We study the effects of temperature on the topological nature of ${\mathrm{ZrTe}}_5$, which sits near the phase boundary between strong and weak topological insulating orders. Using first-principles calculations, we show that the band gap and the topological indices of ${\mathrm{ZrTe}}_5$ are extremely sensitive to thermal expansion and that the electron-phonon interaction accounts for more than a third of the total temperature-dependent effects in ${\mathrm{ZrTe}}_5$. We find that the temperature dependence of the band gap has an opposite sign in the strong and weak topological insulator phases. Based on this insight, we propose a robust and unambiguous method to determine the topological nature of any given sample of ${\mathrm{ZrTe}}_5$: If the band gap decreases with temperature it is a strong topological insulator, and if it increases with temperature it is a weak topological insulator. An analogous strategy is expected to be generally applicable to other materials and to become particularly important in the vicinity of topological phase boundaries where other methods provide ambiguous results.

• Received 20 September 2019

DOI:https://doi.org/10.1103/PhysRevResearch.1.033181

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Published by the American Physical Society