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

TL;DR

This study uses first-principles calculations to analyze how temperature influences the electronic band structure of PbTe, focusing on the direct gap and valence band maxima, with results aligning well with experimental data.

Contribution

It provides a comprehensive ab-initio analysis of temperature effects on PbTe's band structure, including electron-phonon interactions and thermal expansion, which was not fully explored before.

Findings

The direct gap increases with temperature, matching experimental observations.

Valence band maxima at L and Σ align around 600-700 K due to temperature effects.

Both thermal expansion and electron-phonon interactions significantly influence band structure changes.

Abstract

We report a fully {\it ab-initio} calculation of the temperature dependence of the electronic band structure of PbTe. We address two main features relevant for the 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 $\Sigma$. We account for the energy shift of the electronic states due to thermal expansion, as well as electron-phonon interaction computed using the non-adiabatic Allen-Heine-Cardona formalism within density functional perturbation theory and the local density approximation. 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 $\Sigma$ become aligned at $\sim 600-700$ K. We find that both thermal expansion and electron-phonon interaction have a considerable effect on these temperature variations. The Fan-Migdal and Debye-Waller terms are of almost equal magnitude but have an opposite sign, and the delicate balance of these terms gives the correct band shifts. The electron-phonon induced renormalization of the direct gap is produced mostly by high-frequency optical phonons, while acoustic phonons are also responsible for the alignment of the valence band maxima at L and $\Sigma$.