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.