Localization versus inhomogeneous superfluidity: Submonolayer He4 on fluorographene, hexagonal boron nitride, and graphene

We study a submonolayer 4 He adsorbed on fluorographene (GF) and on hexagonal boron nitride (hBN) at low coverage. The adsorption potentials have been computed ab initio with a suitable density functional theory including dispersion forces. The properties of the adsorbed 4 He atoms have been computed at finite temperature with path integral Monte Carlo and at T = 0 K with variational path integral. From both methods we find that the lowest energy state of 4 He on GF is a superfluid. Due to the very large corrugation of the adsorption potential this superfluid has a very strong spatial anisotropy, the ratio between the largest and smallest areal density being about 6, the superfluid fraction at the lowest T is about 55%, and the temperature of the transition to the normal state is in the range 0.5–1 K. Thus, GF offers a platform for studying the properties of a strongly interacting highly anisotropic bosonic superfluid. At a larger coverage 4 He has a transition to an ordered commensurate state with occupation of 1/6 of the adsorption sites. This phase is stable up to a transition temperature located between 0.5 and 1 K. The system has a triangular order similar to that of 4 He on graphite but each 4 He atom is not confined to a single adsorption site and the atom visits also the nearest neighboring sites giving rise to a novel three-lobed density distribution. The lowest energy state of 4 He on hBN is an ordered commensurate state with occupation of 1/3 of the adsorption sites and triangular symmetry. A disordered state is present at lower coverage as a metastable state. In the presence of an electric field the corrugation of the adsorption potential is slightly increased but up to a magnitude of 1 V/Å the effect is small and does not change the stability of the phases of 4 He on GF and hBN. We have verified that also in the case of graphene such electric field does not modify the stability of the commensurate √3 × √3R30◦ phase.