The Bose--Hubbard Model and Superfluid Staircases in ${}^4$He Films

Abstract

The recent experimental observation of step-like structure in the superfluid density of ${}^4$He films on graphite is interpreted in terms of passage close to Mott insulating lobes in the Bose--Hubbard model. Plateaus develop in the superfluid density near the completion of each layer because of the He-He repulsion. We modify the Bose--Hubbard Hamiltonian, using a density-dependent He-He interaction term to model the He-substrate potential. Quantum Monte Carlo simulations yield results which agree well with the experimental data.

11 pages+3 figures upon request, Revtex 3.0, UCD 93-112

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