Anharmonic phonon frequency and ultralow lattice thermal conductivity in β-Cu₂Se liquid-like thermoelectrics

The prototype phonon-liquid electron-crystal β-Cu2Se has been ranked among the best thermoelectric material with its ultralow lattice thermal conductivity (κL). The atomic fluidity, harmonic approximation failure, and the existence of a large number of imaginary phonon modes hinder the atomistic analysis of phonon transport in β-Cu2Se. Thus, the atomistic origins of its ultralow κL remain elusive. In this study, we present a self-consistent phonon (SCPH) calculation of the lattice dynamical properties of β-Cu2Se by including quartic anharmonicity and stiffening imaginary phonon modes in the anharmonic phonon dispersion, aiming to unravel the atomistic origins of ultralow κL. Upon renormalizing harmonic phonon dispersion with quartic anharmonicity, those imaginary phonon modes arising from copper fluidity diminish as temperature increases and anharmonic phonon dispersions are obtained. By solving the Boltzmann transport equation within the relaxation time approximation (BTE-RTA), we predicted ultralow κL which demonstrated an overall agreement with previous experiments. After analyzing the harmonic as well as anharmonic phonon density of states, it was found that the inclusion of quartic anharmonicity induces the suppression of low-lying phonon modes, which coincides with the experimental observation of the selective breakdown of long-wave transverse acoustic phonons. However, for the propagative heat-carriers, the anharmonic scattering enhances and phonon relaxation lifetime decreases as temperature increases, leading to a further reduction of κL. This study provides an extra insight into the atomistic origins of ultralow κL in β-Cu2Se from first-principles anharmonic force constants and helps engineer the lattice dynamical properties for better thermoelectric performance.