Excitonic gap generation in thin-film topological insulators

In this work, we analyze the excitonic gap generation in the strong-coupling regime of thin films of three-dimensional time-reversal-invariant topological insulators. We start by writing down the effective gauge theory in 2 + 1-dimensions from the projection of the 3 + 1-dimensional quantum electrodynamics. Within this method, we obtain a short-range interaction, which has the form of a Thirring-like term, and a long-range one. The interaction between the two surface states of the material induces an excitonic gap. By using the large-N approximation in the strong-coupling limit, we find that there is a dynamical mass generation for the excitonic states that preserves time-reversal symmetry and is related to the dynamical chiral-symmetry breaking of our model. This symmetry breaking occurs only for values of the fermion-flavor number smaller than N-c approximate to 11.8. Our results show that the inclusion of full dynamical interaction strongly modifies the critical number of flavors for the occurrence of exciton condensation, and therefore cannot be neglected.