Dispersion interaction of two graphene sheets

TL;DR

This paper investigates the dispersive Casimir force between two graphene sheets using two theoretical models, revealing how the force varies with distance and chemical potential, including the presence of minima and maxima.

Contribution

It applies two different theoretical approaches to calculate the Casimir force between graphene sheets, comparing their results and analyzing the effects of chemical potential on the force.

Findings

At large distances, the force decreases as the inverse fourth power of distance.

At short distances, the force remains finite and attractive.

Chemical potential influences the force, causing minima and maxima at specific distances.

Abstract

The Casimir method for determining the dispersive force by varying zero vacuum energy fluctuations is applied to two graphene sheets in the approximation of the Drude model for surface conductivity. As an alternative, the Van Kampen summation method is used. The force is determined for small and for large distances between the sheets. The results of both models are quite similar. Precisely, at large distances, the attractive force decreases inversely proportional to the fourth power of the distance. At short distances, the force is a finite attractive one. With a small chemical potential, the force can have a minimum at distances of the order of 0.3 nm, then increases, reaches a maximum at distances of the order of 200 nm, and at large distances decreases inversely proportional to the fourth power of the distance. At a chemical potential of significantly more than 1 eV, a minimum is not observed.