Anisotropic superfluidity of ⁴He on a C₃₆ fullerene molecule

We have performed path-integral Monte Carlo calculations to study the adsorption of ⁴He atoms on two different C₃₆ isomers with the D_6h and the D_2d symmetries. The radial ⁴He density distributions reveal layer-by-layer growth with the first layer being located at a distance of ∼5.5 Å from the C₃₆ molecular center and the second layer at ∼8.3 Å. From the angular density profiles of ⁴He, we find different quantum states as the number of ⁴He adatoms N varies. For N = 20, we observe commensurate solid structures on both D_6h and D_2d isomers, where each of 8 hexagon and 12 pentagon centers of the fullerene surfaces is occupied by a single ⁴He atom. The second-layer promotion starts beyond N = 38 on both isomers, where a compressible incommensurate structure is observed on the D_6h isomer and another commensurate structure on D_2d. Between N = 20 and N = 38, the ⁴He monolayer on D_6h shows several distinct rings of delocalized ⁴He atoms along with strongly anisotropic superfluid responses at low temperatures, while isotropic but weak superfluid responses are observed in the ⁴He layer on D_2d