Apparent critical currents and rf steps in a second-order proximity-induced Josephson effect

Numerical I(V) results for superconductor–insulator–normal-metal (S-I-N) tunnel junctions suggest that a unified treatment of the weak excess currents (pair-field susceptibility) and proximity-induced Josephson-effect (PJE) phenomena [apparent critical currents, rf steps, and Fraunhofer-like ${\mathit{I}}_{\mathit{c}}$(B)] is provided by the Geshkenbein-Sokol time-dependent Ginzburg-Landau theory of second-order Josephson effects in S-I-N tunnel junctions. The numerical results and other considerations speak against a recent suggestion that a phase-slip center in the superconducting tip may play a role in PJE point-contact experiments. These considerations confirm the utility of proximity Josephson-effect experiments to probe unconventional superconductivity in materials such as ${\mathrm{UBE}}_{13}$, as first pointed out by Han et al.