Thermal transport measurements of the charge density wave transition in CsV$_3$Sb$_5$

We study thermalization and thermal transport in single crystals of CsV$_3$Sb$_5$ through the CDW transition by directly measuring thermal diffusivity ($D$), thermal conductivity ($κ$), resistivity ($ρ$), and specific heat ($c$). Commensurate with previous reports, we observe a sharp, narrow anomaly in specific heat associated with a first order transition that results in a CDW state below $\sim94$ K. While a corresponding sharp anomaly in thermal diffusivity is also observed, resistivity and thermal conductivity only exhibit small steps at the transition, where the feature is sharp for resistivity and broader for thermal conductivity. Scrutinizing the thermal Einstein relation $κ=cD$, we find that this relation is satisfied in the entire temperature range, except in a narrow range around the transition. The Wiedemann-Franz law seems to work outside the critical region as well. Below the transition and persisting below the two-phase regime we find strong resemblance between the resistivity anomaly and the specific heat, which may point to a secondary electronic order parameter that emerges continuously below the transition.