Spin Hall effect (SHE) has been discussed in the context of Kubo formulation, geometric physics, spin orbit force, and numerous semi-classical treatments. It can be confusing if the different pictures have partial or overlapping claims of contribution to the SHE. In this article, we present a gauge-theoretic, time-momentum elucidation, which provides a general SHE equation of motion, that unifies under one theoretical framework, all contributions of SHE conductivity due to the kinetic, the spin orbit force (Yang-Mills), and the geometric (Murakami-Fujita) effects. Our work puts right an ambiguity surrounding previously partial treatments involving the Kubo, semiclassical, Berry curvatures, or the spin orbit force. The full treatment shows the Rashba 2DEG SHE conductivity to be +e/8π instead of -e/8π , and Rashba heavy hole +9e/8π instead of -9e/8π .
We show the inconsistency of the argument linking the integral quantum Hall effect to gauge invariance. The inconsistency mainly consists of equating gauge and real vector potential transformations for a particular system geometry. Correct handling gives no Hall quantization.
We show that the gauge symmetry of the nonequilibrium quantum transport of Chern insulator in a uniform electric field is governed by the Wilson line of parallel transport operator coupled with the dynamical translation operator. This is dictated by the minimal coupling of derivatives with gauge fields in U (1) gauge theory. This parallel transport symmetry consideration leads to the integer quantum Hall effect in electrical conductivity obtained to first-order gradient expansion of the nonequilibrium quantum transport equations.
Artificial Gauge Field and Quantum Spin Hall States in a Conventional Two-dimensional Electron Gas
在Born-Oppemheimer近似下，我们将自旋轨道耦合系统中的总电子哈密顿量分解为慢轨道运动和快带间跃迁过程。我们发现，快速运动诱导规范场慢轨道运动，垂直于电子动量，诱导拓扑相。从这个一般设计原理出发，我们提出了一种在抛物线渐变GaAs/In $_{x}$ Ga $_{1-x}$ As/GaAs量子阱中产生人工规范场和拓扑相的理论。通过调整反点晶格的刻蚀深度和周期，叠加势引起的能带折叠导致了能带的形成和相邻子带之间的能带反转。子带间的自旋轨道相互作用打开了相当大的非平凡的迷你间隙，并导致许多对螺旋边缘状态在这些间隙。
Any departure from graphene's flatness leads to the emergence of artificial gauge fields that act on the motion of the Dirac fermions through an associated pseudomagnetic field. Here, we demonstrate the tunability of strong gauge fields in non-local experiments using a large planar graphene sheet that conforms to the deformation of a piezoelectric layer by a surface acoustic wave. The acoustic wave induces a longitudinal and a giant synthetic Hall voltage in the absence of external magnetic fields. The superposition of a synthetic Hall potential and a conventional Hall voltage can annihilate t…
Comments on "Gauge Theory of Composite Fermions:Particle-Flux Separation in Quantum Hall Systems" by I. Ichinose and Tetsuo Matsui, cond-mat/0210142 v2, 7 Feb. 2003
Vortex magnetic structure in artificial honeycomb lattice provides a unique platform to explore emergent properties due to the additional Berry phase curvature imparted by chiral magnetization to circulating electrons via direct interaction. We argue that while the perpendicularly-aligned magnetic component leads to the quantized flux of monopole at the center of the Berry sphere, the in-plane vortex circulation of magnetization gives rise to unexpected non-trivial topological Berry phase due to the gauge field transformation. The unprecedented effect signifies the importance of vector potenti…
For a particle confined to the two-dimensional helical surface embedded in four-dimensional (4D) Euclidean space, the effective Hamiltonian is deduced in the thin-layer quantization formalism. We find that the gauge structure of the effective dynamics is determined by torsion, which plays the role of U(1) gauge potential, and find that the topological structure of associated states is defined by orbital spin which originates from 4D space. Strikingly, the response to torsion contributes a quantum Hall effect, and the response to the deformation of torsion contributes Hall viscosity that is per…
The electronic behavior in graphene under arbitrary uniaxial deformations, such as foldings or flexural fields is studied by including in the Dirac equation pseudoelectromagnetic fields. General foldings are thus studied by showing that uniaxial deformations can be considered pseudomagnetic fields in the Coulomb gauge norm. This allows to give an expression for the Fermi (zero) energy modes wavefunctions. For random deformations, contact is made with previous works on the quantum Hall effect under random magnetic fields, showing that the density of states has a power law behavior and that the …
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…
