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Possible Field-Temperature Phase Diagrams of Two-Band Superconductors with Paramagnetic Pair-Breaking

Possible field-temperature superconducting (SC) phase diagrams in two-band quasi-two-dimensional materials with a strong paramagnetic pair-breaking (PPB) are considered theoretically. Attention is paid to the case under a magnetic field $perpendicular$ to the SC layers and to essential differences from the counterpart in the ordinary single-band material. It is found by examining the $H_{c2}(T)$ curve and the vortex lattices to be realized close to $H_{c2}$ that a PPB-induced SC phase with a spatial modulation parallel to the field tends to occur more easily than in the single-band case, and that a crisscrossing vortex lattice proposed previously can occur in place of the conventional Fulde-Ferrell-Larkin-Ovchinnikov state within a parameter range. The relevance of the obtained results to FeSe and other iron-based superconductors is discussed.