# Casimir interaction between a perfect conductor and graphene described by the Dirac model

## TL;DR

This paper calculates the Casimir interaction between a graphene sheet modeled by the Dirac theory and a perfect conductor, revealing a weak interaction strongly dependent on the quasi-particle mass.

## Contribution

It introduces two methods for calculating the Casimir effect with graphene, demonstrating the dominance of the quantum field theory approach and the influence of quasi-particle mass.

## Key findings

- Casimir interaction is weak in this system.
- Interaction strength depends strongly on quasi-particle mass.
- Quantum field theory approach is effective for this calculation.

## Abstract

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the Quantum Field Theory (QFT) approach and evaluate the leading order diagram in a theory with 2+1 dimensional fermions interacting with 3+1 dimensional photons. Next, we consider an effective theory for the electromagnetic field with matching conditions induced by quantum quasi-particles in graphene. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak. It exhibits a strong dependence on the mass of the quasi-particles in graphene.