Understanding the pressure dependence on thermal transport of metals is crucial for high-pressure applications and fundamental research in earth science. As high-pressure thermal measurements are challenging, the theoretical approach and first-principles methods are widely adopted to investigate the pressure-dependent thermal transport in metals. However, these approaches are generally limited to the free-electron metals and the phonon contributions are neglected. The mechanisms behind the pressure effect on thermal transport of metals are not fully addressed. In this work, we implement rigorous mode-level first-principles calculations to reveal different mechanisms behind the pressure-dependent electronic and phonon thermal conductivity in aluminum (Al), tungsten (W), and platinum (Pt). While the overall thermal conductivity values of the three metals all increase with pressure, the mechanisms are different. For the electronic thermal conductivity part, the main contribution for the positive pressure effect on free-electron metal Al is the decrease of the electron-phonon scattering rate, while the dominant contribution in Pt and W, whose $d$ state electrons are abundant around the Fermi energy, is the increase of electron group velocity. Phonon thermal conductivity of Pt and Al is found to increase with pressure, but the rates of increase are different. In contrast, phonon thermal conductivity of W is nearly independent with pressure. Such pressure invariance is due to the competing effect between phonon lifetime decrease and phonon group velocity increase under pressure.

The electronic and lattice thermal conductivities of the a-axis and c-axis of PdTe₂.