Andreev reflections and resonance tunneling in Josephson junctions

The current-voltage characteristics (I-V) and Josephson critical current for the tunneling junctions with the resonant levels in the weak link are calculated. It seems likely that the current in these structures occurred due to resonant tunneling through a localized state. This resonant state effects the formation of long-range proximity effect. The subgap structure that appears on I-V characteristic of such junctions is caused by multiple Andreev reflections of quasiparticles at the interfaces. The I-V dependence is calculated for different values of the resonance parameter. This parameter is proportional to the ratio of the escape of the quasiparticle from the localized state into the superconducting electrodes. It is then shown that the larger subgap current corresponds to a smaller value of the resonant parameter.