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

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.

Five pages, three figures; ReVTeX. Supplementary material

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• Intertwined Topological Phases induced by Emergent Symmetry Protection
• Dirac parameters and topological phase diagram of Pb1-xSnxSe from magneto-spectroscopy
• Optical conductivity of an interacting Weyl liquid in the collisionless regime
• Avoided level crossing at the magnetic field induced topological phase transition due to spin-orbital mixing
• Pressure and Inversion Symmetry Breaking Field Driven First Order Phase Transition and Formation of Dirac Circle in Perovskites
• Unconventional topological transitions in a self-organized magnetic ladder