Superfluid state of ⁴He on graphane and graphene-fluoride: Anisotropic roton states

We explore the phase behavior of Helium films on two variants of graphene: graphane (graphene coated with H, denoted GH) and graphene-fluoride (GF). A semiempirical interaction with these substrates is used in T=0 K Path Integral Ground State and finite temperature Path Integral Monte Carlo simulations. We predict that ⁴He forms anisotropic fluid states at low coverage. This behavior differs qualitatively from that on graphite because of the different surface composition, symmetry and spacing of the adsorption sites. The ⁴He ground state on both substrates is thus a self-bound anisotropic superfluid with a superfluid fraction ρ _s /ρ lower than 1 due to the corrugation of the adsorption potential. In the case of GF such corrugation is so large that ρ _s /ρ=0.6 at T=0 K and the superfluid is essentially restricted to move in a multiconnected space, along the bonds of a honeycomb lattice. We predict a superfluid transition temperature T≠0.25 (1.1) K for ⁴He on GF (GH). We have studied the elementary excitation spectrum of ⁴He on GF at equilibrium density finding a phonon-maxon-roton dispersion relation that is strongly anisotropic in the roton region. We conclude that these new platforms for adsorption studies offer the possibility of studying novel superfluid phases of quantum condensed matter.