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

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.

💡 Research Summary

The paper presents a comprehensive study of the low‑temperature dc resistivity of two moderately correlated perovskite oxides, SrVO₃ and SrMoO₃, using a combination of density‑functional theory (DFT) and dynamical mean‑field theory (DMFT). The authors aim to resolve a long‑standing ambiguity in the interpretation of the ubiquitous T² resistivity law, which in a textbook Fermi‑liquid (FL) picture originates from electron‑electron (el‑el) Umklapp scattering, but in real materials can be obscured by impurity, phonon scattering, and details of the Fermi‑surface geometry.

Methodology

1. Electronic structure – The Kohn‑Sham band structures from DFT are down‑folded onto a minimal t₂g Wannier basis, yielding a three‑orbital Hubbard model for each compound.
2. Many‑body solver – Single‑site DMFT is solved with two complementary impurity solvers: continuous‑time hybridisation‑expansion quantum Monte‑Carlo (CT‑HYB) and the numerical renormalisation group (NRG). The CT‑HYB data are analytically continued via Padé approximants, while NRG provides high‑resolution real‑frequency self‑energies.
3. Transport – The dc conductivity is evaluated with the Kubo formula in the DMFT framework, neglecting vertex corrections (justified by the locality of the self‑energy). The transport function Φ(ε_F) is obtained by adaptive Brillouin‑zone integration using the Julia package AutoBZ.jl.
4. FL analysis – In the FL regime the imaginary part of the self‑energy obeys Im Σ(ω,T)=−C(ω²+π²T²). By plotting −Im Σ(ω,T)/(πT)² versus |ω|/T for several temperatures, the authors demonstrate a collapse onto the universal curve C