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

Understand

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.