Voltage in a charge-imbalance experiment, taking into account the approximate charge neutrality in the superconductor

Abstract

We consider the two-fluid model description of the “branch imbalance” experiment first carried out by Clarke and interpreted by Tinkham. We show that when approximate charge neutrality is taken into account, the analysis of the tunneling process has to be slightly modified to allow for the shifts in the pair chemical potential when imposing energy conservation. As a consequence we find that nearTc, most of the voltage differenceVd measured between the superconducting and normal probes develops across the nonequilibrium region and not across the junction coupled to the normal probe. We show that as the temperature is lowered more of the measured voltageVd develops across the junction as the shift of the pair chemical potential δμs decreases and the corresponding quasiparticle chemical potential shift δμn increases. Our expression for the measured voltageVd agrees with the ones obtained previously, but we note that at lower temperatures it can no longer be identified with the difference between the pair and quasiparticle chemical botentials in the nonequilibrium region.