Enhancement of Fulde-Ferrell-Larkin-Ovchinnikov instability in ultraclean layered superconductors by orbital quantization

We investigate the superconducting instability for a layered superconductor in the magnetic field oriented perpendicular to the layers and study conditions for the formation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with the modulation of the order parameter between the layers, i. e., along the magnetic field. It is well known that within the quasiclassical approximation such modulation only appears at anomalously high Maki parameter corresponding to very large Zeeman splitting energy and/or very shallow band. We found, however, that the Landau-quantization effects strongly promote formation of the interlayer FFLO state with large modulation period. The conditions for such state can be satisfied in many layered materials provided they are sufficiently clean.