Asymmetric nanowire SQUID: Linear current-phase relation, stochastic switching, and symmetries

We study nanostructures based on two ultrathin superconducting nanowires connected in parallel to form a superconducting quantum interference device (SQUID). The measured function of the critical current versus magnetic field, I-C (B), is multivalued, asymmetric, and its maxima and minima are shifted from the usual integer and half integer flux quantum points. We also propose a low-temperature-limit model which generates accurate fits to the I-C (B) functions and provides verifiable predictions. The key assumption of our model is that each wire is characterized by a sample-specific critical phase phi(C) defined as the phase difference at which the supercurrent in the wire is the maximum. For our nanowires fC is much greater than the usual pi/2, which makes a qualitative difference in the behavior of the SQUID. The nanowire current-phase relation is assumed linear, since the wires are much longer than the coherence length. The model explains single-valuedness regions where only one vorticity value n(v) is stable. Also, it predicts regions where multiple vorticity values are stable because the Little-Parks (LP) diamonds, which describe the region of stability for each winding number nv in the current-field diagram, can overlap. We also observe and explain regions in which the standard deviation of the switching current is independent of the magnetic field. We develop a technique that allows a reliable detection of hidden phase slips and use it to determine the boundaries of the LP diamonds even at low currents where IC (B) is not directly measurable.