However, it has not been experimentally explored in great depth so far how the flat dispersion affects the ground state of bosons and fermions except the very recent work in which the decay of the bosons from the flat excited band has been studied 19. In the ultracold atomic system, a bulk flat band appears though the whole system when the hopping matrix elements are destructively interfered such as in kagome 5, Lieb 17, sawtooth 9, 18 lattices. In addition, the interaction-induced localised state reveals crystalline phases in fractional-filled bosons and fermions in a flat band 9 and more interestingly topological flat bands with nonzero Chern number open a new way for realising a fractional quantum hall state without Landau levels 12, 15, 16. Intriguingly, the divergence in the density of states at the energy of the flat band prevents natural ordering in the system 11, 12 and the question still remains whether or not Bose-Einstein condensation is stable in a flat band 13, 14. Such flattened band structures significantly enhance interaction effects and show a wide range of interaction-driven many-body phenomena from supersolidity 9 to flat-band ferromagnetism 10. Flat band occurs in a variety of condensed-matter systems, ranging from the Landau levels of an electron gas 6, edge states of graphene 7 to unconventional superconductors 8. Furthermore, the highly tunable optical lattices 3, 4, 5 would realise unconventional band structures that are not easy to study in solid-state materials, including flat bands with completely quenched kinetic energies or topological bands. ![]() Recent experimental and theoretical advancements in optical lattices hold out a promise of engineering the band structures, the amplitude and the phase of inter-site tunnelling energies and on-site interactions in the Hubbard regime 1, 2.
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