Quantum mechanical prediction of four-phonon scattering rates and reduced thermal conductivity of solids

Recently, first principle-based prediction of lattice thermal conductivity\n$\\kappa$ from the perturbation theory has achieved significant success.\nHowever, it only includes three-phonon scattering due to the assumption that\nfour-phonon and higher-order processes are generally unimportant. Also,\ndirectly evaluating the scattering rates of four-phonon and higher-order\nprocesses has been a long-standing challenge. In this work, however, we have\ndeveloped a formalism to explicitly determine quantum mechanical scattering\nprobability matrices for four-phonon scattering in the full Brillouin Zone, and\nby mitigating the computational challenge we have directly calculated\nfour-phonon scattering rates. We find that four-phonon scattering rates are\ncomparable to three-phonon scattering rates at medium and high temperatures,\nand they increase quadratically with temperature. As a consequence, $\\kappa$ of\nLennard-Jones argon is reduced by more than 60% at 80 K when four-phonon\nscattering is included. Also, in less anharmonic materials -- diamond, silicon,\nand germanium, $\\kappa$ is still reduced considerably at high temperature by\nfour-phonon scattering. Also, the thermal conductivity of optical phonons is\ndominated by the fourth and higher orders phonon scattering even at low\ntemperature.\n