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We theoretically investigate a voltage-biased normalmetal-superconductor-normal metal (N-S-N) junction. Using the nonequilibriumGreen's function technique, we derive a quantum kinetic equation, to determinethe superconducting order parameter self-consistently. The derived equation isan integral-differential equation with memory effects. We solve this equationby converting it into a system of ordinary differential equations with the useof a pole expansion of the Fermi-Dirac function. When the applied voltageexceeds the critical value, the superconductor switches to the normal state. Wefind that when the voltage is decreased from the normal phase, the systemrelaxes to a Larkin-Ovchinnikov (LO)-type inhomogeneous superconducting state,even in the absence of a magnetic Zeeman field. We point out that the emergenceof the LO-type state can be attributed to the nonequilibrium energydistribution of electrons due to the bias voltage. We also point out that thesystem exhibits bistability, which leads to hysteresis in the voltage-currentcharacteristic of the N-S-N junction.

Emergence of Larkin-Ovchinnikov-type superconducting state in a voltage-driven superconductor