Anomalous proximity effect in a superconductor under a strong electric field

We considered a superconductor subjected to a strong dc electric field. We show that even a short distance penetrating electric field can strongly affect a superconducting-normal interface. Using the Ginzburg-Landau equation complemented by the boundary conditions modified by the electric field we calculated the order parameter, distribution at the surface, the surface energy, the critical Josephson current and the voltage current characteristic of a superconductor, separated by a thin layer where a strong electric field is applied.