The Lorenz ratio as a guide to scattering contributions to Planckian transport

In many physical situations in which many-body assemblies exist at temperature $T$, a characteristic quantum-mechanical time scale of approximately $\hbar/k_{B}T$ can be identified in both theory and experiment, leading to speculation that it may be the shortest meaningful time in such circumstances. When this behaviour is investigated by probing the scattering rate of strongly interacting electrons in metals, it is clear that in some cases only electron-electron scattering can be its cause, while in others it arises from high-temperature scattering of electrons from quantised lattice vibrations, i.e. phonons. In metallic oxides, which are among the most studied materials, analysis of electrical transport does not satisfactorily identify the relevant scattering mechanism at 'high' temperatures near room temperature. We employ a contactless optical method to measure thermal diffusivity in two Ru-based layered perovskites, Sr$_3$Ru$_2$O$_7$ and Sr$_2$RuO$_4$, and use the measurements to extract the dimensionless Lorenz ratio. By comparing our results to the literature data on both conventional and unconventional metals we show how the analysis of high-temperature thermal transport can both give important insight into dominant scattering mechanisms, and be offered as a stringent test of theories attempting to explain anomalous scattering.