Theory of third-harmonic generation in graphene: A diagrammatic approach

We present a finite-temperature diagrammatic perturbation theory of third-harmonic generation 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 interband nature. Only logarithms survive in the final result. We conclude by presenting quantitative results for the upconversion efficiency at zero and finite temperature. Our approach can be easily generalized to other materials and to include many-body effects.