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

TL;DR

This study numerically investigates two-dimensional Josephson junction arrays using RSJ and TDGL models, revealing fractional giant Shapiro steps and highlighting the importance of boundary conditions in accurately modeling the system.

Contribution

It demonstrates that the TDGL model with global current conservation reproduces the fractional giant Shapiro steps seen in the RSJ model, showing local current conservation can be relaxed.

Findings

Fractional giant Shapiro steps are observed in both models.

The FTBC boundary condition minimizes boundary effects.

Qualitative differences appear at higher frequencies.

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.