The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase can arise in a superconductor in large magnetic field. Among its characteristics are Cooper pairs with nonzero total momentum and a spatially non-uniform order parameter.
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Two independent publications in the year 1964, one by Peter Fulde and Richard A. Ferrell [1] and the other by Anatoly Larkin and Yuri Ovchinnikov,[2][3] theoretically predicted a new state in a certain regime of superconductors in high magnetic fields. This particular superconducting state is nowadays known as the Fulde-Ferrell-Larkin-Ovchinnikov state, abbreviated FFLO state (also LOFF state). Since then, experimental observation of the FFLO state has been searched for in different classes of superconducting materials, first in thin films and later in exotic superconductors such as heavy-fermion [4] and organic [5] superconductors, but so far there is no undisputed experimental evidence. In recent years, the concept of the FFLO state was taken up in the field of atomic physics and experiments to detect the FFLO state in atomic ensembles in optical lattices.[6]
If a BCS superconductor with a ground state consisting of Cooper pair singlets (and center-of-mass momentum q=0) is subjected to an applied magnetic field, then the spin structure is not affected until the Zeeman energy is strong enough to flip one spin of the singlet and break the Cooper pair, thus destroying superconductivity (paramagnetic or Pauli pair breaking). If instead one considers the normal, metallic state at the same finite magnetic field, then the Zeeman energy leads to different Fermi surfaces for spin-up and spin-down electrons, which can lead to superconducting pairing where Cooper pair singlets are formed with a center-of-mass momentum q which is finite, corresponding to the displacement of the two Fermi surfaces. The non-vanishing q of the Cooper pairs leads to a spatially modulated order parameter (periodic with wave vector q).[5]
For the FFLO phase to appear, it is required that Pauli pair breaking is the relevant mechanism to suppress superconductivity (Pauli limiting field, also Chandrasekhar-Clogston limit). In particular, orbital pair breaking (when the vortices induced by the magnetic field overlap in space) has to be weaker, which is not the case for conventional superconductors. Certain unconventional superconductors, on the other hand, may favor Pauli pair breaking: materials with large effective electron mass or layered materials (with quasi-two-dimensional electrical conduction).[4]
Heavy-fermion superconductivity is caused by electrons with a drastically enhanced effective mass (the heavy fermions, also heavy quasiparticles), which suppresses orbital pair breaking. Furthermore, certain heavy-fermion superconductors, such as CeCoIn5, have a layered crystal structure, with somewhat two-dimensional electronic transport properties.[4] Therefore, detailed studies close to the critical field have been performed on CeCoIn5, and there is evidence that certain regimes in the phase diagram of this material should be interpreted in terms of the FFLO state.[7][4]
Some organic superconductors have very anisotropic conductivity; in particular there are compounds which are good realizations of quasi-two-dimensional electronic transport. Also here there are candidate materials for the FFLO phase, and for the organic superconductors of the κ-(ET)2X and λ(BETS)2X there is experimental data indicating an FFLO region in the phase diagram of these materials.[5]