Effect of electron–phonon coupling on thermal transport in metals: A Monte Carlo approach for solving the coupled electron–phonon Boltzmann transport equation

In this work, the effect of electron–phonon (e–ph) coupling on both electron and phonon transport of metals is investigated. A Monte-Carlo (MC) approach for solving the coupled electron–phonon Boltzmann transport equation is developed to study the thermal conductivity of α-U and Ag. In this approach, the anisotropic electron band structure, phonon dispersion in the full Brillouin zone, and mode-dependent thermal relaxation time of electrons and phonons are calculated from first principles. Using this approach, MC simulations of coupled e–ph thermal transport at different temperatures in α-U and Ag are performed. Results indicate the e–ph relaxation time is orders of magnitude smaller than the phonon relaxation time. In phonon thermal transport, the impact of ph–e scattering is almost negligible and the ph–ph scattering dominates phonon transport. At high temperatures, the electrons dominate thermal transport in both α-U and Ag. However, at low temperatures, the phonon contribution to the total thermal conductivity of α-U is significant. Moreover, the Lorenz ratio deviates from the Sommerfeld value at low to intermediate temperatures, where the Wiedemann–Franz law is not applicable. Finally, we show that the Ag electron thermal conductivity shows a stronger size effect than the phonon thermal conductivity.