Se: Liquid-like Behavior and Electro-Phonon Coupling Effects at Finite Temperatures*

ß-Cu₂Se is one of the most promising thermoelectric materials due to its abundance, low cost and toxicity yet high figure of merit. The reason lies in superionic Cu vibrations, which creates the phonon-liquid electron-crystal effect, inhibiting heat transport while maintaining high electrical conductivity. However, accurate characterization of the electronic structure  remains a challenge due to the strong effects of polymorphism (local disorder), electron-phonon coupling and phonon anharmonicity. DFT calculations on the high symmetry structure yields semi-metallic behavior. In this work, we address the problem by treating the effects of symmetry breaking and high-temperature anharmonic vibrations utilizing the anharmonic special displacement method (ASDM). We determined the ground-state polymorphous structure following the recipe in ASDM and obtained a converged bandgap of 0.9 eV with a 4x4x4 supercell, which is in excellent agreement with experimental values. Further, we applied ASDM starting from the polymorphous structure and investigated the bandgap renormalization as a function of temperature, and found that increasing temperature reduces the bandgap by 0.06 eV. We layout a framework to elucidate how anharmonicity impacts the electronic properties and the thermoelectric performance of Cu₂Se.