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, here, the effect largely stems from boundary states associated with the real-space magnetic dipole. Our findings pave a new way to engineer current rectification and higher harmonic generation in two-dimensional materials having or not crystal inversion symmetry.
We have investigated the complex two-dimensional electron system with unequal Rashba and Dresselhaus spin-orbit interactions in the presence of a perpendicular magnetic field. The spin polarizations are obtained in a wide range of magnetic fields. It is shown that such a system is hard to be magnetized. We also find that the resonant charge and spin Hall conductances occurs simultaneously at a certain magnetic field, at which two (nearly) degenerate Landau levels are filled partly. The resonant Hall effects are universal in this type of semiconductor materials, and could have potential applica…
The Spin Hall Effect (SHE) is a promising way for transforming charge currents into spin currents in spintronic devices. Large values of the Spin Hall Angle, the characteristic parameter of the yield of this transformation, have been recently found in noble metals doped with nonmagnetic impurities. We show that this can be explained by resonant scattering off impurity states split by the spin-orbit interaction. We apply our calculation to the interpretation of experiments on copper doped with 5d impurities and we describe the conditions to obtain the largest effects.
We study the disorder effect of resonant spin Hall effect in a two-dimension electron system with Rashba coupling in the presence of a tilted magnetic field. The competition between the Rashba coupling and the Zeeman coupling leads to the energy crossing of the Landau levels, which gives rise to the resonant spin Hall effect. Utilizing the Streda's formula within the self-consistent Born approximation, we find that the impurity scattering broadens the energy levels, and the resonant spin Hall conductance exhibits a double peak around the resonant point, which is recovered in an applied titled …
Recent experimental observations of unexpectedly large thermal Hall conductivities, $κ_H$, in insulating materials, including the parent compounds of the high temperature superconducting cuprates, likely reflect an extrinsic contribution from a yet to be identified extrinsic source of skew scattering of acoustic phonons. We show that resonant scattering of phonons from a certain class of three-level systems produces strong skew scattering in the presence of a modest magnetic field. We interpret this as a first step towards understanding the experiments.
We show that the extrinsic spin Hall effect can be engineered in monolayer graphene by decoration with small doses of adatoms, molecules, or nanoparticles originating local spin-orbit perturbations. The analysis of the single impurity scattering problem shows that intrinsic and Rashba spin-orbit local couplings enhance the spin Hall effect via skew scattering of charge carriers in the resonant regime. The solution of the transport equations for a random ensemble of spin-orbit impurities reveals that giant spin Hall currents are within the reach of the current state of the art in device fabrica…
Resonant tunneling through a quantum dot weakly coupled to quantum wires or quantum Hall edge states
讨论了弱耦合量子点与Tomonaga-Luttinger液体的共振隧穿。由于顺序隧穿的线性电导计算通过求解主方程的温度低于和高于平均水平间距的点。当表征Tomonaga-Luttinger液体的参数g小于1/2时，共振隧穿过程在零温度下是不相干的。在低温T下，库仑阻塞振荡中电导峰的高度和宽度分别与T^{（1/g）-2}和T成正比。隧道通过一个虚拟的中间状态（cotunneling）的贡献也包括在内。所得的电导公式可以应用于填充因子nu=1/（2 m +1）=g的分数量子霍尔液体边缘态之间的共振隧穿。
Giant resonant nonlinear THz valley Hall effect in 2D Dirac semiconductors
Guangdong Technion – Israel Institute of Technology（广东以色列理工学院）；Rzhanov Institute of Semiconductor Physics, Siberian Branch of Russian Academy of Science（俄罗斯科学院西伯利亚分院热诺夫半导体物理研究所）；Novosibirsk State Technical University（新西伯利亚国立技术大学）；Technion – Israel Institute of Technology（以色列理工学院）
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…
We use spin torque ferromagnetic resonance to measure the spectral properties of dipole-exchange spin waves in permalloy nanowires. Our measurements reveal that geometric confinement has a profound effect on the damping of spin waves in the nanowire geometry. The damping parameter of the lowest-energy quantized spin wave mode depends on applied magnetic field in a resonant way and exhibits a maximum at a field that increases with decreasing nanowire width. This enhancement of damping originates from a nonlinear resonant three-magnon confluence process allowed at a particular bias field value d…
