# Excitonic gap generation in thin-film topological insulators

## TL;DR

This paper investigates how excitonic gaps form in thin-film topological insulators by analyzing the effects of strong interactions and dynamical mass generation, revealing a critical flavor number for symmetry breaking.

## Contribution

It introduces a 2+1D effective gauge theory derived from 3+1D QED to study excitonic gap formation, highlighting the importance of full dynamical interactions.

## Key findings

- Dynamical mass generation occurs for fermion flavors below N_c≈11.8.
- Time-reversal symmetry is preserved during excitonic gap formation.
- Full dynamical interactions significantly alter the critical flavor number.

## Abstract

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 $N_{c}\approx 11.8$. Our results show that the inclusion of the full dynamical interaction strongly modifies the critical number of flavors for the occurrence of exciton condensation, and therefore, cannot be neglected.