Influence of the Electron–Phonon Interaction on the Topological Phase Transition in BiTeI

The topological order of a material is intrinsically related to its bulk electronic structure. Topological phase transitions require that the bulk band gap vanishes. However, the gap is affected by atomic motion through electron–phonon interaction, even at T = 0 K. As a consequence, electron–phonon interaction can either promote or suppress topologically non-trivial phases. In this work, the temperature dependence of the pressure-induced topological phase transition in Rashba semiconductor BiTeI is investigated through first-principles methods. We first present an overview of electron–phonon interaction within the framework of density-functional perturbation theory (DFPT) and derive a qualitative argument to understand how it will affect the band gap for both typical semiconductors and topological insulators. Then, by tracking both the pressure and temperature dependence of the bulk band gap, we show how the Weyl semimetal and topological insulator phases of BiTeI evolve with temperature, thus providing a guideline for experimental detection.