Structurally asymmetric d.c. SQUID’s in the presence of coupling energy inhomogeneity of the junctions studied by means of the reduced two-junction interferometer model

The effects of structural asymmetries and of inhomogeneities in the junction parameters on the electrodynamic response of conventional d.c. SQUID’s are studied both analytically and numerically. By a first-order perturbative expansion with respect to the parameter β and to the deviation parameters describing structural asymmetry and inhomogeneity, we write the reduced dynamical equation for the average superconducting phase difference of a conventional d.c. SQUID. As in homogeneous and symmetric SQUID’s, the resulting dynamical equation is seen to be similar to that of a single junction with an unconventional current-phase relation characterized by a second harmonic contribution; in addition, a cosine term appears as a consequence of superconducting coupling inhomogeneity. By means of the reduced dynamical equation, the I-V characteristics in the presence of an external rf field and the critical current of the device are studied in the absence of noise. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005