反常霍尔效应理论的研究进展

文章介绍了在铁磁性材料中反常霍尔效应的发现及其机制研究的历史；阐述了反常霍尔效应理论研究最近取得的重大进展，即倒空间中布洛赫态的贝里曲率（规范场）特性决定了霍尔电导率；同时指出，建立系统地解释反常霍尔效应机制的理论仍然是一个挑战性的任务．     

Linear magnetization dependence of the intrinsic anomalous Hall effect

The anomalous Hall effect is investigated experimentally and theoretically for ferromagnetic thin films of Mn5Ge3. We have separated the intrinsic and extrinsic contributions to the experimental anomalous Hall effect and calculated the intrinsic anomalous Hall conductivity from the Berry curvature of the Bloch states using first-principles methods. The intrinsic anomalous Hall conductivity depends linearly on the magnetization, which can be understood from the long-wavelength fluctuations of the spin orientation at finite temperatures. The quantitative agreement between theory and experiment is remarkably good, not only near 0 K but also at finite temperatures, up to about approximately 240 K (0.8TC).     

Strain-dependent resistance and giant gauge factor in monolayer WSe_2

We report the strong dependence of resistance on uniaxial strain in monolayer WSe_2 at various temperatures, where the gauge factor can reach as large as 2400. The observation of strain-dependent resistance and giant gauge factor is attributed to the emergence of nonzero Berry curvature dipole. Upon increasing strain, Berry curvature dipole can generate net orbital magnetization, which would introduce additional magnetic scattering, decreasing the mobility and thus conductivity. Our work demonstrates the strain engineering of Berry curvature and thus the transport properties, making monolayer WSe_2 potential for application in the highly sensitive strain sensors and high-performance flexible electronics.     

Anomalous Hall effect of heavy holes in III-V semiconductor quantum wells

The anomalous Hall effect of heavy holes in semiconductor quantum wells is studied in the intrinsic transport regime, where the Berry curvature governs the Hall current properties. Based on the first--order perturbation of wave function the expression of the Hall conductivity the same as that from the semiclassical equation of motion of the Bloch particles is derived. The dependence of Hall conductivity on the system parameters is shown. The amplitude of Hall conductivity is found to be balanced by a competition between the Zeeman splitting and the spin--orbit splitting.     

Characteristics of anomalous Hall effect in spin-polarized two-dimensional electron gases in the presence of both intrinsic, extrinsic, and external electric-field induced spinben orbit couplings

The various competing contributions to the anomalous Hall effect in spin-polarized two-dimensional electron gases in the presence of both intrinsic, extrinsic and external electric-field induced spin-orbit coupling were investigated theoretically. Based on a unified semiclassical theoretical approach, it is shown that the total anomalous Hall conductivity can be expressed as the sum of three distinct contributions in the presence of these competing spin-orbit interactions, namely an intrinsic contribution determined by the Berry curvature in the momentum space, an extrinsic contribution determined by the modified Bloch band group velocity and an extrinsic contribution determined by spin-orbit-dependent impurity scattering. The characteristics of these competing contributions are discussed in detail in the paper.     

Interplay between carrier and impurity concentrations in annealed Ga1-xMnxAs: intrinsic anomalous hall effect

Investigating the scaling behavior of annealed Ga1-xMnxAs anomalous Hall coefficients, we note a universal crossover regime where the scaling behavior changes from quadratic to linear. Furthermore, measured anomalous Hall conductivities in the quadratic regime when properly scaled by carrier concentration remain constant, spanning nearly a decade in conductivity as well as over 100 K in T_[C] and comparing favorably to theoretically predicated values for the intrinsic origins of the anomalous Hall effect. Both qualitative and quantitative agreements strongly point to the validity of new equations of motion including the Berry phase contributions as well as the tunability of the anomalous Hall effect.     

Spin Hall effect and Berry phase of spinning particles

We consider the adiabatic evolution of the Dirac equation in order to compute its Berry curvature in momentum space. It is found that the position operator acquires an anomalous contribution due to the non-Abelian Berry gauge connection making the quantum mechanical algebra noncommutative. A generalization to any known spinning particles is possible by using the Bargmann–Wigner equation of motions. The noncommutativity of the coordinates is responsible for the topological spin transport of spinning particles similarly to the spin Hall effect in spintronic physics or the Magnus effect in optics. As an application we predict new dynamics for nonrelativistic particles in an electric field and for photons in a gravitational field.     

