We theoretically investigate a voltage-biased normal metal–superconductor–normal metal (NSN) junction. Using the nonequilibrium Green's function technique, we derive a quantum kinetic equation to determine the superconducting order parameter self-consistently. The derived equation is an integral-differential equation with memory effects. We solve this equation by converting it into a system of ordinary differential equations with the use of a pole expansion of the Fermi-Dirac function. When the applied voltage exceeds the critical value, the superconductor switches to the normal state. We find that when the voltage is decreased from the normal phase, the system relaxes to a Larkin-Ovchinnikov-type (LO) inhomogeneous superconducting state, even in the absence of a magnetic Zeeman field. We point out that the emergence of the LO-type state can be attributed to the nonequilibrium energy distribution of electrons due to the bias voltage. We also point out that the system exhibits bistability, which leads to hysteresis in the voltage-current characteristic of the NSN junction.

• Received 9 January 2024
• Revised 12 February 2024
• Accepted 28 February 2024

DOI:https://doi.org/10.1103/PhysRevB.109.104502