Larkin-Ovchinnikov-Fulde-Ferrell state in quasi-one-dimensional superconductors.

The properties of a quasi-one-dimensional (quasi-1D) superconductor with an open Fermi surface are expected to be unusual in a magnetic field. On the one hand, the quasi-1D structure of the Fermi surface strongly favors the formation of a non-uniform state (Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state) in the presence of a magnetic field acting on the electron spins. On the other hand, a magnetic field acting on an open Fermi surface induces a dimensional crossover by confining the electronic wave-functions along the chains of highest conductivity, which results in a divergence of the orbital critical field and in a stabilization at low temperature of a cascade of superconducting phases separated by first order transistions. In this paper, we study the phase diagram as a function of the anisotropy by taking into account on the same footing the paramagnetic and the orbital effects of the field. We discuss in details the experimental situation in the quasi-1D organic conductors of the Bechgaard salts family and argue that they appear as good candidates for the observation of the LOFF state, provided that their anisotropy is large enough. Recent experiments on the organic quasi-1D superconductor (TMTSF)2ClO4 are in agreement with the results obtained in this paper and could be interpreted as a signature of a high-field superconducting phase. We also point out the possibility to observe a LOFF state in some of the recently discovered