Dynamics of single-plaquette Josephson-junction arrays

Abstract

We have studied, both analytically and numerically, the response of a single-plaquette square array to a combined ac and dc current. The array consists of 2\ifmmode\times\else\texttimes\fi{}2 superconductors coupled by overdamped Josephson junctions. Our study shows that even a single-plaquette array exhibits all the essential features found in the large arrays; in zero magnetic field, or with a current in the diagonal direction, the array does not show any fractional Shapiro step. On the other hand, in a transverse external field except with diagonal application of a current, the dc I-V characteristics exhibit very rich structure, i.e., a step at every rational number of 2e〈V〉/h\ensuremath{\nu}. The step widths \ensuremath{\Delta}${\mathit{I}}_{\mathit{n}}$ calculated for n=1/2,1/3, 1) / 4 , 1/5, and 1/6 with varying filling factor f show varied characteristic features.