Comparison of the hydrodynamic and Dirac models of the dispersion interaction between graphene and H, He${}^{\ast}$, or Na atoms

TL;DR

This paper compares the Dirac and hydrodynamic models of graphene in predicting van der Waals and Casimir-Polder interactions with various atoms, proposing experiments to distinguish between these models based on quantum reflection data.

Contribution

It introduces a comparative analysis of the Dirac and hydrodynamic models for graphene's electronic structure in dispersion interactions, highlighting their differences and experimental implications.

Findings

Dirac model predicts smaller van der Waals coefficients than hydrodynamic model.

The models' predictions differ significantly regardless of the gap parameter.

Proposed quantum reflection experiments can discriminate between the models.

Abstract

The van der Waals and Casimir-Polder interaction of different atoms with graphene is investigated using the Dirac model which assumes that the energy of quasiparticles is linear with respect to the momentum. The obtained results for the van der Waals coefficients of hydrogen atoms and molecules and atoms of metastable He${}^{\ast}$ and Na as a function of separation are compared with respective results found using the hydrodynamic model of graphene. It is shown that, regardless of the value of the gap parameter, the Dirac model leads to much smaller values of the van der Waals coefficients than the hydrodynamic model. The experiment on quantum reflection of metastable He${}^{\ast}$ and Na atoms on graphene is proposed which is capable to discriminate between the two models of the electronic structure of graphene. In this respect the parameters of the phenomenological potential for both these atoms interacting with graphene described by different models are determined.