Retarded interactions in Graphene systems

TL;DR

This paper develops a formalism for retarded interactions in graphene systems, analyzing the effects between free-standing sheets and substrates at various temperatures and doping levels, with numerical results for different substrates.

Contribution

It introduces a method to calculate retarded interactions in graphene structures, including effects of temperature, doping, and substrate material, which was not previously detailed.

Findings

Retarded interactions vary with doping and temperature.

Numerical results show differences between substrates.

Interaction strength depends on doping and substrate type.

Abstract

We first demonstrate how two-dimensional sheets are incorporated in the formalism for planar structures. Then we derive the interaction in the geometry of two free-standing graphene sheets and of one graphene sheet above a substrate. Numerical results are produced for the fully retarded interaction at 0 K and at room temperature for undoped and doped graphene. Additional results are given both for a gold substrate and for an ideal metal substrate.