Antibonding-Induced Anomalous Temperature Dependence of the Band Gap in Crystalline Ge₂Sb₂Te₅

The band gap of most semiconductors decreases with temperature, but a few semiconductors exhibit an increase of the gap with temperature. This abnormal behavior is usually attributed to thermal expansion, band inversion, or d-states at the valence band maximum (VBM). However, the temperature-induced increase of the band gap in hexagonal (hex) crystalline Ge₂Sb₂Te₅cannot be understood by the current available mechanisms. Here, we propose a new mechanism, i.e., the interplay between antibonding states and phonon processes. In hex-Ge₂Sb₂Te₅, the abnormal presence of antibonding-like states below the Fermi level induces weaker two-phonon processes than one-phonon processes at the VBM, resulting in a decrease in energy of the VBM with temperature. Moreover, p-d orbital hybridization leads to a comparable strength of two-phonon processes with one-phonon processes at the conduction band minimum (CBM), and thus this makes the CBM position almost temperature-independent. Furthermore, by considering the effects of the temperature-dependent electronic structure (TDES), the calculated electrical conductivity is in good agreement with the experiment, while the conventional rigid band approximation overestimates the values of the electrical conductivity over a wide range of temperature. Our work reveals the origin of the increase of the band gap with temperature in hex-Ge₂Sb₂Te₅and demonstrates the importance of TDES in electrical conductivity calculations.