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Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb opticallattice are computed. We find that the topological structure of the Bloch bandsat the Dirac point is changed completely by the atomic interaction of arbitrarysmall strength: the Dirac point is extended into a closed curve and anintersecting tube structure arises around the original Dirac point. These tubedBloch bands are caused by the superfluidity of the system. Furthermore, theyimply the inadequacy of the tight-binding model to describe an interactingBoson system around the Dirac point and the breakdown of adiabaticity byinteraction of arbitrary small strength.

Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point