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

It is commonly assumed that the transition between topologically distinct non-interacting gapped phases of fermions is necessarily accompanied by the closing of the gap as long as the symmetries of the Hamiltonian 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 [1]. We demonstrate this by calculating the free energy of 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 phase transition in a family of topological crystalline insulators. [1] V. Juricic, D. S. L. Abergel, and A. V. Balatsky, arXiv: 1608.07819.