Sign-alternating deviation of a single-particle current–voltage characteristic of a dirty SIN junction

A formula for the single-particle current–voltage characteristic $J(V,T,c,\beta)$ of “dirty” (with low concentrations of identical nonmagnetic impurities in the disordered insulator layer) SIN junctions (S is a superconductor, I is a disordered insulator, and N is a normal metal) has been obtained in the region of low temperatures and voltages $0 \leqslant \vert eV \vert \ll T \ll \Delta_{0}$, where $e$ is the elementary charge, $\Delta_{0}$ is the superconducting gap in the S edge of a junction at the temperature $T = 0$, $V$ is the voltage across the junction, $c \ll 1$ is the dimensionless concentration of impurities in the I layer, $\beta = (\varepsilon_{0}^{} - \mu)/\Delta_{0}^{}$ is the dimensionless deviation of the single-impurity electron energy level $\varepsilon_0$ relevant for this problem (on identical impurities in the I layer) from the electron chemical potential $\mu$ of the junction. It has been shown that an anomalously large sign-alternating deviation of the single-particle current–voltage characteristic of the dirty SIN junction from the value calculated by the existing theoretical expression is observed in a certain limited region $\Omega_{d}(c, \beta)$ on the $(c, \beta)$ parameter plane in the presence of random narrow-band quantum jumpers in the disordered I layer. A numerical example has demonstrated that the relative deviation of the single-particle current–voltage characteristic at typical values of the parameters of the dirty SIN junction in the region $\Omega_{d}(c, \beta)$ can reach several orders of magnitude, which ensures the possibility of the experimental observation of this effect. The conditions for the applicability of the considered model of the dirty SIN junction have been discussed and the scheme of the corresponding experiment has been proposed.