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Multi-band effects on Fulde-Ferrell-Larkin-Ovchinnikov states of Pauli-limited superconductors

Multi-band effects on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states of a Pauli-limiting two-band superconductor are studied theoretically, based on self-consistent calculations of the Bogoliubov-de Gennes equation. First, we examine the phase diagrams of two-band systems with a passive band in which the intraband pairing interaction is absent and superconductivity is induced by a Cooper pair tunneling from an active band. It is demonstrated that the temperature of the Lifshitz point at which three second-order transition lines meet is independent of the Cooper pair tunneling strength. The BCS-FFLO critical field becomes lower than the Lifshitz point with increasing the interband tunneling strength, and the resultant phase diagram is qualitatively different from that in a single-band superconductor. We also study the thermodynamics of Pauli-limiting two-band superconductors with comparable intraband pairing interactions. As a consequence of a competing effect between two bands, the FFLO phase is divided into two phases: $Q_1$- and $Q_2$-FFLO phases. The $Q_1$-FFLO is favored in a high field regime and the $Q_2$-FFLO becomes stable in the lower field. In a particular case, the latter is further subdivided into a family of FFLO states with rational modulation lengths, leading to a devil's staircase structure in the field-dependence of physical quantities. The critical field, above which the FFLO is stabilized, is lower than that in a single band superconductor, while the temperature of tricritical Lifshitz point is invariant under the change of two-band parameters.