Efficient First-Principles Framework for Phonon-Liquid-Like Behavior and Anharmonic Electron-Phonon Coupling in Cu-Based Materials

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 create the phonon-liquid electron-crystal effect, inhibiting heat transport while maintaining high electrical conductivity. Accurate electronic structure calculations in Cu₂Se remain a challenge, since up to now no systematic approach exists to describe the liquid-like behavior and high degree of anharmonicity in this system. Here, utilizing the anharmonic special displacement method (ASDM), we introduce a quasi-static picture relying on symmetry-breaking polymorphous networks to capture anharmonicity in the phonons and structural disorder. We demonstrate the validity of polymorphous networks to describe overdamped anharmonic lattice dynamics in Cu₂Se by computing the phonon spectral function and phonon density of states, yielding an unprecedented agreement with experiments. We also show the effect on the electronic structure by computing the electron spectral function at the hybrid functional level. In contrast to standard first-principles calculations on the high-symmetry structure, which reveal a semi-metallic behavior, our results using a polymorphous network yield a band gap of around 0.85 eV. Using the Burstein-Moss shift, we obtained a further correction to the bandgap of 0.26 eV in Cu-deficient Cu₂Se, which yields excellent agreement with experimental values (1.23 eV). Further, we employed the ASDM in conjunction with the polymorphous structure to explore anharmonic electron-phonon coupling effects. Our work opens the way for systematic ab-initio anharmonic and electron-phonon coupling calculations in liquid-like crystals and thus understanding their compelling vibrational and electronic properties.