  The effect of impurities on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in
a layered superconductor with d-wave pairing symmetry is investigated using the
tight-binding model and the Bogoliubov-de Gennes equations. At low temperature
and a strong exchange field applied parallel to its conducting plane, a
two-dimensional (2D) square lattice-like Larkin-Ovchinnikov state is more
energetically favorable in a clean system. In the presence of impurities, the
spatial profile of the order parameter remains as a 2D square lattice, and it
is distorted only near the impurities when the impurity concentration is low.
As impurity concentration is increased to a certain level,
quasi-one-dimensional (1D) like FFLO state becomes more energetically
favorable. Increasing temperature with fixed impurity concentration can also
induce a 2D to 1D FFLO state transition. Within the present finite size
calculation, we did not find the existence of the Fulde and Ferrell state
before the system becoming normal as the impurity concentration is raised.
