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The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state has received renewedinterest recently due to the experimental indication of its presence inCeCoIn$_5$, a quasi 2-dimensional (2D) d-wave superconductor. However directevidence of the spatial variation of the superconducting order parameter, whichis the hallmark of the FFLO state, does not yet exist. In this work we explorethe possibility of detecting the phase structure of the order parameterdirectly using conductance spectroscopy through micro-constrictions, whichprobes the phase sensitive surface Andreev bound states of d-wavesuperconductors. We employ the Blonder-Tinkham-Klapwijk formalism to calculatethe conductance characteristics between a normal metal (N) and a 2D $s$- or$d_{x^2-y^2}$-wave superconductor in the Fulde-Ferrell state, for all barrierparameter $z$ from the point contact limit ($z=0$) to the tunneling limit ($z\gg 1$). We find that the zero-bias conductance peak due to these surfaceAndreev bound states observed in the uniform d-wave superconductor is split andshifted in the Fulde-Ferrell state. We also clarify what weighted bulk densityof states is measured by the conductance in the limit of large $z$.Comment: 10 pages, 13 figure

Conductance characteristics between a normal metal and a two-dimensional Fulde-Ferrell-Larkin-Ovchinnikov superconductor: The Fulde-Ferrell state