Quasi-one-dimensional superconductors at high magnetic field

Summary form only given. We determine the phase diagram of a quasi-one-dimensional conductor (weakly coupled chains system with an open Fermi surface) in a magnetic field perpendicular to the chains, taking into account exactly the quantum effects of the field. The usual Ginzburg-Landau regime is followed, when the field is increased, by a cascade of superconducting phases separated by first order transitions, which ends with a strong reentrance of the superconducting phase. This high-field superconductivity can survive even in the presence of Pauli pair breaking because the quasi-one-dimensional Fermi surface allows to construct a Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state which can exist far above the Pauli limited field. We show that the superconducting state evolves from an Abrikosov vortex lattice in weak field towards a Josephson vortex lattice in the reentrant phase. Between these two limits, the vortex lattice show a novel kind of symmetry of a laminar type. For a very weak coupling between chains, the cascade of phase transitions disappears: the Ginzburg-Landau regime is followed by a regime characterized by an upward curvature of the critical field H/sub c2/(T) due to the existence of the LOFF state. This latter result is in agreement with recent measurements of the critical field of some quasi-one-dimensional organic superconductors.