Tree-level electron-photon interactions in graphene

TL;DR

This paper derives analytical expressions for electron-photon interactions in graphene, revealing how spontaneous emission contributes to Ohmic dissipation and affecting optical properties like opacity and conductivity.

Contribution

It extends the Dirac Hamiltonian for graphene to include quantized electromagnetic interactions and calculates key photon emission and recombination amplitudes at tree level.

Findings

Analytic angular dependence of photon emission in graphene

Recombination rate mediated by photons

Spontaneous emission causes Ohmic dissipation in perfect graphene

Abstract

Graphene's low-energy electronic excitations obey a 2+1 dimensional Dirac Hamiltonian. After extending this Hamiltonian to include interactions with a quantized electromagnetic field, we calculate the amplitude associated with the simplest, tree-level Feynman diagram: the vertex connecting a photon with two electrons. This amplitude leads to analytic expressions for the 3D angular dependence of photon emission, the photon-mediated electron-hole recombination rate, and corrections to graphene's opacity $\pi \alpha$ and dynamic conductivity $\pi e^2/2 h$ for situations away from thermal equilibrium, as would occur in a graphene laser. We find that Ohmic dissipation in perfect graphene can be attributed to spontaneous emission.