2D Extended Bose-Hubbard Model for Light Atoms on Graphene*

An exciting development in the field of correlated systems is the possibility of superfluidity for a single layer of helium atoms adsorbed on novel two-dimensional quantum materials such as Graphene. This complex many-body problem can be mapped onto an effective extended Bose-Hubbard model on the triangular lattice extracted with high precision from a high-energy microscopic description. The helium atoms behave as hard-core bosons, and the ratios of the hopping parameter to the interaction strengths control the nature of the emergent many-body state. Using mean-field theory we show how the insulating phases at fillings 1/3, 2/3, and 1 emerge and compete with superfluidity as the graphene substrate is uniformly strained. In contrast to pristine unstrained graphene - where the 1/3 atomic solid is always favorable and 2D superfluidity is not present - applying a moderate uniform strain allows 2D superfluidity to emerge in a large region of parameter space, now competing with the higher filled (2/3 and 1) solid phases. This analysis opens the door towards designing purely 2D superfluids by manipulating the atomically thin substrate underneath.