Multiband effects on the Fulde-Ferrell-Larkin-Ovchinnikov state in superconducting metallic nanofilms

In superconducting nanofilms the energy quantization induced by the confinement in the direction perpendicular to the film leads to a multiband character of the system which results in the thickness-dependent oscillations of the in-plane critical field (shape resonances). In this paper, we study the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in nanofilms and examine its interplay with the shape resonances as well as the influence of the multiband effects on its stability. We demonstrate that the range of the magnetic field for which the FFLO state is stable oscillates as a function of the film thickness with the phase shift equal to one half of the period corresponding to the critical magnetic field oscillations. Moreover, the multiband effects lead to a division of the FFLO phase stability region into subregions number of which depends on the number of bands participating in the formation of the paired state.