Monolayer 1T’-${\mathrm{WTe}}_2$ has been the first two-dimensional crystal where a quantum spin Hall phase was experimentally observed. In addition, recent experiments and theoretical modeling reported the presence of a robust excitonic insulating phase. While first-principles calculations with hybrid functionals and several measurements at low temperatures suggest the presence of a band gap of the order of 50 meV, experiments could confirm the presence of the helical edge states only up to 100 K. Here, we study with first-principle simulations the temperature effects on the electronic structure of monolayer 1T’-${\mathrm{WTe}}_2$ and consider the contributions of both thermal expansion and electron-phonon coupling. First, we show that thermal expansion is weak but tends to increase the indirect band gap. Then, we calculate the effect of electron-phonon coupling on the band structure with nonperturbative methods and observe a small reduction of the band inversion with increasing temperature. Notably, the topological phase and the presence of a finite gap are found to be particularly robust to thermal effects up to and above room temperature.

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• Electronic structure
• First-principles calculations
• Spin-orbit coupling
• Temperature
• Thermal expansion
• Topological insulators
• 2-dimensional systems
• Topological materials
• Density functional theory