First-Principles Theory of Five- and Six-Phonon Scatterings

Abstract

Higher-order phonon scatterings beyond fourth order remain largely unexplored despite their potential importance in strongly anharmonic materials at elevated temperatures. We develop a theoretical formalism for first-principles calculation of five- and six-phonon scatterings using Green's function techniques based on a diagrammatic formalism, and systematically investigate multi-phonon interactions in Si, MgO, and BaO from room temperature to near melting points. Our calculations reveal dramatically different material-dependent behaviors: while five- and six-phonon processes remain negligible in Si even at high temperatures, they become increasingly important in MgO near its melting point (3100~K) and in BaO at intermediate temperatures (1200~K). Most remarkably, five- and six-phonon scatterings surpass three- and four-phonon scattering intensity in BaO near its melting point (2100~K), reducing lattice thermal conductivity by over 50\%. We demonstrate that the strength of higher-order interactions is primarily governed by interatomic force constants, with BaO exhibiting five- and six-phonon scattering rates over one order of magnitude stronger than MgO despite identical crystal structures, due to large scattering phase space arising from softened harmonic interactions. Our work provides theoretical insights into the lattice dynamics and thermal transport in strongly anharmonic materials and at elevated temperatures.