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

TL;DR

This study investigates how topological properties in SnTe persist at finite temperatures, revealing a characteristic temperature where coherence is lost due to phonon coupling, using -initio methods and quantum fidelity.

Contribution

It demonstrates the existence of a temperature-induced topological transition in SnTe caused by phonon interactions, extending understanding of topological phase stability at finite temperatures.

Findings

Topological coherence in SnTe diminishes below the gap-closing temperature.

Coupling with soft phonons triggers the topological phase transition.

Fidelity susceptibility reveals temperature-dependent topological changes.

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 so, 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 \emph{ab-initio} methods supplemented by an effective dissipative theory built on the top of the \emph{ab-initio} electron and phonon band structures. In the case of SnTe, the prototypical crystal topological insulator, we reveal the presence of a characteristic temperature, much lower than the gap-closing one, that marks a loss of coherence of the topological state. 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 for valley topological insulators, but in principle can be generalized to the broader class of topological insulators which host any symmetry-breaking boson.