Abstract
Experimental evidence suggests that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state may be realized in the unconventional, heavy-fermion superconductor ${\mathrm{CeCoIn}}_{5}$. We present a self-consistent calculation of the field versus temperature phase diagram and order parameter structures for the FFLO states of quasi-two-dimensional $d$-wave superconductors. We calculate the spatially nonuniform order parameter, free energy density, and local density of states for magnetic fields parallel to the superconducting planes. We predict that the lower critical magnetic field transition between the spatially uniform and nonuniform FFLO state is second order. We discuss the signatures of the nonuniform FFLO state which should be observable in scanning tunneling microscopy measurements of the local density of states.
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