Charge transport in doped SrTiO₃

Recent experiments identified an unusual T² dependence of the resistivity in doped strontium titanate (SrTiO₃). That this dependence is observed even at low doping, when umklapps are essentially impossible, and at temperatures far exceeding the Fermi energy eliminates electron-electron interaction as a possible source of the T² resistivity. The T² term may come from the interaction of electrons with two soft transverse optic (TO) phonons, characteristic for this material (the Epifanov-Levanyuk-Levanyuk mechanism). However, it is unclear within this model why the T² term would be observed at temperatures smaller than the TO phonon frequency. We show that this behavior can be understood within a model in which the TO frequency varies over the sample from a larger value, observed in neutron and Raman scattering experiments, to a smaller value. A mictroscopic justification of this model relies on the experimentally observed polar boundaries between antiphase domains. Within the same model, we showed that the next-order correction to T² term is T⁶ which is due to interaction of electrons with four TO phonons. Therefore, the TO phonon scattering is not able to explain the T³ behavior of the resistivity observed at higher temperatures.