Half-integer Mott-insulator phases in the imbalanced honeycomb lattice

Using mean-field theory, we investigate the ground state properties of ultracold bosons loaded in a honeycomb lattice with on-site repulsive interactions and imbalanced nearest-neighbor hopping amplitudes. Taking into account correlations between strongly coupled neighboring sites through an improved Gutzwiller ansatz, we predict the existence of half-integer Mott-insulator phases, i.e. states with half-integer filling and vanishing compressibility. These insulating phases result from the interplay between quantum correlations and the topology of the honeycomb lattice, and could be easily addressed experimentally as they have clear signatures in momentum space.