Interplay between quantum confinement and Fulde–Ferrell–Larkin–Ovchinnikov phase in superconducting nanofilms

•Interplay between the quantum confinement and the FFLO state is studied in nanofilms.•The FFLO stability region oscillates as a function of the nanofilm thickness.•The shape resonant conditions are detrimental to the FFLO state.•The FFLO stability region is divided into the subphases.•Number of subphases is equal to the number of bands participated in the paired phase.

In superconducting nanofilms the energy quantization induced by the confinement in the direction perpendicular to the film splits the band of single-electron states into series of subbands. The quantum size effect leads to the experimentally observed oscillations of the critical magnetic field with increasing nanofilm thickness. Here, we study the influence of the quantum confinement on the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase in superconducting nanofilms. We show that the range of the magnetic fields for which the FFLO phase 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. Due to the multiband character of the system a division of the FFLO phase stability region appears leading to a phase diagram which is qualitatively different than the one corresponding to a single-band situation. The number of subregions created in such manner depends on the number of bands participating in the formation of the paired state.