Thermal topological phase transition in SnTe from \emph{ab-initio} calculations

Abstract

One of the key issues in the physics of topological insulators is whether the topologically non-trivial properties survive at finite temperatures and, if yes, whether they disappear only at the temperature of topological gap closing. Here we study this problem, using quantum fidelity as a measure, by means of ab-initio methods supplemented by an effective dissipative theory built on the top of the abinitio electron and phonon band structures. We reveal the presence of a characteristic temperature that can be associated with a change of curvature of the conduction band. The transition is not present in a purely electronic system but it appears once we invoke coupling with a dissipative bosonic bath. Features in the dependence with temperature of the fidelity susceptibility can be related to changes in the band curvature, but signatures of a topological phase transition appear in the fidelity only though the non-adiabatic coupling with soft phonons. Our argument is valid in valley topological insulators, but in principle can be generalized to the broader class of topological insulators which host any symmetry-breaking boson.