Temperature effects in the band structure of topological insulators

We study the effects of temperature on the band structure of the Bi$_2$Se$_3$ family of topological insulators using first-principles methods. Increasing temperature drives these materials towards the normal state, with similar contributions from thermal expansion and from electron-phonon coupling. The band gap changes with temperature reach $0.3$ eV at $600$ K, of similar size to the changes caused by electron correlation. Our results suggest that temperature-induced topological phase transitions should be observable near critical points of other external parameters.