Mean-Field Theory of a Quasi-One-Dimensional Superconductor in a High Magnetic Field

In a quasi-1D superconductor (weakly coupled chains system) with an open Fermi surface, a high magnetic field stabilizes a cascade of superconducting phases wich ends in a strong reentrance of the superconducting phase. The superconducting state evolves from a triangular Abrikosov vortex lattice in the weak field regime towards a Josephson vortex lattice in the reentrant phase. We study the properties of these superconducting phases from a microscopic model in the mean-field approximation. The critical temperature is calculated in the quantum limit approximation (QLA) where only Cooper logarithmic singularities are retained while less divergent terms are ignored. The effects of Pauli pair breaking (PPB) and impurity scattering are taken into account. The Gor'kov equations are solved in the same approximation but ignoring the PPB effect. We derive the GL expansion of the free energy and obtain the specific heat jump at the transition. We show that a gap opens at the Fermi level in the quasi-particle excitation spectrum. The QLA clearly shows how the system evolves from a quasi-2D and BCS-like behavior in the reentrant phase toward a gapless behavior at weaker field. The calculation is extended beyond the QLA whose validity is discussed in detail