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).