Fractional Shapiro steps in ladder Josephson arrays

Abstract

We study the response of Josephson ladder arrays (1\ifmmode\times\else\texttimes\fi{}N plaquettes) to a combined ac and dc current. For N\ensuremath{\ge}1, the arrays are predicted to exhibit Shapiro steps at voltages 〈V〉=nN\ensuremath{\Elzxh}\ensuremath{\omega}/(2e) for n=1/2,1,3/2, . . ., over a broad range of fields f=\ensuremath{\Phi}/${\mathrm{\ensuremath{\Phi}}}_{0}$ (\ensuremath{\Phi}=flux per plaquette, ${\mathrm{\ensuremath{\Phi}}}_{0}$=hc/2e). The calculated half-steps persist even in single-plaquette ``arrays'' at all fields f\ensuremath{\ne}0, and, when the critical currents parallel to the applied current are sufficiently unequal, even at f=0. Measurements of the step widths \ensuremath{\Delta}${\mathit{I}}_{1/2}$(f) and \ensuremath{\Delta}${\mathit{I}}_{1}$(f) for 1\ifmmode\times\else\texttimes\fi{}600 ladder arrays of Nb-Au-Nb junctions are in good agreement with the calculations.