Radiative Processes in Graphene and Similar Nanostructures at Strong Electric Fields

TL;DR

This paper develops a nonperturbative quantum field theory approach to analyze photon emission in graphene under strong electric fields, accounting for vacuum instability and electron-hole pair creation effects.

Contribution

It introduces a Fock-space representation for the Dirac model in graphene, incorporating vacuum instability effects into photon emission calculations.

Findings

Constructed the Fock-space representation for the Dirac model.

Derived total probabilities for photon emission considering vacuum effects.

Accounted for nonperturbative electron-hole pair creation in strong fields.

Abstract

Low-energy single-electron dynamics in graphene monolayers and similar nanostructures is described by the Dirac model, being a 2+1 dimensional version of massless QED with the speed of light replaced by the Fermi velocity v_{F}=c/300. Methods of strong-field QFT are relevant for the Dirac model, since any low-frequency electric field requires a nonperturbative treatment of massless carriers in case it remains unchanged for a sufficiently long time interval. In this case, the effects of creation and annihilation of electron-hole pairs produced from vacuum by a slowly varying and small-gradient electric field are relevant, thereby substantially affecting the radiation pattern. For this reason, the standard QED text-book theory of photon emission cannot be of help. We construct the Fock-space representation of the Dirac model, which takes exact accounts of the effects of vacuum instability caused by external electric fields, and in which the interaction between electrons and photons is taken into account perturbatively, following the general theory (the generalized Furry representation). We consider the effective theory of photon emission in the first-order approximation and construct the corresponding total probabilities, taking into account the unitarity relation.