Nonlinear transport theory for hybrid normal-superconducting devices

We report a theory for analyzing nonlinear DC transport properties of mesoscopic or nanoscopic normal-superconducting (NS) systems. Special attention was paid such that our theory satisfies gauge invariance. At the nonlinear regime, our theory allows the investigation of a number of important problems: for NS hybrid systems we have derived the general nonlinear current-voltage characteristics in terms of the scattering Green's function, the second-order nonlinear conductance at the weakly nonlinear regime, and nonequilibrium charge pileup in the device that defines the electrochemical capacitance coefficients.