Non-uniform Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state

We provide a general review of the properties of the non-uniform superconducting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Special emphasis is made on the orbital and crystal structure effects which may result in the quantum transitions between the higher Landau level states and should be responsible for the strong modification of the anisotropy of the critical field. The FFLO-type instability may be also expected in ultracold Fermi gases. In these systems it is caused not by the Zeeman interaction but by the tuning of the population imbalance between two lowest hyperfine states of the atoms. We also briefly discuss their properties.