First-order quantum phase transition in three-dimensional topological band insulators

TL;DR

This paper reveals that three-dimensional topological insulators can undergo a first-order quantum phase transition without closing the band gap, challenging the common assumption that gap closing is necessary for topological phase changes.

Contribution

It demonstrates that a first-order topological phase transition can occur without gap closing in 3D topological insulators, supported by calculations on the Bernevig-Hughes-Zhang model.

Findings

First-order phase transition without gap closing in 3D topological insulators

Re-entrant topological phase transition predicted

Connection to recent experimental observations

Abstract

Topological states of matter are characterized by global topological invariants which change their value across a topological quantum phase transition. It is commonly assumed that the transition between topologically distinct noninteracting gapped phases of fermions is necessarily accompanied by the closing of the band gap as long as the symmetries of the system are maintained. We show that such a quantum phase transition is possible without closing the gap in the case of a three-dimensional topological band insulator. We demonstrate this by calculating the free energy of the minimal model for a topological insulator, the Bernevig-Hughes-Zhang model, and show that as the band curvature continuously varies, a jump between the band gap minima corresponding to the topologically trivial and nontrivial insulators occurs. Therefore, this first order phase transition is a generic feature of three-dimensional topological band insulators. For a certain parameter range we predict a re-entrant topological phase transition. We discuss our findings in connection with the recent experimental observation of a discontinuous topological phase transition in a family of topological crystalline insulators.