Theory of third harmonic generation in graphene: a diagrammatic approach

TL;DR

This paper develops a diagrammatic perturbation theory for third harmonic generation in doped graphene, revealing that only logarithmic terms remain after cancellations and providing quantitative efficiency results.

Contribution

It introduces a finite-temperature diagrammatic approach to THG in graphene, clarifying the role of Fermi surface and inter-band contributions and resolving existing disputes.

Findings

Logarithmic dependence of THG on carrier concentration

Quantitative efficiency results at various temperatures

Cancellation of power-law contributions in the final theory

Abstract

We present a finite-temperature diagrammatic perturbation theory of third harmonic generation (THG) in doped graphene. We carry out calculations of the third-order conductivity in the scalar potential gauge, highlighting a subtle cancellation between a Fermi surface contribution, which contains only power laws, and power-law contributions of inter-band nature. Only logarithms survive in the final result. We conclude by presenting quantitative results for the up-conversion efficiency at zero and finite temperature. Our results shed light on the on-going dispute over the dependence of THG on carrier concentration in graphene.