Josephson tunneling spectroscopy of negative-Ucenters

We consider a superconductor-insulator-superconductor (SIS) junction in which the tunneling through the insulating barrier is dominated by a localized “negative-$U”$ center. We show that the $I_{c}R$ product of the junction depends sensitively on the spectrum of impurity states, and in near-resonant conditions exhibits an anomalously large $I_{c}R$ product which can exceed the famous Ambegoakar-Baratoff limit by an arbitrarily large factor. The analysis is extended to problems in which there is an array of negative-$U$ centers in the junction. We also discuss general reasons to expect significant violations of the optical conductivity sum rule in most SIS junctions and of the Ambegoakar-Baratoff result when the superconductors emerge from a non-Fermi liquid normal state.