Temperature-Dependent Band Renormalization in CoSb3 Skutterudites Due to Sb-Ring-Related Vibrations

The temperature-dependent electronic structures in the thermoelectric semiconductor CoSb3 and its Yb-filled counterpart are studied by using the electron-phonon renormalization (EPR) method, considering both lattice expansion and phonon-induced atomic vibrations. The primary direct band gaps at the Gamma-point for skutterudites decrease with increasing temperature, largely due to the increase in the energy level at the valance band maximum (VBM). The energy difference between the conduction band minimum (CBM) and second CB also decreases with temperature, inducing band convergence at high temperatures. The phonon vibrations of the Sb rings are responsible for these temperature-dependent electronic structures. Specifically, the four Sb-ring-related A(g) phonon mode in CoSb3 plays a decisive role in causing the increase in the VBM with temperature and decrease in the primary band gap. The band convergence at high temperatures is due to the different responses to lattice vibrations of the second CB and the CBM for both systems. Our work sheds light on the relation between chemical bonds and phonon-assisted electronic structures.