Breakdown of the Wiedemann-Franz law at the Lifshitz point of strained Sr$_2$RuO$_4$

TL;DR

This paper predicts a violation of the Wiedemann-Franz law in strained Sr$_2$RuO$_4$ near the Lifshitz point, due to distinct scattering processes affecting thermal and electrical resistivities, with specific temperature dependencies.

Contribution

It introduces a theoretical framework explaining the breakdown of the Wiedemann-Franz law at the Lifshitz point in Sr$_2$RuO$_4$, highlighting different mechanisms for charge and heat transport.

Findings

Thermal resistivity scales as T^{3/2} near the Lifshitz point.

Electrical resistivity follows a T^2 log(1/T) behavior.

Lorenz ratio deviates from the Wiedemann-Franz law with a T^{1/2} log(1/T) dependence.

Abstract

Strain tuning Sr$_{2}$RuO$_{4}$ through the Lifshitz point, where the Van Hove singularity of the electronic spectrum crosses the Fermi energy, is expected to cause a change in the temperature dependence of the electrical resistivity from its Fermi liquid behavior $\rho\sim T^{2}$ to $\rho\sim T^{2}{\rm log}\left(1/T\right)$, a behavior consistent with experiments by Barber et al. [Phys. Rev. Lett. 120, 076601 (2018)]. This expectation originates from the same multi-band scattering processes with large momentum transfer that were recently shown to account for the linear in $T$ resistivity of the strange metal Sr$_{3}$Ru$_{2}$O$_{7}$. In contrast, the thermal resistivity $\rho_{Q}\equiv T/\kappa$, where $\kappa$ is the thermal conductivity, is governed by qualitatively distinct processes that involve a broad continuum of compressive modes, i.e. long wavelength density excitations in Van Hove systems. While these compressive modes do not affect the charge current, they couple to thermal transport and yield $\rho_{Q}\propto T^{3/2}$. As a result, we predict that the Wiedemann-Franz law in strained Sr$_{2}$RuO$_{4}$ should be violated with a Lorenz ratio $L\propto T^{1/2}{\rm log}\left(1/T\right)$. We expect this effect to be observable in the temperature and strain regime where the anomalous charge transport was established.