The quantum anomalous Hall effect on a star lattice with spin-orbit coupling and an exchange field

We study a star lattice with Rashba spin-orbit coupling and an exchange field and find that there is a quantum anomalous Hall effect in this system, and that there are five energy gaps at Dirac points and quadratic band crossing points. We calculate the Berry curvature distribution and obtain the Hall conductivity (Chern number ν) quantized as integers, and find that ν?=-?1,2,1,1,2 when the Fermi level lies in these five gaps. Our model can be viewed as a general quantum anomalous Hall system and, in limit cases, can give what the honeycomb lattice and kagome lattice give. We also find that there is a nearly flat band with ν?=?1 which may provide an opportunity for realizing the fractional quantum anomalous Hall effect. Finally, the chiral edge states on a zigzag star lattice are given numerically, to confirm the topological property of this system.     

Anomalous Hall effect in noncommutative mechanics

The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space, as found recently in some ferromagnetic semiconductors while observing the anomalous Hall effect, we get a transverse shift, similar to that in the optical Hall effect.     

Geometric curvature and phase of the Rabi model

We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.     

First principles calculation of anomalous Hall conductivity in ferromagnetic bcc Fe

We perform a first principles calculation of the anomalous Hall effect in ferromagnetic bcc Fe. Our theory identifies an intrinsic contribution to the anomalous Hall conductivity and relates it to the k-space Berry phase of occupied Bloch states. This dc conductivity has the same origin as the well-known magneto-optical effect, and our result accounts for experimental measurement on Fe crystals with no adjustable parameters.     

Artificial electric field in fermi liquids

Based on the Keldysh formalism, we derive an effective Boltzmann equation for a quasiparticle constrained within a particular Fermi surface in an interacting Fermi liquid. This provides a many-body derivation of Berry curvatures in electron dynamics with spin-orbit coupling, which has received much attention in recent years in noninteracting models. As is well known, the Berry curvature in momentum space modifies na?ve band dynamics via an "artificial magnetic field" in momentum space. Our Fermi liquid formulation completes the reinvention of modified band dynamics by introducing in addition an artificial electric field, related to Berry curvature in frequency and momentum space. We show explicitly how the artificial electric field affects the renormalization factor and transverse conductivity of interacting U(1) Fermi liquids with nondegenerate bands.     

Quantum anomalous Hall effect and related topological electronic states

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that the intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time-reversal symmetry (TRS) broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as TIs and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.     

Optical injection and terahertz detection of the macroscopic Berry curvature

We propose an experimental scheme to probe the Berry curvature of solids. Our method is sensitive to arbitrary regions of the Brillouin zone and employs only basic optical and terahertz techniques to yield a background-free signal. Using semiconductor quantum wells as a prototypical system, we discuss how to inject Berry curvature macroscopically and probe it in a way that provides information about the underlying microscopic Berry curvature.     

Topological nature of the phonon Hall effect

We provide a topological understanding of the phonon Hall effect in dielectrics with Raman spin-phonon coupling. A general expression for phonon Hall conductivity is obtained in terms of the Berry curvature of band structures. We find a nonmonotonic behavior of phonon Hall conductivity as a function of the magnetic field. Moreover, we observe a phase transition in the phonon Hall effect, which corresponds to the sudden change of band topology, characterized by the altering of integer Chern numbers. This can be explained by touching and splitting of phonon bands.     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

New method for calculating the Berry connection in atom-molecule systems

In the mean-field theory of atom-molecule systems,where the bosonic atoms combine to form molecules,there is no usual U(1) symmetry,which presents an apparent hurdle for calculating the Berry connection in these systems.We develop a perturbation expansion method of Hannay’s angle suitable for calculating the Berry curvature in the atom-molecule systems.With this Berry curvature,the Berry connection can be computed naturally.We use a three-level atom-molecule system to illustrate our results.In particular,with this method,we compute the curvature for Hannay’s angle analytically,and compare it to the Berry curvature obtained with the second-quantized model of the same system.An excellent agreement is found,indicating the validity of our method.     

On the Onsager-Casimir reciprocal relations in a tilted Weyl semimetal

The Onsager-Casimir reciprocal relations are a fundamental symmetry of nonequilibrium statistical systems. Here we study an unusual chirality-dependent Hall effect in a tilted Weyl semimetal Co₃Sn₂S₂ with broken time-reversal symmetry. It is confirmed that the reciprocal relations are satisfied. Since two Berry curvature effects, an anomalous velocity and a chiral chemical potential, contribute to the observed Hall effect, the reciprocal relations suggest their intriguing connection.     

Mn_(3)Sn的高压物性研究

非共线三角晶格的反铁磁体Mn_(3)Sn,由于其动量空间中非零的贝里曲率而表现出反常霍尔效应.利用金刚石对顶砧研究压力对Mn_(3)Sn低温电输运性质和反常霍尔效应的影响.结果表明:Mn_(3)Sn在0~60GPa压力范围内保持金属导电行为;从非共线磁有序到螺旋磁有序的转变温度随压力增加先降低,在5.5GPa以上迅速升高,对应一个等结构电子拓扑转变;Mn_(3)Sn的反常霍尔效应在5.5GPa被完全抑制.