4He adsorbed outside a single carbon nanotube

The phase diagrams of ${}^4$He adsorbed on the external surfaces of single armchair carbon nanotubes with radii in the range 3.42 – 10.85 \AA \ are calculated using the diffusion Monte Carlo method. For nanotubes narrower than a (10,10) one, the ground state is an incommensurate solid similar to the one found for H${}_2$ on the same substrates. For wider nanotubes, the phase with the minimum energy per particle is a liquid layer. Curved $\sqrt{3}\times \sqrt{3}$ registered solids similar to the ones found on graphene and graphite were unstable for all the tubes considered.