The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but is sensitive to the breaking of discrete and crystal symmetries. It is a quantum transport phenomenon that has deep connection with the Berry curvature. However, a full quantum description is still absent. Here we construct a quantum theory of the nonlinear Hall effect by using the diagrammatic technique. Quite different from nonlinear optics, nearly all the diagrams account for the disorder effects, which play decisive role in the electronic transport. After including the disorder contributions in terms of the Feynman diagrams, the total nonlinear Hall conductivity is enhanced but its sign remains unchanged for the 2D tilted Dirac model, compared to the one with only the Berry curvature contribution. We discuss the symmetry of the nonlinear conductivity tensor and predict a pure disorder-induced nonlinear Hall effect for point groups $C_{3}$, $C_{3h}$, $C_{3v}$, $D_{3h}$, $D_{3}$ in 2D, and $T$, $T_{d}$, $C_{3h}$, $D_{3h}$ in 3D. This work will be helpful for explorations of the topological physics beyond the linear regime.
Detecting the orientation of the Néel vector is a major research topic in antiferromagnetic spintronics. Here we recognize the intrinsic nonlinear Hall effect, which is independent of the relaxation time, as a prominent contribution to the time-reversal-odd second order conductivity and can be used to detect the flipping of the Néel vector. In contrast, the Berry-curvature-dipole-induced nonlinear Hall effect depends linear on relaxation time and is time-reversal-even. We study the intrinsic nonlinear Hall effect in an antiferromagnetic metal: tetragonal CuMnAs, and show that its nonlinear Hal…
The Hall effects comprise one of the oldest but most vital fields in condensed matter physics, and they persistently inspire new findings, such as quantum Hall effects and topological phases of matter. The recently discovered nonlinear Hall effect is a new member of the family of Hall effects. It is characterized as a transverse Hall voltage in response to two longitudinal currents in the Hall measurement, but it does not require time-reversal symmetry to be broken. It has deep connections to symmetry and topology and, thus, opens new avenues by which to probe the spectral, symmetry and topolo…
Recently, signatures of nonlinear Hall effects induced by Berry-curvature dipoles have been found in atomically thin 1T'/Td-WTe$_2$. In this work, we show that in strained polar transition-metal dichalcogenides(TMDs) with 2H-structures, Berry-curvature dipoles created by spin degrees of freedom lead to strong nonlinear Hall effects. Under an easily accessible uniaxial strain of order 0.2%, strong nonlinear Hall signals, characterized by a Berry-curvature dipole on the order of 1Å, arise in electron-doped polar TMDs such as MoSSe, and this is easily detectable experimentally. Moreover, the magn…
We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed -- the Weyl cones are "tilted" -- the concerted actions of the anomalous velocity and the chiral anomaly give rise to the nonlinear Hall effect. This Hall conductivity is linear in both electric and magnetic fields, and depends critically on the tilting of the Weyl cones. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast to the intrinsic quantum nonlinear Hall effect that was recently observed in…
Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials - an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a rema…
NbSe$_2$ is one of metallic two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials. Because of broken crystal inversion symmetry, large spin splitting is induced by Ising-type spin-orbit coupling in odd-number-layered NbSe$_2$, but absent for even-number-layered NbSe$_2$ with the inversion symmetry. In this paper, we numerically calculate nonlinear optical charge and spin Hall conductivities of few-layered NbSe$_2$ based on an effective tight-binding model which includes $d_{z^2}$, $d_{x^2-y^2}$ and $d_{xy}$ orbitals of Nb atom. We show that the nonlinear optical Hall conductivi…
The spin Hall effect and its inverse play key roles in spintronic devices since they allow conversion of charge currents to and from spin currents. The conversion efficiency strongly depends on material details, such as the electronic band structure and the nature of impurities. Here we show an anomaly in the inverse spin Hall effect in weak ferromagnetic NiPd alloys near their Curie temperatures with a shape independent of material details, such as Ni concentrations. By extending Kondo's model for the anomalous Hall effect, we explain the observed anomaly as originating from the second-order …
The nonlinear Hall effect has opened the door towards deeper understanding of topological states of matter. It can be observed as the double-frequency Hall voltage response to an ac longitudinal current in the presence of time-reversal symmetry. Disorder plays indispensable roles in various linear Hall effects, such as the localization in the quantized Hall effects and the extrinsic mechanisms of the anomalous, spin, and valley Hall effects. Unlike in the linear Hall effects, disorder enters the nonlinear Hall effect even in the leading order. However, the disorder-induced contribution to the …
