Abstract
This paper presents calculations of the current-voltage, dI/dV- and d2I/dV2-characteristics for a Josephson junction with a short one-dimensional channel, taking into account a “deformed” (anomalous) energy-dependent Andreev reflection function. Depending on the degree of deviation from the classical Andreev reflection coefficient, the “anomalous” functions are conditionally divided into weakly and strongly deformed coefficients. The excess Andreev current decrease is demonstrated with increasing anomaly factor due to the low probability of multiple Andreev reflections compared to the classical case. It has been shown that anomalous fractional (fractal) gap structures arise in the spectra, which require experimental verification. The analysis shows that on the spectrum of modified dynamic conductivity, when considering the anomalous function of Andreev reflections, the second Andreev feature becomes more pronounced as a minimum and the first feature manifests as a notable kink, which is absent in the classical dependencies for cases of high transparency obtained within the Averin–Bardas model. In the anomalous mode, the Andreev features appear as “dips” in the relatively high-energy region, which have also been detected in the Josephson junction spectra, indicating the possibility of generating high-frequency phonons.