Phonon transport in ultrahigh thermal conductivity materials beyond the relaxation time approximation

In electrical insulators, heat is carried by the quantized collective lattice vibrations called phonons. Resistance to heat flow in these materials is caused by phonon scattering processes. Thermal phonon transport in these materials is governed by the semi-classical Boltzmann Transport Equation (BTE). Solutions of the BTE are commonly derived assuming the validity of relaxation time approximation (RTA), where all phonon scattering events are assumed to be momentum-dissipative in nature. While the RTA-based BTE solution describes the heat flow in several materials reasonably well, it fails to capture the ultrahigh thermal conductivity and the exceptional phonon transport properties of materials like diamond and boron nitride. Here we present the solutions of the BTE without the RTA for phonon transport through these ultrahigh thermal conductivity materials and demonstrate that accurately distinguishing momentum-conserving (Normal) and momentum-dissipative (Umklapp) scattering events in our formulation is crucial to correctly predict their thermal transport properties.