Higher odd-order nonlinear Hall effect in magnetic topological insulator Mn(Bi1-xSbx)2Te4
National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Jiangsu Physical Science Research Center, and School of Physics, Nanjing University（南京大学固体微观结构国家重点实验室、先进微结构协同创新中心、江苏省物理科学研究中心组和物理学院）；Institute of Atom Manufacturing, Nanjing University（南京大学原子制造研究所）；Nanjing Institute of Atomic Scale Manufacturing（南京原子尺度制造研究所）；School of Materials Science and Intelligent Engineering, Nanjing University（南京大学材料科学与智能工程学院）；Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, State Key Laboratory of Spintronics Devices and Technologies, School of Electronic Science and Engineering, Nanjing University（南京大学电子科学与工程学院、江苏省先进光子与电子材料重点实验室、自旋电子学器件与技术国家重点实验室）；Center for Quantum Transport and Thermal Energy Science, Institute of Physics Frontiers and Interdisciplinary Sciences, School of Physics and Technology, Nanjing Normal University（南京师范大学物理科学与技术学院、前沿交叉科学研究院、量子输运与热能科学中心）；Suzhou Laboratory（苏州实验室）
Nonlinear anomalous Hall effect is the Berry curvature dipole induced second-order Hall voltage or temperature difference in response to a longitudinal electric field or temperature gradient. These are the prominent Hall responses in time reversal symmetric systems. Here, we investigate the family of second-order nonlinear anomalous Hall effects, the electrical, thermoelectric and thermal nonlinear Hall effects in the moiré system of twisted double bilayer graphene. We demonstrate that the nonlinear anomalous Hall signals can be used to probe the topological phase-transitions in moiré systems,…
An intriguing property of three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi2Se3 film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a π/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of π/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Ha…
Unconventional responses upon breaking discrete or crystal symmetries open avenues for exploring emergent physical systems and materials. By breaking inversion symmetry, a nonlinear Hall signal can be observed, even in the presence of time-reversal symmetry, quite different from the conventional Hall effects. Low-symmetry two-dimensional materials are promising candidates for the nonlinear Hall effect, but it is less known when a strong nonlinear Hall signal can be measured, in particular, its connections with the band-structure properties. By using model analysis, we find prominent nonlinear …
We numerically investigate the second-order nonlinear Hall transport properties of a four-terminal system with time-reversal symmetry and broken inversion symmetry. Within the nonequilibrium Green's function formalism, the second-order nonlinear conductances are derived, where the internal Coulomb potential in response to external voltages is explicitly included to guarantee the gauge invariance. For the system with single mirror symmetry Mx, nonlinear Hall properties are only observable in the y direction and contributed solely from the second-order nonlinear effect. From the symmetry point o…
Orbital enhanced intrinsic nonlinear planar Hall effect for probing topological phase transition in CuTlSe$_{2}$
School of Physics, Beihang University（北京航空航天大学物理学院）；Interdisciplinary Center for Theoretical Physics and Information Sciences (ICTPIS), Fudan University（复旦大学理论物理与信息科学交叉中心）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武研究院）；Research Laboratory for Quantum Materials, IAPME, University of Macau（澳门大学量子材料研究实验室（IAPME））
When a magnon passes through two-dimensional magnetic textures, it will experience a fictitious magnetic field originating from the $3\times 3$ skew-symmetric gauge fields. To date, only one of the three independent components of the gauge fields has been found to play a role in generating the fictitious magnetic field while the rest two are perfectly hidden. In this work, we show that they are concealed in the nonlinear magnon transport in magnetic textures. Without loss of generality, we theoretically study the nonlinear magnon-skyrmion interaction in antiferromagnets. By analyzing the scatt…
We study the Hall conductivity of a two-dimensional electron gas under an inhomogeneous magnetic field $B(x)$. First, we prove using the quantum kinetic theory that an odd magnetic field can lead to a purely nonlinear Hall response. Second, considering a real-space magnetic dipole consisting of a sign-changing magnetic field and based on numerical semiclassical dynamics, we unveil a parametric resonance involving the cyclotron ratio and a characteristic width of $B(x)$, which can greatly enhance the Hall response. Different from previous mechanisms that rely on the bulk Berry curvature dipole,…
We study nonlinear response of a quantum Hall system in semiconductor-heterostructures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility.
