Gap symmetry and a revival of superconductivity in high parallel magnetic fields in Q2D and Q1D organic, high-T_c, and Sr₂RuO ₄ compounds

From the BCS theory, we derive an equation determining the upper critical field, H_c2(T), parallel to conducting planes of both layered Q2D and Q1D superconductors. It extends the quasiclassical Ginzburg-Landau-Abrikosov- Gor'kov (GLAG) and Lawrence-Doniach descriptions of H_c2(T) to the case of high magnetic fields where the quantum nature of an electron motion along open Fermi surfaces is important. This equation demonstrates two new phenomena: (1) a complete restoration of superconductivity at H ≃ H _c5 > H_c2(0) in the case of p-wave pairing of electrons; (2) a surviving of superconductivity at H_c2(0) < H < H _p* in the case of s(d)-wave pairing, where H_p* ≠ H_p [Here, H_c2(0) and H_p are the quasiclassical GLAG upper critical field and the paramagnetic Clogston-Chandrasekhar limiting field, correspondingly; H_c5 and H_p* are defined in the text]. Our analysis of recent experimental data on (TMTSF)₂PF₆ by I. J. Lee et al. and M. J. Naughton et al. shows that superconductivity significantly exceeds H _p*. This demonstrates a strong suppression of the Pauli pair-breaking effects and may reflect a p-wave pairing of electrons. We propose to measure H_c2(T) in Sr₂RuO₄ (which is believed to be a p-wave superconductor) to prove a symmetry of a superconducting order parameter.