Spin-Orbit gauge and quantum spin Hall effect

TL;DR

This paper demonstrates that the quantum spin Hall effect can be understood through a non-Abelian spin-orbit gauge field framework, revealing a Landau level structure with spin-dependent chiralities.

Contribution

It introduces a novel gauge-theoretic approach to analyze the quantum spin Hall effect using non-Abelian spin-orbit gauge fields.

Findings

Quantum levels with opposite chirality for up and down spins.

Reformulation of the Hamiltonian as a Landau level problem.

Relation between Rashba and Dresselhaus coupling parameters.

Abstract

We have shown that the non-Abelian spin-orbit gauge field strength of the Rashba and Dresselhaus interactions, when split into two Abelian field strengths, the Hamiltonian of the system can be re-expressed as a Landau level problem with a particular relation between the two coupling parameters. The quantum levels are created with up and down spins with opposite chirality and leads to the quantum spin Hall effect.