Supersolid phases in the magnetic fields

We study the ground state phases of the ultracold atomic condensates loaded in a two-dimensional optical lattice with the magnetic fields. Apart from uniform superfluid (SF) phase, four types of supersolid (SS) phases in the presence of the uniform magnetic fluxes and two types of SS phases in the presence of the staggered magnetic fluxes are found. For the system without magnetic flux, except for a certain unit phase factor ϕx(y)=π, the magnetic field has no effect on the system.