First-principles study of the temperature-induced band renormalization in thermoelectric filled skutterudites

Band structure characteristics, such as band gap and band dispersion, are fundamental properties of materials. Temperature can affect them because of lattice expansion and phonon-induced atomic vibrations. Here, we apply the recently developed electron-phonon renormalization method to study the temperature effect on the band structures of thermoelectric (TE) filled skutterudites BaCo₄Sb₁₂, BaFe₄Sb₁₂, and YbFe₄Sb₁₂ from first-principles. The results reveal that the band gap in BaCo₄Sb₁₂ drops slower with temperature compared with our previous study on CoSb₃, where it considerably reduces from 0 K to 800 K for BaFe₄Sb₁₂ (∼0.222 eV) and YbFe₄Sb₁₂ (∼0.201 eV). Furthermore, the band dispersions near the band edges at the Γ-point in the three systems at high temperatures are similar to those at 0 K, and the electron energies have small linewidths, whereas the linewidths for energies near the Fermi level are large. The different phenomena are due to the different phonon vibration-induced electronic structure disorders, reflecting the strength of electron-phonon coupling. Band renormalization would further affect the TE properties of these filled skutterudites. Our work provides a deeper understanding of the temperature-dependent band structure in skutterudites.