Time domain simulation of Shapiro steps in Josephson junctions

Using the time domain formulation of the theory of the tunnel junction, we investigated Shapiro steps by digital simulation, under the condition of a constant current source given by . The integral kernels for the Josephson and the quasiparticle current were computed assuming a nonzero pair breaking parameter , and T = 0K. We obtained Irfdependence of the zeroth and first Shapiro steps, I0and I1, and the frequency dependence of , the maximum of the first Shapiro step as a function of Irf, for a few values of the junction capacitance. we found the following results. (1) (Ic:the critical current), showed the Riedel peak at , where ωgis the gap frequency 4 Δ/h. (2) For agrees well with that for the constant voltage bias. (3) As the frequency becomes smaller below is severely depressed compared to that for the constant voltage bias.