Simulation of Shapiro Steps in a Josephson Junction Based on the Microscopic Theory of the Tunnel Junction

Abstract

Shapiro steps in a Josephson tunnel junction were investigated by the simulation based on the microscopic theory of the tunnel junction. A nonzero pair-breaking parameter, δ=0.1, was assumed to make the computation tractable. The dependence of the step width of the zeroth- and the first-order Shapiro steps on the rf power was calculated for the frequency range, 0.2fg≦f≦1.5fg, where fg is the energy gap frequency. The steps are unstable at low frequencies, f\\lesssim0.7fg, and for large values of the junction capacitance. They become stable for larger frequencies. The steps are stable, on the whole, for small capacitance. The frequency dependence of the first maximum of the first-order Shapiro step, I1MAX, was obtained. It shows the Riedel peak, with even larger height than the prediction of the theory assuming a constant voltage source for a small capacitance.