Fulde-Ferrell-Larkin-Ovchinnikov state in heavy fermion superconductors

The Fulde-Feffell-Larkin-Ovchinnikov (FFLO) state is a novel superconducting state in a strong magnetic field characterized by the formation of Cooper pairs with nonzero total momentum (k up arrow, -k + q down arrow), instead of the ordinary BCS pairs (k up arrow, -k down arrow). A fascinating aspect of the FFLO state is that it exhibits inhomogeneous superconducting phases with a spatially oscillating order parameter and spin polarization. The FFLO state has been of interest in various research fields, not only in superconductors in solid state physics, but also in neutral Fermion superfluid of ultracold atomic gases and in color superconductivity in high energy physics. In spite of extensive studies of various superconductors, there has been no undisputed experimental verification of the FFLO state, mainly because of the very stringent conditions required of the superconducting materials. Among several classes of materials, certain heavy fermion and organic superconductors are believed to provide conditions that are favorable to the formation of the FFLO state. This review presents recent experimental and theoretical developments of the FFLO state mainly in heavy fermion superconductors. In particular we address the recently discovered quasi-two-dimensional superconductor CeCoIn5, which is a strong candidate for the formation of the FFLO state.