Insulating transport in anisotropic metals: breakdown of Drude transport and the puzzling $c$-axis resistivity of Sr$_2$RuO$_4$ and other layered oxides

Abstract

We reveal a mechanism that may explain the non-metallic out-of-plane resistivity in layered metals. By carefully examining how the Drude-Boltzmann expression for the $c$-axis conductivity emerges out of the Kubo formula, we find, besides the standard metallic term proportional to the carrier lifetime $τ$, a non-Drude contribution proportional to $1/τ$. The Drude behavior breaks down when $1/τ> 2 η^*$, the crossover value $η^*$ being small (and hence observable) when the $c$-axis velocities vary rapidly with the distance from the Fermi surface. We consider the Hund metal Sr$_2$RuO$_4$ as a test case, which we study within a realistic dynamical mean-field theory approach. The non-Drude behavior observed experimentally in $c$-axis transport is reproduced and explained by our considerations, showing that earlier invoked extrinsic mechanisms that involve either impurities or phonons are unnecessary. We point out that the small value of $η^*$ is due to a peculiar accidental cancellation due to destructive interference characteristic of body-centered tetragonal lattices.

Figures (4)

• Figure 1: Measurements of in-plane vs. out-of-plane resistivity in layered Sr$_2$RuO$_4$ (a), Sr$_2$RhO$_4$ (b), and NaCo$_2$O$_4$ (c). The data is digitized from Refs. tyler98Hussey_et_al:1998Nagai2010Valla2002. The out-of-plane resistivity exhibits a maximum near the crossover temperature $T_M$, indicating the breakdown of Drude transport.
• Figure 2: (a) Side view of the body-centered tetragonal lattice of Sr$_2$RuO$_4$ indicating the dominant out-of-plane hopping amplitudes. (b) Top view. (c) The dependence of $v^z$ along a cut perpendicular to the Fermi surface ($k_x = 0.0 \pi/a$) (shown in green in panel d), with expansion in $k$ (with respect to $k_{\text{F}}$) and derived $\eta^*$ values listed, for both the M1 (orange) and M2 model (blue). The position of the Fermi surface at $k_{\text{F}}$ is marked in green, the position of the extrapolated vanishing Fermi velocity for M2 is marked in dashed blue. (d) The dependence of $\eta^*$ along the Fermi surface.
• Figure 3: (a-c) Resistivity $\rho^c$ as a function of scattering $\eta$ for the M1 (top), M2 (middle), and full ab-initio model including SOC (bottom). (d-f) Corresponding contour maps of $v^z$ at $k_z=0.5 \pi/c$.
• Figure 4: Comparison of out-of-plane resistivity (left axis, orange lines) and in-plane resistivity (right axis, blue lines). The $c$-axis resistivity shows a significant dependence on model details, while the in-plane resistivity remains unaffected.