Triplet FFLO superconductivity in the doped Kitaev-Heisenberg honeycomb model

We provide analytical and numerical evidence of spin-triplet Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductivity in the itinerant Kitaev-Heisenberg model (antiferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of six inversion symmetry centers for the Fermi surface at nonzero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these nontrivial momenta, causing spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion analysis, we find that the superconductivity has three separated degenerate ground states with three different spin-triplet pairings. Exact diagonalizations on finite clusters support this picture while ruling out a spin (charge) density wave.