Superconductivity initiated by electric field in high-temperature superconductor at $T>T_{c}$

The theory of occurrence of superconductivity in the plate of high-temperature superconductor under electric field vertical to it, when the carrier concentration lies outside of the region of existence of superconductivity at the temperature $T<T_{c}^{\operatorname{max}}$, was developed. The calculation was carried out for the layer of lanthanum strontium cuprate under the fields of 10$^{-1}$ V/nm $\ge E \ge$ 10$^{-2}$ V/nm at various temperatures and hole concentrations. It was demonstrated that the quasi-two-dimensional superconducting layer of several Angstrom in thickness occurs near surface of the plate, moreover thickness of this layer does not depend on magnitude of the field, and depends only on temperature and on hole concentration.