Restoration of superconductivity in high parallel magnetic fields in layered superconductors

We derive an equation determining the upper critical field H-c2(parallel to)(T) parallel to conducting planes of a layered superconductor from the BCS theory. It extends the descriptions of H-c2(parallel to)(T) within the Ginzburg-Landau-Abrikosov-Gor'kov theory and the Lawrence-Doniach model to the case of strong magnetic fields. From this equation, it follows that orbital effects of an electron motion along an open Fermi surface in a magnetic field start to restore superconductivity at magnetic fields higher than the quasiclassical upper critical field and result in the appearance of a reentrant phase with T-c(H)similar or equal to T-c(O). A stability of the reentrant phase against fluctuations is discussed.