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A topological phase transition from a trivial insulator to a $\mathbb{Z}_2$topological insulator requires the bulk band gap to vanish. In the case ofnoncentrosymmetric materials, these phases are separated by a gapless Weylsemimetal phase. However, at finite temperature, the gap is affected by atomicmotion, through electron-phonon interaction, and by thermal expansion of thelattice. As a consequence, the phase space of topologically nontrivial phasesis affected by temperature. In this paper, the pressure and temperaturedependence of the indirect band gap of BiTeI is investigated from firstprinciples. We evaluate the contribution from both electron-phonon interactionand thermal expansion, and show that their combined effect drives thetopological phase transition towards higher pressures with increasingtemperature. Notably, we find that the sensitivity of both band extrema topressure and topology for electron-phonon interaction differs significantlyaccording to their leading orbital character. Our results indicate that theWeyl semimetal phase width is increased by temperature, having almost doubledby 100 K when compared to the static lattice results. Our findings thus providea guideline for experimental detection of the nontrivial phases of BiTeI andillustrate how the phase space of the Weyl semimetal phase innoncentrosymmetric materials can be significantly affected by temperature.

Temperature dependence of the topological phase transition of BiTeI from first principles