On the Amplitude of Vortex Entropy: A Semiclassical Treatment

Abstract

Despite a long history of Nernst effect in superconductors, a satisfactory theory on its amplitude in vortex liquid phase is still absent. The central quantity of vortex Nernst signals is the entropy $s_{\varphi }$ carried by each vortex. Here we show a semiclassical treatment based on London equation and Pippard nonlocal generalization. The derived $s_{\varphi }$ is a function of both temperatures and magnetic fields. Its magnitude $s_{\varphi }^{amp}$ scales with normal-state conductivity ${\sigma }_n$. Estimations based on our formula show good consistency with experimentally determined values. In dirty limit, the relation is further simplified into a Wiedemann-Franz-like ratio $s_{\varphi }^{amp}/{\sigma }_n\propto k_B\ln 2/{\sigma }_Q$ if taking parameter values deduced from Homes' law, where ${\sigma }_Q=4e^2/h$ is two-dimensional quantum conductivity. We also address related issues, including bounds to $s_{\varphi }$, the Nernst signal and viscosity-entropy density ratio, which are all expressed in fundamental physical constants.