INTEGER AND HALF-INTEGER STEPS OF A JOSEPHSON-JUNCTION SINGLE PLAQUETTE AND A DE SQUID

Abstract

We have calculated the boundaries and the widths of the integer (n = 0 and 1) and the half-integer (n = 1/2) Shapiro steps in a Josephson-junction single plaquette (SP) and a de SQUID in an external magnetic field. By introducing an asymmetry in the critical currents of the junctions, parallel and perpendicular to the external-current direction, the equations of motion for the SP become similar to those of a de SQUID. We have found that the de I - V curve does not depend on the details of the equations of motion, which in turn results in step boundaries for the SP with a high asymmetry ratio almost identical to those for a de SQUID with a small loop inductance, The correspondence between the asymmetry ratio in a SP and the inverse of the inductance parameter in a de SQUID holds even in the intermediate inductance region. Inclusion of the capacitive term in the equations of motion of a SP has minor effects on the step widths in the non-hysteretic region, whereas the change of the external frequency induces a noticeable difference in the characteristics of the step widths.