Gap solitons of spin-orbit coupled Bose-Einstein condensates with Rabi coupling in twisted-bilayer optical lattices

We consider the gap solitons of a two-component Bose-Einstein condensate with spin-orbit coupling and Rabi coupling confined in twisted-bilayer optical lattices. Our results show that the band structure of the twisted-bilayer optical lattices exhibits flattening one, which shows strong dependence not only on the amplitude of sublattice and the twist angle, but also on the spin-orbit coupling and Rabi coupling. We also find a series of solutions of gap solitons existing in the Bloch band gap, and its shapes show strongly dependence on the chemical potential, spin-orbit coupling and Rabi couplings. Finally, the stability of such gap solitons is analyzed using the non-linear methods, and the results show that both the spin-orbit coupling and Rabi coupling play significant roles on the stability of the gap solitons.