Revival of superconductivity in high magnetic fields and a possible (formula presented)-wave pairing in (formula presented)

From the BCS theory, we derive an equation which accounts for quantum effects of an electron motion along open Fermi surfaces and determines the upper critical field (Formula presented) perpendicular to the chains of a quasi-one-dimensional conductor. This equation demonstrates two unusual phenomena: (1) restoration of superconductivity at (Formula presented) in (Formula presented)-wave superconductors, where (Formula presented) is the quasiclassical upper critical field; (2) surviving of superconductivity at (Formula presented) (Formula presented) in (Formula presented)-wave superconductors, where (Formula presented) is the Clogston-Chandrasekhar paramagnetic limiting field; the critical field (Formula presented) is introduced in the paper. An analysis of recent experimental data by I. J. Lee, M. J. Naughton, G. M. Danner, and P. M. Chaikin [Phys. Rev. Lett. 78, 3555 (1997)] shows that superconductivity significantly exceeds (Formula presented) for b direction of a magnetic field in (Formula presented) This demonstrates a strong suppression of the Pauli pair breaking effects and may reflect a (Formula presented)-wave pairing of electrons.