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, $κ$, 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.

Figures (4)

• Figure 1: Temperature-dependent resistivity of RuO$_2$. (a) Resistivity plotted on a log-log scale over the full temperature range. The inset shows a linear scale. (b) Resistivity versus $T^2$ for samples S1-S3 below 30 K. Experimental data (open circles) can be fit to $\rho=\rho_0+A_2T^2$ (solid lines) below $\approx$ 20 K. An upward deviation indicates the predominance of a larger exponent at higher temperatures. (c) The subtracted resistivity $\delta\rho=\rho-\rho_0-A_2T^2$ plotted versus $T^5$ for samples S1-S3. Solid lines represent fits to $\delta \rho=A_5T^5$ below $\approx$ 40 K. A downward deviation is visible at higher temperatures.
• Figure 2: RuO$_2$ in Kadowaki-Woods plots. (a) The prefactor A$_2$ plotted as a function of fermionic specific heat $\gamma$ in a log-log scale. RuO$_2$: red circle (this work); data collected from tsujii2003: gray circle; semimetal WTe$_2$, WP$_2$ and Mogourgout2024electronic: orange inverted triangle. (b) The prefactor A$_2$ plotted as a function of Fermi temperature $E_F/k_B$ in a log-log scale. RuO$_2$: red circle(this work); data collected from BiOSe2020t: gray circle; BaSnO$_3$ film: purple open square; Bi$_2$O$_2$Se: pink open circle; Sr$_2$RuO$_4$: black pentagon; UPt$_3$, CeRu$_2$Si$_2$: green diamond; Bi$_{0.96}$Sb$_{0.04}$, graphite: brown open hexagon; SrTiO$_{3-\delta}$STOlin2015: blue square; semimetal Bi, Sb, Mo, WTe$_2$, WP$_2$gourgout2024electronic: orange inverted triangle. Most materials are located between the upper (Kadowaki-Woods) bound and the lower (Rice) bound (blue dots line).
• Figure 3: Temperature-dependent thermal conductivity of RuO$_2$ below 30 K.a Temperature-dependent thermal conductivity of RuO$_2$ plotted on log-log scale under 0 T (black circle) and 12 T (gray circle) magnetic field. b Temperature-dependence of $\Delta \kappa/T$ (blue circle) and $L_0\Delta \sigma$ (red open circle). $\Delta \kappa$ and $\Delta \sigma$ equal to $\kappa(0 T)-\kappa(12T)$ and $\sigma(0T)-\sigma(12T)$ respectively. Error bars caused by signal fluctuations and geometrical errors are shown in the figure. c Temperature-dependence of electronic (red triangle) and phononic (blue triangle) contributions to thermal conductivity in a log-log scale.
• Figure 4: Temperature dependence of electronic thermal resistivity$WT$ is defined as the inverse of $\kappa/T$. Normalized by $L_0$, it can be expressed in units of electric resistivity. Plotting it as function of T$^2$ reveals an intercept, due to scattering by impurities and a slope, due to e-e scattering.