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The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of a two-dimensional (2D)orthorhombic lattice superconductor is studied based on theBogoliubov-de-Gennes equations. It is illustrated that the 2D FFLO state issuppressed and only one-dimensional (1D) stripe state is stable. The stripechanges its orientation with the increasing Zeeman field. There exists acrossover region where the gap structure has some local 2D features. Theseresults are significantly different from those of the tetragonal latticesystem. The local density of states is also studied which can be checked andcompared with experiments in future.

The Fulde-Ferrell-Larkin-Ovchinnikov states for the d-wave superconductor in the two-dimensional orthorhombic lattice