Fulde-Ferrell-Larkin-Ovchinnikov state induced by antiferromagnetic order in $\kappa$-type organic conductors

We theoretically investigate superconductivity under a spin-split band structure owing to a collinear-type antiferromagnetic order in quasi-two-dimensional organic compounds $\kappa$-(BEDT-TTF)${}_{2}X$. We find that the magnetic order can induce a Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state, where the Cooper pair possesses a finite center-of-mass momentum. We show this from two types of analyses: (1) an effective model where simple intraband attractive interactions are assumed, and (2) many-body calculations of the repulsive Hubbard model based on the fluctuation-exchange approximation and the linearized Eliashberg equation. Our results show the possibility of realizing the FFLO state without applying an external magnetic field.