T-square electric resistivity and its thermal counterpart in RuO$_2$

Abstract

We present a study of low-temperature electric and thermal transport in RuO$_2$, a metallic oxide which has attracted much recent attention. Careful scrutiny of electric resistivity reveals a quadratic temperature dependence below $\sim$ 20 K undetected in previous studies of electronic transport in this material. The prefactor of this T$^2$ resistivity, given the electronic specific heat, corresponds to what is expected by the Kadowaki-Woods scaling. The variation of its amplitude across 4 different samples is negligible despite an eightfold variation of residual resistivity. There is also a T$^5$ resistivity due to scattering by phonons. By measuring thermal conductivity, $\kappa$, at zero field and at 12 T, we separated its electronic and the phononic components and found that the electronic component respects the Wiedemann-Franz law at zero temperature and deviates downward at finite temperature. The latter corresponds to a threefold discrepancy between the prefactors of the two (thermal and electric) T-square resistivities. Our results, establishing RuO$_2$ as a weakly correlated Fermi liquid, provide new input for the ongoing theoretical attempt to give a quantitative account of electron-electron scattering in metallic oxides starting from first principles.