Two-component Ginzburg–Landau theory of superconducting surfaces in transverse electric field

A boundary condition for the Ginzburg–Landau wave function of a two-component superconductor at surfaces biased by a strong transverse electric field is derived within the de Gennes approach. This boundary condition depends on two correlation lengths of order parameters. A small correlation length leads to the oscillations of the shift of the critical temperature of superconducting layers in the transverse electric field on layer width L. The superconducting temperature Tc oscillates with the layer width also in the absence of the electric field in the two-band model. A simple theory of the field effect on the superconducting temperature of layers is developed.