Theoretical Study of The Dispersion Spectrum of A Two-Dimensional (2D) Roton Subjected To A Van Der Waals Field Generated by The Atoms of A Solid Graphite Substrate

Abstract

Two-dimensional systems represent a vibrant field in contemporary physical research due to their unique properties. This paper presents a theoretical investigation of a two-dimensional roton within superfluid helium adsorbed on a solid graphite substrate under the influence of the Van der Waals potential. This potential was employed to model the liquid-substrate interaction, precisely determining the solid-like layer thickness as 6.32 Å based on the equilibrium condition, alongside calculating the attraction coefficient (364.13 ). By solving the Schrödinger equation via MATLAB, the optimal confinement parameter yielding the minimum energy state was obtained. Findings indicate that the energy reduction magnitude correlates directly with the roton's specific momentum. Furthermore, the study demonstrated a significant 8.47% decrease in the surface roton's effective mass. Graphical representations illustrated the energy shift corresponding to each momentum, providing a comparative analysis between bulk and surface states. A comprehensive thermodynamic analysis was conducted at a specific temperature, calculating density, entropy, heat capacity, and internal energy across various momenta. These results, compared with bulk parameters, rigorously proved an increased roton density near the substrate surface.