Theory of Phonon-Assisted Tunneling in Superconductors

Taylor and Burstein have found a temperature-dependent current in Pb-Pb superconductor-oxide-superconductor tunnel junctions in excess of the usual thermally excited quasiparticle current. We here calculate the current arising from a process in which a phonon is absorbed by a ground-state pair on one side of the oxide barrier resulting in a pair of quasiparticles, one on each side of the barrier, and the transfer of one electron across the barrier. One-phonon normal and umklapp as well as two-phonon umklapp processes are examined. The one-phonon umklapp process dominates and yields a current in excellent agreement with the experimental excess current both as a function of temperature and of voltage.