The Effective field theory of 2+1 dimensional topological insulator in the presence of Rashba spin-orbit interaction

TL;DR

This paper develops an effective field theory for a 2+1D topological insulator with Rashba spin-orbit interaction, linking topological invariants to observable spin Hall effects.

Contribution

It derives the effective action incorporating Rashba interaction and relates Chern-Simons coefficients to the first Chern number using Hamiltonian methods.

Findings

Chern-Simons coefficients are given by the first Chern number.

The effective theory supports the spin Hall phase with near-quantized spin Hall conductivity.

The approach confirms the topological nature of the spin Hall effect in this system.

Abstract

2+1 dimensional topological insulator described by the Kane-Mele model in the presence of Rashba spin-orbit interaction is considered. The effective action of the external fields coupled to electromagnetic and spin degrees of freedom is accomplished within this model. The Hamiltonian methods are adopted to provide the coefficients appearing in the action. It is demonstrated straightforwardly that the coefficients of the Chern-Simons terms are given by the first Chern number attained through the related non-Abelian Berry gauge field. The effective theory which we obtain is in accord with the existence of the spin Hall phase where the value of the spin Hall conductivity is very close to the quantized one.