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In materials with strong electron-phonon ($e$-ph) interactions, the electronscarry a phonon cloud during their motion, forming quasiparticles known aspolarons. Predicting charge transport and its temperature dependence in thepolaron regime remains an open challenge. Here, we present first-principlescalculations of charge transport in a prototypical material with largepolarons, SrTiO$_{3}$. Using a cumulant diagram-resummation technique that cancapture the strong $e$-ph interactions, our calculations can accurately predictthe experimental electron mobility in SrTiO$_{3}$ between 150$-$300 K. Theyfurther reveal that for increasing temperature the charge transport mechanismtransitions from band-like conduction, in which the scattering of renormalizedquasiparticles is dominant, to a beyond-quasiparticle transport regime governedby incoherent contributions due to the interactions between the electrons andtheir phonon cloud. Our work reveals long-sought microscopic details of chargetransport in SrTiO$_{3}$, and provides a broadly applicable method forpredicting charge transport in materials with strong $e$-ph interactions andpolarons.

Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime in SrTiO$_{\mathrm{3}}$