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Computing electron–defect (e–d) interactions from first principles has remained impractical due to computational cost. Here we develop an interpolation scheme based on maximally localized Wannier functions (WFs) to efficiently computee–d interaction matrix elements. The interpolated matrix elements can accurately reproduce those computed directly without interpolation and the approach can significantly speed up calculations ofe–d relaxation times and defect-limited charge transport. We show example calculations of neutral vacancy defects in silicon and copper, for which we compute thee–d relaxation times on fine uniform and random Brillouin zone grids (and for copper, directly on the Fermi surface), as well as the defect-limited resistivity at low temperature. Our interpolation approach opens doors for atomistic calculations of charge carrier dynamics in the presence of defects.

Electron-phonon (e–ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading ordere–ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-rangee–ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles.