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Structural phase transitions and soft phonon modes pose a longstandingchallenge to computing electron-phonon (e-ph) interactions in stronglyanharmonic crystals. Here we develop a first-principles approach to computee-ph scattering and charge transport in materials with anharmonic latticedynamics. Our approach employs renormalized phonons to compute thetemperature-dependent e-ph coupling for all phonon modes, including the softmodes associated with ferroelectricity and phase transitions. We show that theelectron mobility in cubic SrTiO$_{3}$ is controlled by scattering withlongitudinal optical phonons at room temperature and with ferroelectric softphonons below 200~K. Our calculations can accurately predict the temperaturedependence of the electron mobility in SrTiO$_{3}$ between 150$-$300~K, andreveal the microscopic origin of its roughly $T^{-3}$ trend. Our approachenables first-principles calculations of e-ph interactions and charge transportin broad classes of crystals with phase transitions and strongly anharmonicphonons.

Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in SrTiO$_{3}$ Perovskite from First Principles