# Colloquium: Strong Electron-Vibrational Coupling and Ab Initio Theory of Heat Transport

## Main Content

Thermal conductivity is a key characteristic of many materials, particularly those used in the energy and environment sectors (thermoelectrics, thermal-barrier coatings, catalysis, etc.). Despite its importance, the thermal conductivity has been experimentally measured for only a tiny minority of substances. Calculations of the thermal conductivity have only been possible, so far, by employing severe approximations (e.g. perturbation theory based on the harmonic approximation, or empirical (classical) force-field potentials). Recently, we developed a first-principles formulation of the Green-Kubo method that allows the accurate assessment of the non-radiative thermal conductivity of solid semiconductors and insulators. It is based on the fluctuation-dissipation theorem and *ab initio* molecular dynamics. It is valid for any temperature gradient achievable on earth. Accurate size- and time-convergence are achieved with moderate computational effort. We demonstrate the capabilities of the technique by investigating the thermal conductivity of very-high and very-low heat-conductivity materials, namely diamond Si and tetragonal ZrO_{2}.