This paper presents experimental evidence of the existence of acoustic valley Hall (AVHE) edge states in topological elastic waveguides. The fundamental lattice is assembled based on a non-resonant unit where space inversion symmetry (SIS) is broken by simply perturbing the underlying lattice geometry. This aspect is in net contrast with existing elastic AVHE designs that exploit locally-resonant units and require the addition of masses in order to break SIS. The experimental results presented in this study validate findings so far presented only at theoretical and numerical level. In particul…
We investigate the finite frequency (f.f.) noise properties of edge states in the quantum Hall regime. We consider the measurement scheme of a resonant detector coupled to a quantum point contact in the weak-backscattering limit. A detailed analysis of the difference between the "measured" noise, due to the presence of the resonant detector, and the symmetrized f.f. noise is presented. We discuss both the Laughlin and Jain sequences, studying the tunnelling excitations in these hierarchical models. We argue that the measured noise can better distinguish between the different excitations in the…
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…
We present computations of the thermal Hall coefficient of phonons scattering off a defect with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is proportional to the phonon lifetime, and has a `side-jump' interpretation. Consequently, the thermal Hall angle is independent of the phonon lifetime. The contribution to the thermal Hall coefficient is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for three different defect models, which a…
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 …
We predict spin Hall angles up to 80% for ultrathin noble metal films with substitutional Bi impurities. The colossal spin Hall effect is caused by enhancement of the spin Hall conductivity in reduced sample dimension and a strong reduction of the charge conductivity by resonant impurity scattering. These findings can be exploited to create materials with high efficiency of charge to spin current conversion by strain engineering.
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）
We propose an efficient spin filter including an antidot fabricated on semiconductor heterostructures with strong spin-orbit interaction. The antidot creates a tunable potential on two-dimensional electron gas in the heterostructures, which may be attractive as well as repulsive. Our idea is based on the enhancement of extrinsic spin Hall effect by resonant scattering when the attractive potential is properly tuned. Numerical studies for three- and four-terminal devices indicate that the efficiency of the spin filter can be more than 50% by tuning the potential to the resonant condition.
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 …
We propose a resonant spin-field-effect transistor for chiral spin-resolved edge states in the integer quantum Hall effect with Rashba spin-orbit interaction. It employs a periodic array of voltage-controlled top gates that locally modulate the Rashba spin-orbit interaction. Strong resonant spin-field effect is achieved when the array periodicity matches the inverse of the wave-vector difference of the two chiral states involved. Well-known techniques of separately contacting the edge states make it possible to selectively populate and read out the edge states, allowing full spin readout. The …
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,…
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…
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…
We theoretically demonstrate that 100\% valley-polarized transport in monolayers of MoS$_{2}$ and other group-VI dichalcogenides can be obtained using off-resonant circularly polarized light. By tuning the intensity of the off-resonant light the intrinsic band gap in one valley is reduced, while it is enhanced in the other valley, enabling single valley quantum transport. As a consequence, we predict (i) enhancement of the longitudinal electrical conductivity, accompanied by an increase in the spin-polarization of the flowing electrons, (ii) enhancement of the intrinsic spin Hall effect, toget…
We demonstrate the new specific phenomenon of the long-time resonant energy exchange in the carbon nanotubes (CNTs) with the radial breathing mode as a carrier. This process turns out to be stable in the wide range of the excitation energy. It is shown that the modified nonlinear Schrödinger equation, obtained in the framework of nonlinear elastic thin shell theory, describes the CNT nonlinear dynamics in the considered frequency band. The numerical integration of the thin shell theory equations confirms the results of the analytical study.
