Interacting bosons in a three-dimensional lattice

We theoretically investigate the extended Bose–Hubbard model using a three-dimensional cubic lattice. In the framework of the dynamical Gutzwiller mean-field theory, we identify a checkerboard supersolid phase. By considering the repulsive interactions between next-nearest-neighbor lattice sites, we further discover an exotic type of supersolid state, whose site occupancies show a stereoscopically arrayed and staggered distribution rather than checkerboard ordering. Intriguingly, if the physical observations of two neighboring layers were superimposed, they would give rise to a checkerboard configuration. This novel structure is convincingly induced by the simultaneous existence of nearest-neighbor and next-nearest-neighbor interactions. We also identify arrayed stripes in the ground state, as well as arrayed holes in the pattern of occupancies.