Orbital effect for the Fulde-Ferrell-Larkin-Ovchinnikov phase in a quasi-two-dimensional superconductor in a parallel magnetic field

We theoretically study the orbital destructive effect against superconductivity in a parallel magnetic field in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF) phase at zero temperature in a quasi-two-dimensional (Q2D) conductor. We demonstrate that at zero temperature a special parameter, λ =l_⊥(H ) /d , is responsible for strength of the orbital effect, where l_⊥(H ) is a typical "size" of the quasiclassical electron orbit in a magnetic field and d is the interplane distance. We discuss applications of our results to the existing experiments on the FFLO phase in the organic Q2D conductors κ -(ET_{) 2}Cu (NCS_{) 2} and κ -(ET_{) 2}Cu [N (CN_{) 2}] Cl .