Electrical conductivity of copper under ultrahigh pressure and temperature conditions by both experiments and first-principles simulations

Copper (Cu) is ubiquitously utilized in industry owing to its exceptional electrical conductivity and serves as a standard material in shock compression experiments. However, a comprehensive understanding of the electrical and thermal transport properties of Cu under extreme pressure-temperature ($P\ensuremath{-}T$) conditions remains a significant challenge due to limited experiments and theoretical constraints. In this work, we have developed a robust methodology for achieving high-quality electrical resistivity measurements of transition metals at ultrahigh $P\ensuremath{-}T$ conditions under shock compression. We conducted electrical resistivity measurements on Cu utilizing a four-probe method in a diamond anvil cell up to 50 GPa at ambient temperature, and in a two-stage light-gas gun up to 118 GPa and 1800 K. Simultaneously, we computed the electrical and thermal conductivity of face-centered cubic (fcc) Cu over a wide $P\ensuremath{-}T$ range using first-principles molecular dynamics simulations. Notably, our experimental and theoretical results are overall consistent with each other. Our results reveal that the electrical resistivity of fcc Cu diminishes with increasing pressure and displays a linear augmentation with rising temperature. The relationship between the electrical resistivity of fcc Cu and temperature can be described by the Bloch-Gr\"uneisen formula, indicating that electron-phonon scattering governs its electrical conductivity.