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We investigate Bloch-Zener oscillations and mean-field Bloch bands of aBose-Einstein condensate (BEC) in a Lieb optical lattice. We find that theatomic interaction will break the point group symmetry of the system, leadingto the destruction of the Dirac cone structure, while the flat band ispreserved on the highly symmetric lines. Due to the nonlinear effect, a tubularband structure with a flat band will appear in the system. Furthermore,comparing with that the tight-binding (TB) model fails to describe theinteracting bosonic systems in the honeycomb lattice, we show that the TB modelis applicable to study the nonlinear energy band structures for the Lieblattice. In addition, we show that the loop structure can be determined by theobservation of the chaos of the state in the Bloch-Zener oscillations.

Nonlinear Bloch-Zener oscillations for Bose-Einstein condensates in a Lieb optical lattice