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 the

dice lattice model, also referred to as the $\mathcal{T}_3$ 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 $\nu$ of the lowest band, including a

classical crystal at $\nu=1/3$, a supersolid state at $\nu=1/2$ and a Mott insulator at $\nu=1$.