Spontaneous appearance of the spin-triplet Fulde-Ferrell-Larkin-Ovchinnikov phase in a two-band model : possible application to LaFeAsO_{1-x}F_{x}

The possibility of a spontaneous spin-triplet paired phase of the Fulde-Ferrell-Larkin-Ovchinnikov type is studied. As it is shown in a system with the dominant interband pairing and two distinct Fermi surface sheets, the Fermi wave-vector mismatch can be compensated by a nonzero center-of-mass momentum of the Cooper pairs. This idea is examined with the use of a model which describes the two hole-like bands in the iron-based superconductor. It is shown that for the proper range of model parameters, the minima of the free energy appear which correspond to a nonzero Cooper pair momentum. Different superconducting gap symmetries are analyzed, and the corresponding phase diagrams are shown.