Effective field theory for the bulk-edge correspondence in a two-dimensional Z2 topological insulator with Rashba interactions

Abstract

We determine the effective field theory in (2+1)-dimensional space and time so that it captures the long-wavelength and low-energy limit of fermions hopping on a honeycomb lattice at half-filling when both dominant intrinsic and subdominant Rashba spin-orbit couplings are present. This effective field theory for a Z2 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 with spin conservation explicitly broken due to the Rashba spin-orbit coupling. Nonetheless, we find that the effective field theory has a Becchi-Rouet-Stora-Tyutin symmetry that allows us to construct the bulk-edge correspondence.