Voltage controllable superconducting state in the multiterminal superconductor-normal-metal bridge

We study voltage controllable superconducting state in a multiterminal bridge composed of the dirty superconductor/pure normal metal (SN) bilayer and pure normal metal. In the proposed system small control current I-ctrl flows via normal bridge, creates voltage drop V, and modifies the distribution function of electrons in a connected SN bilayer. In the case of a long normal bridge the voltage-induced nonequilibrium effects could be interpreted in terms of increased local electron temperature. In this limit we experimentally find the large sensitivity of critical current I-c of Cu/MoN/Pt-Cu bridge to I-ctrl and relatively large current gain which originate from steep dependence of I-c on temperature and large I-c (comparable with theoretical depairing current of the superconducting bridge). In the short normal bridge deviation from equilibrium cannot be described by a simple increase in local temperature, but we also theoretically find large sensitivity of I-c to control current/voltage. In this limit we predict existence at finite V of the so-called in-plane Fulde-Ferrell state with spontaneous currents in the SN bilayer. We argue that its appearance is connected with voltage-induced paramagnetic response in the N layer.