  We study a sub monolayer He-4 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 He-4 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 He-4 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 He-4 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 He-4 on graphite. The
lowest energy state of He-4 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/Ang. the effect is small and does not
change the stability of the phases of He-4 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 sqrt{3}*sqrt{3}R30 phase.
