Bi-stability in voltage-biased NISIN structures

TL;DR

This paper investigates voltage-driven bi-stability in a superconductor-normal metal structure, revealing two stable states with distinct order parameters and currents, and analyzing their stability and dynamics under voltage perturbations.

Contribution

It demonstrates the existence of bi-stable superconducting states in a voltage-biased NISIN structure and analyzes their stability and dynamic response.

Findings

Identification of two stable stationary states at a given voltage.

Determination of the multi-valued superconducting order parameter Δ.

Establishment of the stability of stationary states under voltage changes.

Abstract

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 of the system 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 bi-stable states are distinguished by distinct values of the superconducting order parameter $\Delta$ and of the current between the leads. We have evaluated (1) the multi-valued 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 the stationary states are stable and that no complicated non-stationary 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.