Many-Body Theory of Nonlinear Response in Dirac Materials

We show that the standard concepts of nonlinear response to electromagnetic fields break down in two dimensional Dirac systems, like graphene, in the quantum regime close to the Dirac point. Using a conserving Baym-Kadanoff approach, we present a fully compelling theory of nonlinear optical and transport response of a Dirac system to electric fields in the presence of disorder scattering. We show that the nonlinear terms are strikingly ruled by the appearance of a dominant two-photon vertex which is absent at the bare level and finite even in the weak-coupling limit. Such two-photon vertex self-generation [1] highlights the crucial role of the frequency and field dependence of the scattering rates in the nonlinear regime. Moreover, we surprisingly predict four- and five-photon incoherent features in the third order optical response of the system. Our study reveals a novel many-body mechanism in the nonlinear response of Dirac materials whose effects are predicted to be observable in nonlinear dc transport and terahertz third-harmonic generation of graphene.

[1] Habib Rostami and Emmanuele Cappelluti, arXiv:2007.08282 (2020).