Phonon-induced topological transitions and crossovers in Dirac materials

We show that electron-phonon interactions can alter the topological properties of Dirac insulators and semimetals, both at zero and nonzero temperature. Contrary to the common belief that increasing temperature always destabilizes topological phases, our results highlight instances in which phonons may lead to the appearance of topological surface states above a crossover temperature in a material that has a topologically trivial ground state.