LAUSR

We have derived the adsorption potential of $$^4\hbox {He}$$4He 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 stability of the commensurate $$\sqrt{3}\times \sqrt{3}R30^\circ $$3×3R30∘ phase of $$^4\hbox {He}$$4He on GF and on hBN is studied by state-of-the-art quantum simulations at $$T=0$$T=0 K. With our adsorption potentials, we find that in both cases this commensurate state of $$^4\hbox {He}$$4He is unstable toward a fluid state in which the $$^4\hbox {He}$$4He atoms are delocalized, and not localized like in the case of $$^4\hbox {He}$$4He on graphite or 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 (Nava et al. in Phys Rev B 86:174509, 2012). This fluid state of $$^4\hbox {He}$$4He on GF and on hBN is characterized by a very large density modulation. For instance, the local density changes by a factor of order 2 along the path connecting two adsorption sites. Recent experiments (Nyeki et al. in Nat Phys 13:455, 2017) have discovered a superfluid phase in the second layer $$^4\hbox {He}$$4He. 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 $$^4\hbox {He}$$4He on GF and on hBN that we predict to be a superfluid with a much stronger spatial modulation.