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

The charge-imbalance voltage induced in a clean superconductor by a supercurrent density →Jₛ in the presence of a temperature gradient ∇T is shown to be $V={2{π}{v}Fl{{λ}}²{Δ}({{{→}}{J}}ₛ·{}{∇}T)}{3{c}²{k}B{T}²{cosh}²({{Δ}}{2{k}BT}){g}NS(1{-}Z)}$, where ${v}F$, $l$, and ${λ}(T)$ are the Fermi velocity, mean free path, and penetration depth, ${g}NS$ is the normalized tunnel conductance of the probe junction, and $Z({{Δ}}{T})$ is a known function. This result agrees well with the experiments of Clarke, Fjordb{}ge, and Lindelof.