Effective Extended Bose-Hubbard Model for Helium on Graphene

The possibility of two-dimensional (2D) helium superfluidity mitigated by adsorption on novel 2D quantum materials, is an exciting development. For helium on graphene, superfluidity competes with insulating (1/3 filled) states, and the phase boundary between them is highly sensitive to the details of the van der Waals interactions between system components. We present a mapping of the full, complex many-body problem onto an effective extended Bose-Hubbard (t-V-V’) model, which describes how the Helium atoms hop (t) on the graphene lattice and interact at nearest-neighbor (V) and next-nearest neighbor (V’) sites. Helium atoms behave effectively as hard-core bosons (U=∞) and V/t controls the nature of the emergent many-body state. We compare the results of a variety of accurate techniques: large-scale Monte Carlo simulations, band structure calculations and ab-initio calculations on finite systems. We find that V/t is large enough across all techniques to favor the insulating 1/3-filled state. Therefore our effective model provides an accurate description which can be also used as a starting point in more complex situations where atomic and materials parameters are modified and consequently new phases could emerge.