Excitations in Two-Dimensional 4He

We present the study of the ground state and of the low-energy excited states of liquid⁴He in two dimensions (2D) within the Variational Monte Carlo method. As trial wave function a shadow wave function is used. The energies of the maxon and of the roton are close together at the equilibrium density ρ_eq due to the low value of ρ_eq in 2D but at higher densities a well developed roton minimum is present. The short range backflow effects are stronger in 2D than in 3D and close to freezing the roton energy is about 5 K. This value is close to the lowest branch of excitations found from inelastic neutron scattering from thin⁴He film on graphite and interpreted as due to layer rotons. Some strong similarities between the 2D and 3D case are present: the maxon energy close to freezing is about twice the roton energy, the relative strength of the single roton peak in the dynamical structure factor is essentially density independent and very close in value to the 3D case, there is a similar shift between the wave vectors of the roton and of the position of the main maximum of the static structure factor.