Four-Step Evolution of Spin-Hall Conductance: Tight-Binding Electrons with Rashba Coupling in a Magnetic Field

TL;DR

This paper investigates how Rashba spin-orbit coupling influences spin-Hall and charge-Hall conductances in a lattice system under magnetic field, revealing a four-step evolution with size-dependent resonances and topological changes.

Contribution

It uncovers a four-step evolution pattern of conductances with increasing Rashba SOC, including sign changes and quantum jumps, linked to topological and edge state properties.

Findings

SHC shows size-dependent resonances and sign changes at critical SOC values.

CHC exhibits three quantized jumps at specific SOC strengths.

The four-step evolution is robust against weak disorder.

Abstract

An intriguing magneto-transport property is demonstrated by tight-binding lattice electrons with Rashba spin-orbit coupling (SOC) in a magnetic field. With the flux strength $\phi={2\pi/N}$ ($N$ is an integer) and the Zeeman splitting fixed, when increasing the Rashba SOC $\lambda$, the spin-Hall and charge-Hall conductances (SHC and CHC) undergo four-step evolutions: the SHC shows size-dependent resonances and jumps at three critical $\lambda_{c}$'s, and changes its sign at $\lambda_{c1}$ and $\lambda_{c3}$; while the CHC exhibits three quantum jumps by $-Ne^2/h$, $+2Ne^2/h$ and $-Ne^2/h$. Such four-step evolutions are also reflected in topological characters and spin polarizations of edge states of a cylindrical system, and are robust against weak disorder.