Restoration of superconductivity at high magnetic fields in layered high-T_c and organic superconductors

An integral equation determining the upper critical field parallel to the conducting plane of a layered superconductor is derived from microscopic BCS theory. From this equation, it follows that the superconductivity-destruction mechanism due to the orbital effect becomes ineffective at magnetic fields higher than a critical field H_c4 due to a quantum nature of an electron motion in a magnetic field. This leads to the appearance of reentrant superconducting phase with dT_c/dH > 0 in the case of p-pairing and under certain conditions in the case of s(d)-pairing. We also show that the orbital effect cannot destroy superconductivity at T = 0 at arbitrary magnetic fields. Therefore qualitative deviations from the description of GLAG (WHH) theory have to appear for arbitrary symmetry of the order parameter at low enough temperatures. We argue that p(s)-wave superconductor Sr₂RuO₄ as well as s(d)-wave superconductors TlBa₂CaCu₂O₇, Tl₂Ba₂Ca₃Cu₄O_x, β-(ET)₂AuI₂, and κ-(ET)₂I₃ are good candidates for the observation of the above mentioned phenomena.