Theory of tunneling in metal–superconductor devices: Supercurrents in the superconductor gap at zero temperature

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Abstract
Tunneling experiments in metal-oxide superconductor have shown the existence of ‘‘leakage’’ currents for applied voltages V smaller than one-half of the superconductor gap Δ. These currents are independent of temperature T. Recently experiments with scanning tunneling microscopy (STM) and squeezable tunnel junctions have shown that the observation of the superconductor gap depends strongly on the resistance in the junction. In fact only for resistances larger than ∼106 Ω the gap is clearly observable. These experiments have been explained in terms of the perturbative Hamiltonian formalism of Bardeen. However, it may happen that this theory while applicable for very large resistances may not be so for small tunnel resistances. We present here a nonperturbative theory in all orders of the transmitivity ‖To‖2 and show the existence of supercurrents for values of V<Δ at T=0. This is done by performing a matching in the junction between the superconductor Bogolubov wave functions for Copper pairs and the electron and hole wave functions in the normal metal. Typical numerical results are presented for several values of ‖To‖2. We believe that experiments in STM and other junctions should be interpreted in the frame of this theory.

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