| Summary: | The phase diagram of ultracold bosons in a 2D optical lattice subjected to a uniform magnetic flux is studied by the inhomogeneous Gutzwiller variational method. With a harmonic external potential, the density profile exhibits wedding-cake shape and the Mott phase forms a series of circular platforms with integer fillings. There are annular rings of superfluid between these platforms. We identify a lot of phases, including the unicirculation phase, the Meissner phase, the vortex phase, the reversed current phase and the vortex superfluid phase, by examining the super-currents. The circular chiral currents of the reversed current phase are opposite to other phases in annular superfluid and we analyzed the transitions between different phases.
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