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Using mean-field theory, we investigate the ground state properties ofultracold bosons loaded in a honeycomb lattice with on-site repulsiveinteractions and imbalanced nearest-neighbor hopping amplitudes. Taking intoaccount correlations between strongly coupled neighboring sites through animproved Gutzwiller ansatz, we predict the existence of half-integerMott-insulator phases, i.e. states with half-integer filling and vanishingcompressibility. These insulating phases result from the interplay betweenquantum correlations and the topology of the honeycomb lattice, and could beeasily addressed experimentally as they have clear signatures in momentumspace.

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