Onset of superconductivity in a voltage-biased normal-superconducting-normal microbridge

We study the stability of the normal state in a mesoscopic NSN junction biased by a constant voltage V with respect to the formation of the superconducting order. Using the linearized time-dependent Ginzburg-Landau equation, we obtain the temperature dependence of the instability line, V-inst(T), where nucleation of superconductivity takes place. For sufficiently low biases, a stationary symmetric superconducting state emerges below the instability line. For higher biases, the normal phase is destroyed by the formation of a nonstationary bimodal state with two superconducting nuclei localized near the opposite terminals. The low-temperature and large-voltage behavior of the instability line is highly sensitive to the details of the inelastic relaxation mechanism in the wire. Therefore, experimental studies of V-inst(T) in NSN junctions may be used as an effective tool to access the parameters of the inelastic relaxation in the normal state. DOI: 10.1103/PhysRevB.87.020501