Fulde-Ferrell-Larkin-Ovchinnikov state in d-wave superconductors

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can be found in layered d-wave superconductors such as high $T_c$ cuprates and $\kappa$-(ET)$_2$ salts in a planar magnetic field. We show the superconducting order parameter forms two dimensional crystalline lattice in the FFLO state for d-wave superconductors. Also the quasiparticle density of states and the thermodynamics of FFLO state are constructed. Therefore STM or NMR will provide a definitive test for the existence of the FFLO state.