An Extended Extrinsic Mechanism for Anomalous Hall Effect

The extrinsic mechanism for anomalous Hall effect in ferromagnets is extended to include the contributions both from spin-orbit-dependent impurity scattering and from the spin-orbit coupling induced by external electric fields. The results obtained suggest that, within the framework of the extrinsic mechanisms, the anomalous Hall current in a ferromagnet may also contain asubstantial amount of dissipationless contribution independent of impurity scattering. After the contribution from the spin-orbit coupling induced by external electric fields is included, the total anomalous Hall conductivity is about two times larger than that due to spin-orbit dependent impurity scatterings.     

Anomalous Hall Effect in Spin-Polarized Two-Dimensional Hole Gas with Cubic-Rashbsa Spin-Orbit Interaction

Based on the Kubo formalism, the anomalous Hall effect in a magnetic two-dimensional hole gas with cubic-Rashba spin-orbit coupling is studied in the presence of δ-function scattering potential. When the weak, short-ranged disorder scattering is considered in the Born approximation, we find that the self-energy becomes diagonal in the helicity basis and its value is independent of the wave number, and the vertex correction to the anomalous Hall conductivity due to impurity scattering vanishes when both subbandsare occupied. That is to say, the anomalous Hall effect is not vanishing or influenced by the vertex correction for two-dimensional heavy-hole system, which is in sharp contrast to the case of linear-Rashba spin-orbit coupling in the electron band when the short-range disorder scattering is considered and the extrinsic mechanism as well as the effect of external electric field on the SO interaction are ignored.     

An Extended Extrinsic Mechanism for Anomalous Hall Effect

The extrinsic mechanism for anomalous Hall effect in ferromagnets is extended to include the contributions both from spin-orbit-dependent impurity scattering and from the spin-orbit coupling induced by external electric fields. The results obtained suggest that, within the framework of the extrinsic mechanisms, the anomalous Hall current in a ferromagnet may also contain a substantial amount of dissipationless contribution independent of impurity scattering. After the contribution from the spin-orbit coupling induced by external electric fields is included, the total anomalous Hall conductivity is about two times larger than that due to soin-orbit dependent impurity scatterings.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Spin Hall and spin Nernst effects in graphene with intrinsic and Rashba spin-orbit interactions

The spin Hall and spin Nernst effects in graphene are studied based on Green’s function formalism.We calculate intrinsic contributions to spin Hall and spin Nernst conductivities in the Kane-Mele model with various structures.When both intrinsic and Rashba spin-orbit interactions are present,their interplay leads to some characteristics of the dependence of spin Hall and spin Nernst conductivities on the Fermi level.When the Rashba spin-orbit interaction is smaller than intrinsic spin-orbit coupling,a weak kink in the conductance appears.The kink disappears and a divergence appears when the Rashba spin-orbit interaction enhances.When the Rashba spin-orbit interaction approaches and is stronger than intrinsic spin-orbit coupling,the divergence becomes more obvious.     

Absence of skew scattering in two-dimensional systems: testing the origins of the anomalous Hall effect

We study the anomalous Hall conductivity in spin-polarized, asymmetrically confined two-dimensional electron and hole systems, taking into account the intrinsic, side-jump, and skew-scattering contributions to the transport. We find that the skew scattering, principally responsible for the extrinsic contribution to the anomalous Hall effect, vanishes for the two-dimensional electron system if both chiral Rashba subbands are partially occupied, and vanishes always for the two-dimensional hole gas studied here, regardless of the band filling. Our prediction can be tested with the proposed coplanar two-dimensional electron-hole gas device and can be used as a benchmark to understand the crossover from the intrinsic to the extrinsic anomalous Hall effect.     

半导体中自旋轨道耦合及自旋霍尔效应

本文主要评述和介绍半导体微结构中自旋轨道耦合的研究和最近的研究进展。我们细致地讨论了半导体微结构中自旋轨道耦合的物理起源和窄带隙半导体量子阱中的自旋霍尔效应。我们发现目前国际上广泛采用的线性Rashba模型在较大的电子平面波矢处失效:即自旋轨道耦合导致的能带自旋劈裂不再随电子波矢的增加而增加,而是开始下降,即出现强烈的非线性行为。这种非线性的行为起源于导带和价带间耦合的减弱。这种非线性行为还会导致电子的D’yakonov-Perel’自旋弛豫速率在较高能量处下降,与线性模型的结果完全相反。在此基础上,我们构造统一描述电子和空穴自旋霍尔效应的理论框架。我们的方法可以非微扰地计入自旋轨道耦合对本征自旋霍尔效应的影响。我们将此方法应用于强自旋轨道耦合的情形,即窄带隙CdHgTe/CdTe半导体量子阱。我们发现调节外电场或量子阱的阱宽可以作为导致量子相变和本征自旋霍尔效应的开关。我们的工作可能会为区别和实验验证本征自旋霍尔效应提供物理基础。     

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.     

