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Recently, first principle-based prediction of lattice thermal conductivity$\kappa$ from the perturbation theory has achieved significant success.However, it only includes three-phonon scattering due to the assumption thatfour-phonon and higher-order processes are generally unimportant. Also,directly evaluating the scattering rates of four-phonon and higher-orderprocesses has been a long-standing challenge. In this work, however, we havedeveloped a formalism to explicitly determine quantum mechanical scatteringprobability matrices for four-phonon scattering in the full Brillouin Zone, andby mitigating the computational challenge we have directly calculatedfour-phonon scattering rates. We find that four-phonon scattering rates arecomparable to three-phonon scattering rates at medium and high temperatures,and they increase quadratically with temperature. As a consequence, $\kappa$ ofLennard-Jones argon is reduced by more than 60% at 80 K when four-phononscattering is included. Also, in less anharmonic materials -- diamond, silicon,and germanium, $\kappa$ is still reduced considerably at high temperature byfour-phonon scattering. Also, the thermal conductivity of optical phonons isdominated by the fourth and higher orders phonon scattering even at lowtemperature.

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