Multiple-Nanowire Superconducting Quantum Interference Devices: Critical Currents, Symmetries, and Vorticity Stability Regions

An ordinary superconducting quantum interference device (SQUID) contains two weak links connected in parallel. We model a multiple-wire SQUID (MW-SQUID), generalized in two ways. First, the number of weak links, which are provided by parallel superconducting nanowires, is larger than two. Second, the current-phase relationship of each nanowire is assumed linear, which is typical for a homogeneous superconducting thin wire. For such MW-SQUIDs, our model predicts that the critical current ($I_c$) is a multi-valued function of the magnetic field. We also calculate vorticity stability regions (VSR), i.e., regions in the current-magnetic field plane in which, for a given distribution of vortices, the currents in all wires are below their critical values, so the vortices do not move between the cells. The VSRs have rhombic shapes in the case of two-wire SQUIDS and have more complicated shapes in the case of many nanowires. We present a classification of such VSRs and determine conditions under which VSR is disjoint, leading to 100\% supercurrent modulation and quantum phase transitions. According to the model, the maximum critical current curves obey $IB$ symmetry, while each VSR obeys $IBV$ symmetry. The model predicts conditions at which MW-SQUID exhibits a perfect diode effect in which the critical current of one polarity is zero while it is not zero for the opposite polarity of the bias current. We also provide a classification of the stability regions produced by (1) completely symmetric, (2) phase disordered, (3) position disordered, (4) critical current disordered, and (5) completely disordered multi-wire SQUIDs.