Effective field theory for the bulk-edge correspondence in a two-dimensional Z_2 topological insulator with Rashba interactions

TL;DR

This paper develops an effective field theory for a Z_2 topological insulator with Rashba interactions, capturing low-energy physics and establishing the bulk-edge correspondence despite broken spin conservation.

Contribution

It introduces a perturbative effective field theory around a double Chern-Simons model that accounts for Rashba spin-orbit coupling effects in a honeycomb lattice topological insulator.

Findings

Effective field theory describes low-energy limit of the Kane-Mele model with Rashba interactions.

Bulk-edge correspondence is established using BRST symmetry despite broken spin conservation.

The theory extends understanding of topological insulators with spin-orbit couplings.

Abstract

We determine the effective field theory in (2+1)-dimensional space and time that captures the long wave length and low-energy limit of fermions hopping on a honeycomb lattice at half-filling when both a dominant intrinsic and subdominant Rashba spin-orbit couplings are present. This effective field theory for a Z_2 topological insulator (the Kane-Mele model at vanishing uniform and staggered chemical potentials) is a perturbation around a double Chern-Simons theory, with the U(1) gauge invariance associated to spin conservation explicitly broken due to the Rashba spin orbit coupling. Nonetheless, we find that the effective field theory has a BRST symmetry that allows us to construct the bulk-edge correspondence.