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

Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by the atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adiabaticity by interaction of arbitrary small strength.