Conditions for $T^2$ resistivity from electron-electron scattering

Many complex oxides (including titanates, nickelates and cuprates) show a regime in which resistivity follows a power law in temperature ($\rho\propto T^2$). By analogy to a similar phenomenon observed in some metals at low temperature, this has often been attributed to electron-electron (Baber) scattering. We show that Baber scattering results in a $T^2$ power law only under several crucial assumptions which may not hold for complex oxides. We illustrate this with sodium metal ($\rho_\text{el-el}\propto T^2$) and strontium titanate ($\rho_\text{el-el}\not\propto T^2$). We conclude that an observation of $\rho\propto T^2$ is not sufficient evidence for electron-electron scattering.