Fermi-Liquid $T^2$ Resistivity: Dynamical Mean-Field Theory Meets Experiment

Abstract

Direct-current resistivity is a key probe for the physical properties of materials. In metals, Fermi-liquid (FL) theory serves as the basis for understanding transport. A $T^2$ behavior of the resistivity is often taken as a signature of FL electron-electron scattering. However, the presence of impurity and phonon scattering as well as material-specific aspects such as Fermi surface geometry can complicate this interpretation. We demonstrate how density-functional theory combined with dynamical mean-field theory can be used to elucidate the FL regime. We take as examples SrVO$_{3}$ and SrMoO$_{3}$, two moderately correlated perovskite oxides, and establish a precise framework to analyze the FL behavior of the self-energy at low energy and temperature. Reviewing published low-temperature resistivity measurements, we find agreement between our calculations and experiments performed on samples with exceptionally low residual resistivity. This comparison emphasizes the need for further theoretical, synthesis, and characterization developments in these and other FL materials.

Figures (4)

• Figure 1: Resistivity measurements versus $T^2$ on a linear scale for (a) SrVO$_3$ and (b) SrMoO$_3$, extracted from Refs. Chamberland1971Reyes2000Inoue1998Fouchet2016xu2019mirjolet2021Shoham2020Roth2021Zhang2016Brahlek2015Ahn2022Brahlek2024Wang2001Cappelli2022Lekshmi2005Radetinac2016Nagai2005. The inset in (a) shows $\Delta \rho = \rho - \rho_0$, with $\rho_0$ the $T=0$ residual resistivity, for the data from Ahn et al.Ahn2022 and Brahlek et al.Brahlek2024, clearly showing two different $T^2$ regimes above and below $\sim 20$ K. The inset in (b) shows the same for the data from Nagai et al.Nagai2005.
• Figure 2: $-\mathrm{Im}\Sigma(\omega)/(\pi T)^2$ as a function of $|\omega|/T$ for SrVO$_3$ and SrMoO$_{3}$ on a log-log scale. Solid (dotted) lines denote $\omega > 0$ ($\omega < 0$). Colored (black) lines are obtained with QMC (NRG). Shaded regions indicate a confidence region for the FL collapse to $C[\omega^{2}/(\pi T)^2 + 1]$. Inset shows $\mathrm{Re}\Sigma(\omega,T)-\mathrm{Re}\Sigma(0,T)$ compared with $1 - 1/Z=\partial_{\omega}\mathrm{Re}\Sigma(\omega,T)|_{\omega=0}$.
• Figure 3: $-\mathrm{Im}\Sigma(i\omega_{n})$ at $T = 116$ K for SrVO$_3$ and SrMoO$_3$, from QMC and NRG. Insets show $1/\mathcal{Z}_T$ and $\mathcal{C}_T$ computed from Eq. \ref{['eq:SigMats_FL_formulas']} for decreasing $T$. Error bars show how, by way of example, an error of $0.7$ meV on $\mathrm{Im}\Sigma(i\omega_{n})$ propagates to $1/\mathcal{Z}_T$ and $\mathcal{C}_T$. Shaded regions indicate the range of values estimated from our real-frequency analysis in Fig. \ref{['fig:ImSig_w']}.
• Figure 4: Comparison between DMFT self-energy and ARPES momentum distribution curves (MDCs) for SrVO$_3$, the latter taken from Aizaki et al.aizaki2012 and Kobayashi et al.kobayashi2017 (both measured below $20$ K). We use $2Z|\text{Im}\Sigma(\omega)| \approx \hbar v_{\text{F}}^* \Delta k$, where $\Delta k$ is the MDC FWHM, and we extracted the renormalized Fermi velocity as $\hbar v_{\text{F}}^* = 0.54$ eV$\cdot$Å from ARPES aizaki2012.