Harmonic phonon theory for calculating thermal conductivity spectrum from first-principles dispersion relations

In recent years, nanostructuring of dielectric and semiconducting crystals has enhanced controllability of their thermal conductivity. To carry out computational materials search for nanostructured materials with desirable thermal conductivity, a key property is the thermal conductivity spectrum of the original single crystal, which determines the appropriate length scale of nanostructures and mutual adaptability of different kinds of nanostructures. Although the first-principles phonon transport calculations have become accessible, the anharmonic lattice dynamics calculations are still expensive to scan many materials. To this end, we have developed an empirical model that describes the thermal conductivity spectrum in terms only of harmonic phonon properties and bulk thermal conductivity. The model was tested for several crystals with different structures and thermal conductivities, and was confirmed to reproduce the overall profiles of thermal conductivity spectra and their accumulation functions obtained by the first-principles anharmonic calculations.