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 ${\tau }_Q\approx \left[\frac{\Delta \mathrm{}\left(0\right)\mathrm{}}{\Delta \mathrm{}\left(T\right)\mathrm{}}\right](2\mathrm{}\times {10}^{-10\mathrm{}})$ sec. It is also shown that even a small (∼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.