Self-heating phenomena in superconducting tunneling junctions

We have developed a theory of anomalous sub-gap currents in small gap superconducting multiple tunneling junctions. The sub-gap current at low bath temperature shows a hierarchy of steps, spaced as V=2Δ/en, with n=2,3,… These steps occur as a result of specific mechanism of energy accumulation in cycles of tunneling-back tunneling events. Their shape and magnitude significantly depend on junction parameters and bath temperature.