Quantized voltage plateaus in Josephson-junction arrays: A numerical study.

Abstract

We study numerically the quantized voltage plateaus in an N\ifmmode\times\else\texttimes\fi{}N array of resistively shunted Josephson junctions subjected to a combined dc and ac applied current ${\mathit{I}}_{\mathrm{dc}}$+${\mathit{I}}_{\mathrm{ac}}$sin(2\ensuremath{\pi}\ensuremath{\nu}t), and a transverse magnetic field equal to p/q==f flux quanta per plaquette (p and q relatively prime integers). With periodic transverse boundary conditions, we find plateaus at all voltages satisfying 〈V〉=nNh\ensuremath{\nu}/(2eq), where n is an integer, and the angular brackets 〈...〉 denote a time average. With free transverse boundary conditions, additional steps at 〈V〉=Nh\ensuremath{\nu}/(4eq) sometimes appear. For f=1/5 and 2/5, we study the motion of the vortex lattice on the steps. At both fields, on every step, the lattice moves an integer number of array lattice constants per cycle of the ac field. For both zero and finite applied transverse magnetic field, the width of the steps varies sinusoidally with ${\mathit{I}}_{\mathrm{ac}}$, in a manner reminiscent of that seen in single Josephson junctions. At a given field and current, the steps ``melt'' at a temperature no higher than the transition temperature of the underlying array at the same field and zero current. On the steps, the time-dependent voltage across the array has strong harmonics at multiples of the fundamental frequency. Off the steps, the power spectrum of the voltage has an apparently broad band with possible subharmonic structure.