  We provide analytical and numerical evidence of a spin-triplet FFLO
superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic
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 6 inversion symmetry centers for the Fermi surface at non zero
momenta in the first Brillouin zone. We show how the Cooper pairs condense into
these non-trivial momenta, causing the 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. This picture is also supported by
exact diagonalizations on finite clusters.
