FRACTIONAL SHAPIRO STEPS IN LADDER JOSEPHSON ARRAYS

We study the response of Josephson ladder arrays (1 x N plaquettes) to a combined ac and dc current. For N greater-than-or-equal-to 1, the arrays are predicted to exhibit Shapiro steps at voltages < V > = nN hBAR-omega/(2e). for n = 1/2, 1, 3/2, ..., over a broad range of fields f = PHI/PHI(0) (PHI = flux per plaquette, PHI(0) = hc/2e). The calculated half-steps persist even in single-plaquette "arrays" at all fields f not-equal 0, and, when the critical currents parallel to the applied current are sufficiently unequal, even at f = 0. Measurements of the step widths DELTA-I1/2(f) and DELTA-I1(f) for 1 x 600 ladder arrays of Nb-Au-Nb junctions are in good agreement with the calculations.