Theory of Quasiparticle Charge Imbalance Induced in a Superconductor by a Supercurrent in the Presence of a Thermal Gradient

Abstract

The charge-imbalance voltage induced in a clean superconductor by a supercurrent density ${\overrightarrow{J}}_s$ in the presence of a temperature gradient $\nabla T$ is shown to be $V=\frac{2\pi v_{\mathrm{F}}l{\lambda }^2\Delta \left({\overrightarrow{J}}_s·\nabla T\right)}{3c^2{k}_{\mathrm{B}}{T}^2{cosh}^2\left(\frac{\Delta }{2k_{\mathrm{B}}T}\right)g_{\mathrm{NS}}\mathrm{}(1-Z)\mathrm{}}$, where $v_{\mathrm{F}}$, $l$, and $\lambda \mathrm{}\left(T\right)\mathrm{}$ are the Fermi velocity, mean free path, and penetration depth, $g_{\mathrm{NS}}$ is the normalized tunnel conductance of the probe junction, and $Z\left(\frac{\Delta }{T}\right)$ is a known function. This result agrees well with the experiments of Clarke, Fjordbøge, and Lindelof.