Stable and metastable states in a superconducting "eight" loop in applied magnetic field

The stable and metastable states of different configurations of a loop in the form of an eight is studied in the presence of a magnetic field. We find that for certain configurations the current is equal to zero for any value of the magnetic field leading to a magnetic field independent superconducting state. The state with fixed phase circulation becomes unstable when the momentum of the superconducting electrons reaches a critical value. At this moment the kinetic energy of the superconducting condensate becomes of the same order as the potential energy of the Cooper pairs and it leads to an instability. Numerical analysis of the time-dependent Ginzburg-Landau equations shows that the absolute value of the order parameter changes gradually at the transition from a state with one phase circulation to another although the vorticity change occurs abruptly.