  Using a conserving Baym-Kadanoff approach, we present a fully compelling
theory of nonlinear dc 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 highlights the crucial role of the frequency
and field dependence of the scattering rates in the nonlinear regime. Our study
reveals a novel many-body mechanism in the nonlinear response of Dirac
materials whose effects are predicted to be observable.
