We analytically calculate the intrinsic spin-Hall conductivity (ISHC) ($σ^z_{xy}$ and $σ^z_{yx}$) in a clean, two-dimensional system with generic k-linear spin-orbit interaction. The coefficients of the product of the momentum and spin components form a spin-orbit matrix $\widetildeβ$. We find that the determinant of the spin-orbit matrix $\detbeta$ describes the effective coupling of the spin $s_z$ and orbital motion $L_z$. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical ($σ^z_{xy}\neq-σ^z_{yx}$), and it is governed by the asymmetric response function $\Deltabeta$, which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than $e/8π$, but has an upper bound value of $e/4π$. We will that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature at the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that $\detbeta$ determines the field strength of the SU(2) non-Abelian gauge field.
The intrinsic spin Hall effect plays an important role in spintronics applications, such as spin-orbit torque-based memory. The bulk space group symmetry determines the form of the bulk spin current conductivity tensor. This paper considers materials for which the local point group symmetry of individual atoms is lower than the global (bulk) symmetry. This enables a position-dependent spin current response, with additional tensor components allowed relative to the bulk response. We present a general method to compute the position-dependent intrinsic spin Hall conductivity, with similar computa…
It is generally believed that conductivity platform can only exist in insulator with topological nontrivial bulk occupied states. Such rule exhibits in two dimensional quantum (anomalous) Hall effect, quantum spin Hall effect, and three dimensional topological insulator. In this letter, we propose a spin Hall conductivity (SHC) platform in a kind of three dimensional metallic materials with triply degenerate points around the Fermi level. With the help of a four bands \textbf{k}${\cdot}$\textbf{p} model, we prove that SHC platform can form between $|\frac{3}{2},\pm\frac{3}{2}\rangle$ and $|\fr…
We determine the Hall conductivity of light-driven graphene, with specific focus on its frequency dependence, and compare it to the static effective approximation, based on Floquet states. This approximation gives the Haldane model as the effective model for light-driven graphene, with a gapped spectrum and a quantized Hall conductivity of $-2e^2/h$. We simulate both the light-driven and the effective model, and explicitly include the dissipative environment in our simulations. We investigate the effect of different driving regimes and dissipation strengths on the Hall conductivity in graphene…
Maximizing the spin-orbit torque efficiency of Pt/Ti multilayers by optimization of the tradeoff between the intrinsic spin Hall conductivity and carrier lifetime
Parity anomaly is a quantum mechanical effect that the parity symmetry in a two-dimensional classical action is failed to be restored in any regularization of the full quantum theory and is characterized by a half-quantized Hall conductivity. Here we propose a scheme to explore the experimental signature from parity anomaly in the measurement of optical Hall conductivity, in which the optical Hall conductivity is nearly half quantized for a proper range of frequency. The behaviors of optical Hall conductivity are studied for several models, which reveal the appearance of half-quantized Hall co…
The spin Hall conductivity is usually calculated for periodic solids, while the knowledge of local contributions from inhomogeneous regions like interfaces or surfaces would be desirable. In this work we derive a local expression for the spin Hall conductivity of two-dimensional systems in analogy to the local anomalous Hall conductivity discussed recently. Our approach is applicable to heterogeneous fully bounded systems and nanoribbons with both open and periodic boundary conditions.
Gaussian-Bond Hall Viscosity and Nonlocal Hall Response of a Sampled Landau Level
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论物理研究所）；Institute of Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Department of Physics, Nagoya University（名古屋大学物理学系）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
Quantum corrections to the conductivity and Hall coefficient of a 2D electron gas in a dirty AlGaAs/GaAs/AlGaAs quantum well: transition from diffusive to ballistic regime
本文报道了AlGaAs/GaAs/AlGaAs量子阱中低迁移率、高密度二维电子气在宽温度范围（1.5 K - 110 K）内纵向电导率和霍尔系数的量子修正实验研究。这个温度范围涵盖了我们的样品的扩散和弹道相互作用制度。因此，可以研究纵向电导率和霍尔效应的交叉区域。
Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field
在恒定磁场存在下的量子霍尔电导率可以表示为拓扑TKNN不变量。最近，有人提出将此表达式推广到非均匀磁场中. \rev{The quantum Hall conductivity is represented as the topological invariant in phase space in terms of the Wigner transformed two - point Green function.}这个表达式是在忽略电子间相互作用的情况下导出的.可以很自然地假设，在存在相互作用的情况下，霍尔电导率仍然由相同的表达式给出，其中非相互作用的格林函数被完全的两点格林函数\rev{ including the interaction contributions}代替。我们在相当一般的$2+1$ D紧束缚模型的框架内，用普通微扰理论证明了这个猜想。
Anomalous Hall effect in very clean samples (high conductivity regime) is studied using a two-dimensional network model. We find that the off-diagonal conductivity comprises two parts: one which reflects the bulk properties as obtained by the Kubo formula and another which is sensitive to boundary conditions imposed on the network. The latter scales with the system width in the ideal case and for real-world samples, it will depend on the coherence length. It provides an alternative interpretation of the observed behaviour in the clean limit which is otherwise attributed to the skew scattering.…
