Generation of charge imbalance in a superconductor by a temperature gradient

The charge-imbalance voltage in a superconductor carrying a current in the presence of a temperature gradient is calculated from the Boltzmann equation in the clean limit. We demonstrate why the Green's-function approach in the dirty limit, first performed by Schmid and Schön, generates the same Boltzmann-like equation for the distribution function. In addition, the charge-imbalance voltage in the absence of an impressed current is calculated. It is shown to depend on .