Restoration of Superconductivity in High Parallel Magnetic Fields in Layered Superconductors

We derive an equation determining the upper critical field $H_{c2\mathrm{}}^{\Vert }\left(T\right)$ parallel to conducting planes of a layered superconductor from the BCS theory. It extends the descriptions of $H_{c2\mathrm{}}^{\Vert }\left(T\right)$ 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 $T_c\left(H\right)\simeq T_c\left(0\right)$. A stability of the reentrant phase against fluctuations is discussed.