Numerical investigation and model approximation for the hysteretic current-voltage characteristics of Josephson junctions with nonlinear quasiparticle resistance

We present a model analysis for the current-voltage (I-V) characteristics of Josephson junctions having super-conductor-insulator-superconductor (SIS) structure. The numerical result for the V_m value, which is the product of the maximum supercurrent and the observed subgap resistance, shows a marked decrease with increasing junction critical current density (J_c). The marked decrease is independent of leak current. Increasing J_c reduces he junction capacitance C_J and enlarges the amplitude of the junction voltage oscillation. Nonlinearity of the quasiparticle resistance restricts the voltage oscillation amplitude to the gap voltage, which results in the rapid decrease of the V_m value. In this paper, we introduce a sinusoidal oscillation model for the junction voltage, and derive the approximated expressions for the V_m value. The model approximation results agree well with the numerical results.