Signatures of Rashba Spin-Orbit Interaction in Charge and Spin Properties of Quantum Hall Systems

Abstract

We study the local equilibrium properties of two-dimensional electron gases at high magnetic fields in the presence of random smooth electrostatic disorder, Rashba spin-orbit coupling, and the Zeeman interaction. Using a systematic magnetic length ($l_B$) expansion within a Green's function framework we derive quantum functionals for the local spin-resolved particle and current densities which can be useful for future studies combining disorder and mean-field electron-electron interaction in the quantum Hall regime. We point out that the spin polarization presents a peculiar spatial dependence which can be used to determine the strength of the Rashba coupling by local probes. The spatial structure of the current density, consisting of both compressible and incompressible contributions, also essentially reflects the effects of Rashba spin-orbit interaction on the energy spectrum. We show that in the semiclassical limit $l_B\to 0$ the local Hall conductivity remains, however, still quantized in units of $e^2/h$ for any finite strength of the spin-orbit interaction. In contrast, it becomes half-integer quantized when the latter is infinite, a situation which corresponds to a disordered topological insulator surface consisting of a single Dirac cone. Finally, we argue how to define at high magnetic fields a spin Hall conductivity related to a dissipationless angular momentum flow, which is characterized by a sequence of plateaus as a function of the inverse magnetic field (thus free of resonances).

18 pages + 4 figures, typos corrected and note added in Sec. VI, corresponds to the published version

References in corpus (13)

• Topological Insulators with Inversion Symmetry
• Unconventional Integer Quantum Hall effect in graphene
• On A Proper Definition of Spin Current
• Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field
• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry
• Theory of Edge States in Systems with Rashba Spin-Orbit Coupling
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• Quantum transport properties of two-dimensional electron gases under high magnetic fields
• Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime
• Particle-hole asymmetry on Hall conductivity of a topological insulator
• Edge Spin Current and Spin Polarization in Quantum Hall Regime
• Electron quantum dynamics in closed and open potentials at high magnetic fields: Quantization and lifetime effects unified by semicoherent states

Cited by in corpus (4)

• Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
• Chaotic cyclotron and Hall trajectories due to spin-orbit coupling
• Photoinduced electronic and spin properties of two-dimensional electron gases with Rashba spin-orbit coupling under perpendicular magnetic fields
• Probing the nodal structure of Landau level wave functions in real space