  We have derived the adsorption potential of $^4$He atoms on fluorographene
(GF), on graphane and on hexagonal boron nitride (hBN) by a recently developed
ab initio method that incorporates the van der Waals interaction. The $^4$He
monolayer on GF and on hBN is studied by state-of-the-art quantum simulations
at T=0 K. With our adsorption potentials we find that in both cases the ground
state of $^4$He monolayer is a fluid and not an ordered state with localized
atoms as on graphite and on graphene. In the case of GF the present result is
in qualitative agreement with the superfluid phase that was obtained using an
empirical adsorption potential [M. Nava et al., Phys. Rev. B 86, 174509
(2012)]. This fluid state of $^4$He on GF and on hBN is characterized by a very
large density modulation and at the equilibrium density the ratio $\Gamma$
between the largest and the smallest local density along the direction of two
neighboring adsorption sites and averaged over the perpendicular direction is
$\Gamma$ = 1.91 for GF and $\Gamma$ = 1.65 for hBN. Recent experiments [J.
Nyeki et al., Nature Physics 13, 455 (2017)] have discovered a superfluid phase
in the second layer $^4$He. This is a spatially modulated superfluid that turns
out to have anomalous thermal properties. This gives a strong motivation for an
experimental study of monolayer $^4$He on GF and on hBN that we predict to be a
superfluid with a much stronger spatial modulation.
