Conditions for T² resistivity from electron-electron scattering

Recent experiments in SrTiO₃ and other materials have observed a scattering mechanism for which resistivity (ρ) is proportional to the square of the temperature (T). By analogy to a similar phenomenon observed in metals at low temperature, this mechanism was hypothesized to be Fermi-liquid-like electron-electron scattering (Baber scattering), although it persists to much higher temperatures than Baber scattering in metals. To study this phenomenon, we employ a variational solution of the Boltzmann Transport Equation to solve the electron-electron collision integral directly, going beyond the relaxation-time approximation [1]. We show that the Baber T² power law rests on several crucial assumptions. When these assumptions hold, ρ_el-el is proportional to T² (as we verified using our methodology in sodium metal). However, in the case of SrTiO₃, the assumptions do not hold, and we found that ρ_el-el is no longer proportional to T². The higher the temperature and the lower the doping level, the greater the deviation from T². This suggests that the power law observed in SrTiO₃ may instead be due to another, as yet unidentified, mechanism. More generally, this implies that observation of ρ proportional to T² in a given system is not evidence for electron-electron scattering unless the assumptions behind the Baber T² hold in that system.

[1] M. W. Swift and C. G. Van de Walle, Eur. Phys. J. B 90, 151 (2017).