Quantum anomalous Hall effect and giant Rashba spin-orbit splitting in graphene system co-doped with boron and 5d transition-metal atoms

Quantum anomalous Hall effect (QAHE) is a fundamental quantum transport phenomenon in condensed matter physics. Until now, the QAHE has only been experimentally realized for Cr/V-doped (Bi, Sb)₂Te₃ but at an extremely low observational temperature, thereby limiting its potential application in dissipationless quantum electronics. By employing first-principles calculations, we study the electronic structures of graphene co-doped with 5d transition metal and boron atoms based on a compensated n–p co-doping scheme. Our findings are as follows: i) The electrostatic attraction between the n- and p-type dopants effectively enhances the adsorption of metal adatoms and suppresses their undesirable clustering. ii) Hf-B and Os-B co-doped graphene systems can establish long-range ferromagnetic order and open larger nontrivial band gaps because of the stronger spin-orbit coupling with the non-vanishing Berry curvatures to host the high-temperature QAHE. iii) The calculated Rashba splitting energies in Re–B and Pt–B co-doped graphene systems can reach up to 158 and 85 meV, respectively, which are several orders of magnitude higher than the reported intrinsic spin-orbit coupling strength.     

Dissipationless spin-Hall current contribution in the extrinsic spin-Hall effect

This paper shows that a substantial amount of dissipationless spin-Hall current contribution may exist in the extrinsic spin-Hall effect, which originates from the spin-orbit coupling induced by the applied external electric field itself that drives the extrinsic spin-Hall effect in a nonmagnetic semiconductor (or metal). By assuming that the impurity density is in a moderate range such that the total scattering potential due to all randomly distributed impurities is a smooth function of the space coordinate, it is shown that this dissipationless contribution shall be of the same orders of magnitude as the usual extrinsic contribution from spin-orbit dependent impurity scatterings (or may even be larger than the latter one). The theoretical results obtained are in good agreement with recent relevant experimental results.     

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).     

Tunable valley filter efficiency by spin–orbit coupling in silicene nanoconstrictions

Valley filter is a promising device for producing valley polarized current in graphene-like two-dimensional honeycomb lattice materials. The relatively large spin–orbit coupling in silicene contributes to remarkable quantum spin Hall effect, which leads to distinctive valley-dependent transport properties compared with intrinsic graphene. In this paper,quantized conductance and valley polarization in silicene nanoconstrictions are theoretically investigated in quantum spinHall insulator phase. Nearly perfect valley filter effect is found by aligning the gate voltage in the central constriction region. However, the valley polarization plateaus are shifted with the increase of spin–orbit coupling strength, accompanied by smooth variation of polarization reversal. Our findings provide new strategies to control the valley polarization in valleytronic devices.     

Chaotic Cyclotron and Hall Trajectories Due to Spin-Orbit Coupling

It is demonstrated that the synergistic effect of a gauge field, Rashba spin-orbit coupling (SOC), and Zeeman splitting can generate chaotic cyclotron and Hall trajectories of particles. The physical origin of the chaotic behavior is that the SOC produces a spin-dependent (so-called anomalous) contribution to the particle velocity and the presence of Zeeman field reduces the number of integrals of motion. By using analytical and numerical arguments, the conditions of chaos emergence are studied and the dynamics both in the regular and chaotic regimes is reported. The critical dependence of the dynamic patterns (such as the chaotic regime onset) on small variations in the initial conditions and problem parameters, that is the SOC and/or Zeeman constants, is observed. The transition to chaotic regime is further verified by the analysis of phase portraits as well as Lyapunov exponents spectrum. The considered chaotic behavior can occur in solid state systems, weakly relativistic plasmas, and cold atomic gases with synthetic gauge fields and spin-related couplings.     

Vertex corrections to the anomalous Hall effect in spin-polarized two-dimensional electron gases with a Rashba spin-orbit interaction

We study the effect of disorder on the intrinsic anomalous Hall conductivity in a magnetic two-dimensional electron gas with a Rashba-type spin-orbit interaction. We find that anomalous Hall conductivity vanishes unless the lifetime is spin-dependent, similar to the spin Hall conductivity in the nonmagnetic system. In addition, we find that the spin Hall conductivity does not vanish in the presence of magnetic scatterers.     

