Tunneling Generation, Relaxation, and Tunneling Detection of Hole-Electron Imbalance in Superconductors

The theory of electron tunneling is extended to treat the generation and detection of an imbalance $Q$ between electronlike and holelike quasiparticle populations in superconductors. The equilibration of injected high-energy quasiparticles owing to inelastic phonon processes is discussed, and it is shown that in tin, $Q$ relaxes in ${\ensuremath{\tau}}_{Q}\ensuremath{\approx}[\frac{\ensuremath{\Delta}(0)}{\ensuremath{\Delta}(T)}](2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10})$ sec. It is also shown that even a small (\ensuremath{\sim}1%) anisotropy of the gap can lead to significant $Q$ relaxation by elastic scattering processes. This discussion extends our previous brief interpretation of the pairquasiparticle potential difference measured by Clarke.

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