Polaronic T² Resistivity in Strontium Titanate

Strontium titanate is a bulk insulator that upon doping becomes conducting at remarkably low carrier densities. We argue that this diluteness, which enhances the importance of collective modes of the electron gas, along with strong coupling to longitudinal optic phonons, produces a polaronic liquid of electrons coupled to hybrid plasmon-phonon modes. We argue that these unusual basic excitations of the system provide a microscopic basis for a swath of unusual transport phenomenology in this material, including T² resistivity at low temperature. The latter, arising from electron-electron scattering but requiring a mechanism to dump energy to the lattice, is puzzling in this dilute limit of this material which contains only one species of electron and cannot Umklapp scatter. The experimentally measured scattering cross-section is also inconsistent with classical electron-electron scattering. Our scenario provides a mechanism for both of these observations.