Surface superconducting states in mesoscopic superconductors under different boundary conditions

The surface superconductivity of a mesoscopic superconducting cylinder in an external parallel magnetic field is discussed within the framework of the linearized Ginzburg–Landau equation under different boundary conditions. For the superconductor/insulator interface, our calculations give the corrugation-like phase boundary Hc3(T), with oscillating ripples as a result of the switching of the "giant vortex state" wave function between different angular quantum number L. The tangent for the linear background of the phase boundary Hc3(T) is about 1.7 times Hc2(T), consistent with the well-known result in bulk surface superconductivity. For the superconductor/normal-metal interface, surface superconductivity disappears, accompanied by a decrease in the superconducting transition temperature Tc(H=0).