Current-induced spin polarization in a spin-polarized two-dimensional electron gas with spin-orbit coupling

The current-induced spin polarization (CISP) is investigated in a combined Rashba-Dresselhaus spin-orbit-coupled two-dimensional electron gas, subjected to a homogeneous out-of-plane magnetization. It is found that, in addition to the usual collision-related in-plane parts of CISP, there are two impurity-density-free contributions, arising from intrinsic and disorder-mediated mechanisms. The intrinsic parts of spin polarization are related to the Berry curvature, analogous with the anomalous and spin Hall effects. For short-range collision, the disorder-mediated spin polarizations completely cancel the intrinsic ones and the total in-plane components of CISP equal those for systems without magnetization. However, for remote disorders, this cancellation does not occur and the total in-plane components of CISP strongly depend on the spin-orbit interaction coefficients and magnetization for both pure Rashba and combined Rashba-Dresselhaus models.     

Intrinsic versus extrinsic anomalous Hall effect in ferromagnets

A unified theory of the anomalous Hall effect (AHE) is presented for multiband ferromagnetic metals with dilute impurities. In the clean limit, the AHE is mostly due to extrinsic skew scattering. When the Fermi level is located around anticrossing of band dispersions split by spin-orbit interaction, the intrinsic AHE to be calculated ab initio is resonantly enhanced by its nonperturbative nature, revealing the extrinsic-to-intrinsic crossover which occurs when the relaxation rate is comparable to the spin-orbit coupling.     

Anomalous Hall effect of facing-target sputtered ferrimagnetic Mn4N epitaxial films with perpendicular magnetic anisotropy

Epitaxial Mn$_{4}$N films with different thicknesses were fabricated by facing-target reactive sputtering and their anomalous Hall effect (AHE) is investigated systematically. The Hall resistivity shows a reversed magnetic hysteresis loop with the magnetic field. The magnitude of the anomalous Hall resistivity sharply decreases with decreasing temperature from 300 K to 150 K. The AHE scaling law in Mn$_{4}$N films is influenced by the temperature-dependent magnetization, carrier concentration and interfacial scattering. Different scaling laws are used to distinguish the various contributions of AHE mechanisms. The scaling exponent $\gamma > 2$ for the conventional scaling in Mn$_{4}$N films could be attributed to the residual resistivity $\rho_{xx0}$. The longitudinal conductivity $\sigma_{xx}$ falls into the dirty regime. The scaling of $\rho_{\rm AH}=\alpha \rho_{xx0} +b\rho_{xx}^{n}$ is used to separate out the temperature-independent $\rho_{xx0}$ from extrinsic contribution. Moreover, the relationship between $\rho_{\rm AH}$ and $\rho_{xx}$ is fitted by the proper scaling to clarify the contributions from extrinsic and intrinsic mechanisms of AHE, which demonstrates that the dominant mechanism of AHE in the Mn$_{4}$N films can be ascribed to the competition between skew scattering, side jump and the intrinsic mechanisms.     

Asymmetric Fraunhofer pattern in Josephson junctions from heterodimensional superlattice V5S8

Introduction of spin-orbit coupling (SOC) in a Josephson junction (JJ) gives rise to unusual Josephson effects. We investigate JJs based on a newly discovered heterodimensional superlattice V₅S₈ with a special form of SOC. The unique homointerface of our JJs enables elimination of extrinsic effects due to interfaces and disorder. We observe asymmetric Fraunhofer patterns with respect to both the perpendicular magnetic field and the current. The asymmetry is influenced by an in-plane magnetic field. Analysis of the pattern points to a nontrivial spatial distribution of the Josephson current that is intrinsic to the SOC in V₅S₈.     

Finite size effects on helical edge states in HgTe quantum wells with the spin orbit coupling due to bulk- and structure-inversion asymmetries

There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.     

Spin texturing in quantum wires with Rashba and Dresselhaus spin–orbit interactions and in-plane magnetic field

In this work, we investigate the effects of interplay of spin–orbit interaction and in-plane magnetic fields on the electronic structure and spin texturing of parabolically confined quantum wire. Numerical results reveal that the competing effects between Rashba and Dresselhaus spin–orbit interactions and the external magnetic field lead to a complicated energy spectrum. We find that the spin texturing owing to the coupling between subbands can be modified by the strength of spin–orbit couplings as well as the magnitude and the orientation angle of the external magnetic field.