnetic point groups. For typical magnetic Weyl semimetals Co$_3$Sn$_2$S$_2$ and ferromagnetic MnBi$_2$Te$_4$, Berry curvature induces LMT conductivi…
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