Effects of substrate corrugation during helium adsorption on graphene in the grand canonical ensemble

Gage Erwin, Adrian Del Maestro

arXiv:arXiv:2311.12747

Abstract

Adsorption of ${}^4$He on graphene substrates has been a topic of great interest due to the intriguing effects of graphene corrugation on the manifestation of commensurate solid and exotic phases in low-dimensional systems. In this study, we employ worm algorithm quantum Monte Carlo to study helium adsorbed on a graphene substrate to explore corrugation effects in the grand canonical ensemble. We utilized a Szalewicz potential for helium-helium interactions and a summation of isotropic interactions between helium and carbon atoms to construct a helium-graphene potential. We implement different levels of approximation to achieve a smooth potential, three partially corrugated potentials, and a fully ab initio potential to test the effects of corrugation on the first and second layers. We demonstrate that the omission of corrugation within the helium-graphene potential could lead to finite-size effects in both the first and second layers. Thus, a fully corrugated potential should be used when simulating helium in this low-dimensional regime.

Description

This repository includes links, code, scripts, and data to generate figures and reproduce results in the paper.

Requirements

The data in this project was generated via quantum Monte Carlo simulations with the worm algorithm Processed and the raw simulation data set is available online at .

1. A minimal environment to execute these notebooks can be installed via pip install -r requirements.txt
2. All quantum Monte Carlo data was generated with our open source path integral software also available on github

Support

This research was partially supported by the National Science Foundation Materials Research Science and Engineering Center program through the UT Knoxville Center for Advanced Materials and Manufacturing (DMR-2309083).

Figures

Figure 01: Simulation cell in the x-y plane.

Figure 02: Potential Analysis in the z and xy plane.

Figure 03: Filling fraction in the first layer.

Figure 04: Energy per particle in the first layer regime.

Figure 05: Compressibility as a function of chemical potential.

Figure 06: Filling fraction in the second layer regime and linear density.

Figure 07: Energy per particle in the second layer regime.

Figure 08: Finite Size scaling of the Energy per Particle at -115 K.

Figure 09: Filling Fraction and Energy per Particle for the smooth and corrugated potential, for system sizes 48, 72, and 108.

Figure 10: Finite Size scaling of the Energy per Particle at -87 K.

Figure 11: Finite Size scaling of the Energy per Particle at -41 K.