Precise estimation of spin Hall angle as well as successful maximization of spin-orbit torque (SOT) form a basis of electronic control of magnetic properties with spintronic functionality. Until now, current-nonlinear Hall effect, or second harmonic Hall voltage has been utilized as one of the methods for estimating spin Hall angle, which is attributed to the magnetization oscillation by SOT. Here, we argue the second harmonic Hall voltage in magnetic/nonmagnetic topological insulator (TI) heterostructures, Cr$_x$(Bi$_{1-y}$Sb$_y$)$_{2-x}$Te$_3$/(Bi$_{1-y}$Sb$_y$)$_2$Te$_3$. From the angular, …
We propose a method for broadband long-wavelength photodetection using the nonlinear Hall effect in non-centrosymmetric quantum materials. The inherently quadratic relation between transverse current and input voltage at zero magnetic field is used to rectify the incident terahertz or infrared electric field into a direct current, without invoking any diode. Our photodetector operates at zero external bias with fast response speed and has zero threshold voltage. Remarkably, the intrinsic current responsivity due to Berry curvature mechanism is a material property independent of the incident fr…
Ferroelectric tuning of the valley polarized metal-semiconductor transition in Mn2P2S3Se3/Sc2CO2 van der Waals heterostructures and application to nonlinear Hall effect devices
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 …
MoTe$_2$ has recently attracted much attention due to the observation of pressure-induced superconductivity, exotic topological phase transitions, and nonlinear quantum effects. However, there has been debate on the intriguing structural phase transitions among various observed phases of MoTe$_2$, and their connection to the underlying topological electronic properties. In this work, by means of density-functional theory (DFT+U) calculations, we investigate the structural phase transition between the polar T$_d$ and nonpolar 1T$'$ phases of MoTe$_2$ in reference to a hypothetical high-symmetry…
We study nonlinear optical response of graphene in the quantum Hall regime to an intense laser pulse. In particular, we consider harmonic generation process. We demonstrate that the generalized magneto-optical conductivity of graphene on the harmonics of a strong pump laser radiation has a characteristic Hall plateaus feature. The plateaus heights depend on the laser intensity and broadening of Landau levels, so that are not quantized exactly. This nonlinear effect remains robust against the significant broadening of Landau levels. We predict realization of an experiment through the observatio…
Nonlinear Hall effect (NLHE) is a new type of Hall effect with wide application prospects. Practical device applications require strong NLHE at room temperature (RT). However, previously reported NLHEs are all low-temperature phenomena except for the surface NLHE of TaIrTe4. Bulk RT NLHE is highly desired due to its ability to generate large photocurrent. Here, we show the spin-valley locked Dirac state in BaMnSb2 can generate a strong bulk NLHE at RT. In the microscale devices, we observe the typical signature of an intrinsic NLHE, i.e. the transverse Hall voltage quadratically scales with th…
The Hall effect occurs only in systems with broken time-reversal symmetry, such as solids under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE). Here we show a new Hall effect in a nonmagnetic material under zero magnetic field, in which the Hall voltage depends quadratically on the longitudinal current. We observe the effect (referred to as nonlinear AHE) in two-dimensional Td-WTe2, a semimetal with broken inversion symmetry and only one mirror line in the crystal plane. Our angle-resolved electrical measurements reveal that the…
The second-order nonlinear Hall effect illuminates a frequency-doubling transverse current emerging in quantum materials with broken inversion symmetry even when time-reversal symmetry is preserved. This nonlinear response originates from both the Berry curvature dipole and the chiral Bloch electron skew scatterings, reflecting various information of the lattice symmetries, band dispersions, and topology of the electron wavefunctions. Even though many efforts have been put in detecting the nonlinear Hall effect in diverse condensed matter systems, effective manipulation of the two principal me…
We derive nonlinear wave equations describing the propagation of slowly-varying wavepackets formed by topological valley-Hall edge states. We show that edge pulses break up even in the absence of spatial dispersion due to nonlinear self-steepening. Self-steepening leads to the previously-unattended effect of a gradient catastrophe, which develops in a finite time determined by the ratio between the pulse's nonlinear frequency shift and the size of the topological band gap. Taking the weak spatial dispersion into account results then in the formation of stable edge quasi-solitons. Our findings …
Persistent nonlinear Hall effect driven by parallel field across a topological phase transition and intraband sign-reversing integer quantum Hall effect
Nonlinear optical responses to external electromagnetic field, characterized by second and higher order susceptibilities, play crucial roles in nonlinear optical devices and novel optoelectronics. Herein we present a quantum nonlinear ferroic optical Hall effect (QNFOHE) in multiferroics - a Hall-like direct photocurrent originated from the second order current response to intense electromagnetic field whose direction can be controlled by both internal ferroic orders and external light polarization. QNFOHE consists of two types of nonlinear photocurrent responses - shift current and circular p…
Antiferromagnetic (AFM) spintronics exploits the Néel vector as a state variable for novel spintronic devices. Recent studies have shown that the field-like and antidamping spin-orbit torques (SOT) can be used to switch the Néel vector in antiferromagnets with proper symmetries. However, the precise detection of the Néel vector remains a challenging problem. In this letter, we predict that the nonlinear anomalous Hall effect (AHE) can be used to detect the Néel vector in most compensated antiferromagnets supporting the antidamping SOT. We show that the magnetic crystal group symmetry of these …
By measuring magnetoresistance and Hall effect in classically moderate perpendicular magnetic field in Si-MOSFET-type macroscopic antidot array we found a novel effect: nonlinear with field, temperature- and density-dependent Hall resistivity. We discuss qualitative explanation of the phenomenon and suggest that it might originate from strong temperature dependence of the resistivity and mobility in the shells of the antidots.
We investigate the influence of surface states on the nonlinear Hall response of non-centrosymmetric time-reversal invariant Weyl semimetals. To do so, we perform a tomography of the Berry curvature dipole in a slab system using a minimal two-band model. We find that in the type-I phase, the nonlinear Hall response is not particularly sensitive to the presence of Fermi arcs or other trivial surface states. However, in the type-II phase, we find that these surface states contribute substantially to the Berry curvature dipole, leading to a strong thickness dependence of the nonlinear Hall respon…
