Theory of Fulde-Ferrell-Larkin-Ovchinnikov state of superconductors with and without inversion symmetry: Hubbard model approach

We study Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of superconductors with and without inversion symmetry based on the Hubbard model on the square lattice near half-filling, using the random phase approximation. We show that center of mass momentum Q tends to be parallel to x- or y-axis in the presence of inversion symmetry, while Q vector is likely to be perpendicular to the magnetic field in the absence of inversion symmetry. We also clarify that d + f-wave pairing is favored and the hetero spin triplet f-wave state is present in the FFLO state unlike state in the superconductors only with the Rashba type spin-orbit coupling (RSOC) originating from the broken inversion symmetry. The triplet f-wave state is enhanced by magnetic field and the RSOC. This stems from the reduction of the spin susceptibilities by the magnetic field and the RSOC.