Temperature effects on the electronic band structure of PbTe from first principles

We present a fully ab-initio calculation of the temperature dependence of the electronic band structure of PbTe [1]. We address two main features relevant for its thermoelectric figure of merit: the temperature variations of the direct gap and the difference in energies of the two topmost valence band maxima located at L and Σ [2]. We account for the energy shift of the electronic states due to thermal expansion, as well as electron-phonon interaction computed using the Allen-Heine-Cardona formalism within density functional perturbation theory [3]. We capture the increase of the direct gap with temperature in very good agreement with experiment. We also predict that the valence band maxima at L and Σ become aligned at ~ 620 K. We find that both thermal expansion and electron-phonon interaction have a considerable effect on these temperature variations. The electron-phonon induced renormalization of the direct gap and the two topmost valence band maxima is produced mostly by high-frequency optical phonons.

[1] J. D. Querales-Flores et al, arXiv: 1809.02643.
[2] Z. Gibbs et al, Appl. Phys. Lett. 103, 26 (2013).
[3] S. Poncé et al, J. Chem. Phys. 143, 102813 (2015).