New superconducting phases in field-induced organic superconductor lambda-(BETS)2FeCl4

We derive the parallel upper critical field, Hc2, as a function of the temperature T in quasi-2D organic compound lambda-(BETS)2FeCl4, accounting for the formation of the nonuniform LOFF state. To further check the 2D LOFF model we propose to study the Hc2(T) curve at low T in tilted fields, where the vortex state is described by the high Landau level functions characterized by the index n. We predict a cascade of first order transitions between vortex phases with different n, between phases with different types of the symmetry at given n and the change of the superconducting transition from the second order to the first order as FeCl4 ions are replaced partly by GaCl4 ions.