Breakdown of the Wiedemann-Franz law at the Lifshitz point of strained <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">RuO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>

Abstract

Strain tuning ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ 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 $\ensuremath{\rho}\ensuremath{\sim}{T}^{2}$ to $\ensuremath{\rho}\ensuremath{\sim}{T}^{2}\mathrm{log}(1/T)$, a behavior consistent with experiments by Barber et al. [Phys. Rev. Lett. 120, 076602 (2018)]. This expectation originates from the same multiband scattering processes with large momentum transfer that were recently shown to account for the linear in $T$ resistivity of the strange metal ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$. In contrast, the thermal resistivity ${\ensuremath{\rho}}_{Q}\ensuremath{\equiv}T/\ensuremath{\kappa}$, where $\ensuremath{\kappa}$ 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 ${\ensuremath{\rho}}_{Q}\ensuremath{\propto}{T}^{3/2}$. As a result, we predict that the Wiedemann-Franz law in strained ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ should be violated with a Lorenz ratio $L\ensuremath{\propto}{T}^{1/2}\mathrm{log}(1/T)$. We expect this effect to be observable in the temperature and strain regime where the anomalous charge transport was established.

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