Giant Shapiro steps for two-dimensional Josephson-junction arrays with time-dependent Ginzburg-Landau dynamics

Abstract

Two-dimensional Josephson junction arrays at zero temperature are investigated numerically within the resistively shunted junction (RSJ) model and the time-dependent Ginzburg-Landau (TDGL) model with global conservation of current implemented through the fluctuating twist boundary condition (FTBC). Fractional giant Shapiro steps are found for {\em both} the RSJ and TDGL cases. This implies that the local current conservation, on which the RSJ model is based, can be relaxed to the TDGL dynamics with only global current conservation, without changing the sequence of Shapiro steps. However, when the maximum widths of the steps are compared for the two models some qualitative differences are found at higher frequencies. The critical current is also calculated and comparisons with earlier results are made. It is found that the FTBC is a more adequate boundary condition than the conventional uniform current injection method because it minimizes the influence of the boundary.

arXiv comment6 pages including 4 figures in two columns, final version

References in corpus (4)

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• Dynamics of d-wave Vortices: Angle-Dependent Nonlinear Hall Effect
• Flux noise and Fluctuation conductivity in Unfrustrated Josephson Junction Arrays
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Cited by in corpus (6)

• Residual discrete symmetry of the five-state clock model
• Resistivity scaling and critical dynamics of fully frustrated Josephson-junction arrays with on-site dissipation
• Finite-temperature resistive transition in the two-dimensional XY gauge glass model
• Dynamic transition and Shapiro-step melting in a frustrated Josephson-junction array
• Dynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder
• Critical current from dynamical boundary instability for fully frustrated Josephson junction arrays