Correlated Phases of Bosons in the Flat Lowest Band of the Dice Lattice

We study correlated phases occurring in the flat lowest band of the dice-lattice model at flux density one-half. We discuss how to realize this model, also referred to as the T-3 lattice, in cold atomic gases. We construct the projection of the model to the lowest dice band, which yields a Hubbard Hamiltonian with interaction-assisted hopping processes. We solve this model for bosons in two limits. In the limit of large density, we use Gross-Pitaevskii mean-field theory to reveal time-reversal symmetry breaking vortex lattice phases. At low density, we use exact diagonalization to identify three stable phases at fractional filling factors v of the lowest band, including a classical crystal at v = 1/3, a supersolid state at v = 1/2, and a Mott insulator at v = 1.