Subharmonic structure of Shapiro steps in frustrated superconducting arrays

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Abstract
Two-dimensional superconducting arrays with combined direct and alternating applied currents are studied both analytically and numerically. In particular, we investigate in detail current-voltage characteristics of a square array with 1/2 flux quantum per plaquette and triangular arrays with 1/2 and 1/4 flux quantum per plaquette. At zero temperature reduced equations of motion are obtained through the use of the translational symmetry present in the systems. The reduced equations lead to a series of subharmonic steps in addition to the standard integer and fractional giant Shapiro steps, producing devil’s staircase structure. This devil’s staircase structure reflects the existence of dynamically generated states in addition to the states originating from degenerate ground states in equilibrium. Widths of the subharmonic steps as functions of the amplitudes of alternating currents display Bessel-function-type behavior. We also present results of extensive numerical simulations, which indeed reveal the subharmonic steps together with their stability against small thermal fluctuations. Implications for topological invariance are also discussed.