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 ${\mathbb{Z}}_2^{}$ topological insulator (the Kane-Mele model at vanishing uniform and staggered chemical potentials) is a perturbation around a double Chern-Simons theory, with the $\text{U}\left(1\right)$ 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.

• Received 10 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.115144