In semiconductors, heat is carried by phonons, which are quantized vibrations of the crystal lattice. Standard first principles methods to obtain the thermal properties of solids rely on the phonon quasiparticles being well-defined, and assume that the lowest order interactions among three phonons are sufficient to describe thermal transport. Here we show that this is not the case for strongly anharmonic semiconductors, where phonon scattering is so strong that the standard phonon quasiparticle picture can break down, and three-phonon scattering is insufficient to explain the experiments. To address this issue, we present a novel first principles method that features an anharmonic many-body renormalization scheme to create well-defined phonon quasiparticles with weakened interactions, and rigorously accounts for both three-phonon and four-phonon scattering to obtain thermal transport properties . Using a showcase strongly anharmonic material – sodium chloride (NaCl), we demonstrate that our first-principles method simultaneously captures the apparently contradictory experimental measurements of low thermal conductivity and large lattice thermal expansion of NaCl on the one hand, and the relatively temperature-independent phonon frequencies on the other, while the standard first principles theory fails in all three cases. Furthermore, we show that the higher-order four-phonon scattering significantly lowers the thermal conductivity of NaCl and should be rigorously included for a proper comparison to measurements. Finally, we show that our anharmonic renormalization theory, along with four-phonon scattering, also successfully captures the measured phonon frequencies and thermal transport properties of a weakly anharmonic material – diamond, although the four-phonon scattering and renormalization effects are weak in this material. Our work presents a unified first principles framework to accurately predict the thermal properties of solids with varying bond anharmonicities.
 Navaneetha K. Ravichandran and David Broido, Phys. Rev. B. 98, 085205 (2018).
This work was partially supported by Solid State Solar-Thermal Energy Conversion Center (S3TEC), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001299/DE-FG02-09ER46577 (phonons and thermal expansion) and by the Office of Naval Research MURI, Grant No. N00014-16-1-2436 (thermal conductivity).