Violation of the Ambegaokar–Baratoff relation in dirty S-I-S junctions

It has been shown that the presence of narrow-gap quantum jumpers in “dirty” (low concentrations of identical nonmagnetic impurities in the insulator layer) superconductor-insulator-superconductor (S-I-S) junctions results in a significant deviation of the critical supercurrent (Josephson current) in the temperature range $0 \leqslant T\leqslant T_c$ ($T_c$ is the superconducting transition temperature in the $S$ shores of the junction) from the value given by the known Ambegaokar–Baratoff relation. It has been found that the character of this deviation changes at a certain nonzero temperature $T_b< T_c$: this deviation is negative at $0\leqslant T< T_b$ (deficiency of the supercurrent), whereas it is positive at $T_b<T\leqslant T_c$ (excess of the supercurrent). Estimates indicate that experimental manifestation of this effect can be detected.