Superconductivity of quasi-one-dimensional conductors in a high magnetic field

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Abstract
We determine the phase diagram of a quasi-one-dimensional superconductor (weakly coupled chains system with an open Fermi surface) in a magentic field. A field H(0,H,0) along the y direction (perpendicular the direction x of highest conductivity) tends to confine the electronic motion in the z direction. At low temperature, this effect cannot be neglected and the Ginzburg-Landau theory breaks down. We find that 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 where the chains interact by Josephson coupling. This high-field superconductivity can survive even in the presence of Pauli pair breaking because the quasi-one-dimensional Fermi surface allows one to construct a Larkin-Ovchinnikov-Fulde-Ferrell state that can exist far above the Pauli-limited field. Moreover, elastic scattering does not destroy the superconducting phases in clean materials with sufficiently large anistropy. 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 order parameter and the current distribution show a laminar-type symmetry. The relevance of our results is discussed for quasi-one-dimensional organic superconductors and quasi-two-dimensional superconductors.