Magnetic supersolid phases in spin-orbit coupled extended Bose-Hubbard model

The study of the ultracold atomic spin systems with long-range interaction provides the possibility to search for magnetic supersolid phases in quantum many-body scenarios. In this paper, we consider two-species Bose gases with spin-orbit coupling and nearest-neighbor interaction confined in a two-dimensional optical lattice. The competition between SOC and interactions creates rich ground-state diagrams with supersolid phase exhibiting the phase modulation or magnetic ordering. The combined effect of intraspecies nearest-neighbor interaction and spin-orbit coupling results in the phase-twisted paired checkboard supersolid and phase-striped paired checkboard supersolid phases. The introduction of interspecies nearest-neighbor interaction enriches the quantum phases of the system. The phase-twisted lattice supersolid and phase-striped lattice supersolid phases are preferred. We find that the appearance of some ground-state phases depending on interspecies on-site interaction. A type of lattice supersolid phase with supersolid in one spin species but insulating in the other that exists in the miscible domain, while the paired stripe supersolid phase with stripe structures in each spin species in the immiscible domain. Finally, to further characterize each phase, we discuss their spin-dependent momentum distributions and spin-texture structures. The magnetic textures such as antiferromagnetic, spiral and stripe orders are shown in supersolid phases. The results here in could help in the observe for these magnetic supersolid phases in ultracold atomic experiments with nearest-neighbor interaction and spin-orbit coupling in optical lattice.