Bistability in voltage-biased normal-metal/insulator/superconductor/insulator/normal-metal structures

As a generic example of a voltage-driven superconducting structure, we study a short superconductor connected to normal leads by means of low transparency tunnel junctions with a voltage bias V between the leads. The superconducting order parameter Delta is to be determined self-consistently. We study the stationary states as well as the dynamics after a perturbation. The system is an example of a dissipative driven nonlinear system. Such systems generically have stationary solutions that are multivalued functions of the system parameters. It was discovered several decades ago that superconductors outside equilibrium conform to this general rule in that the order parameter as a function of driving may be multivalued. The main difference between these previous studies and the present work is the different relaxation mechanisms involved. This does not change the fact that there can be several stationary states at a given voltage. It can however affect their stability as well as the dynamics after a perturbation. We find a region in parameter space where there are two stable stationary states at a given voltage. These bistable states are distinguished by distinct values of the superconducting order parameter and of the current between the leads. We have evaluated (1) the multivalued superconducting order parameter Delta at given V, (2) the current between the leads at a given V, and (3) the critical voltage at which superconductivity in the island ceases. With regards to dynamics, we find numerical evidence that only the stationary states are stable and that no complicated nonstationary regime can be induced by changing the voltage. This result is somewhat unexpected and by no means trivial, given the fact that the system is driven out of equilibrium. The response to a change in the voltage is always gradual even in the regime where changing the interaction strength induces rapid anharmonic oscillations of the order parameter.