Nonlinear optical response of doped mono- and bilayer graphene: length gauge tight-binding model

TL;DR

This paper calculates the nonlinear optical response of doped mono- and bilayer graphene using a full dispersion tight-binding model, revealing significant Drude-like divergences and resonances near the Fermi level.

Contribution

It provides a comprehensive analysis of nonlinear optical responses in doped graphene with an exact dispersion model, including all relevant divergences and resonances, and extends the understanding to bilayer systems.

Findings

Nonlinear response includes a large Drude-like divergence.

Resonances are closely related to Fermi level transitions.

Analytic Dirac approximation accurately predicts responses at high doping.

Abstract

We compute the nonlinear optical response of doped mono- and bilayer graphene using the full dispersion based on tight-binding models. The response is derived with the density matrix formalism using the length gauge and is valid for any periodic system, with arbitrary doping. By collecting terms that define effective nonlinear response tensors, we identify all nonlinear Drude-like terms (up to third-order) and show that all additional spurious divergences present in the induced current vanish. The nonlinear response of graphene comprises a large Drude-like divergence and three resonances that are tightly connected with transitions occurring in the vicinity of the Fermi level. The analytic solution derived using the Dirac approximation captures accurately the first- and third-order responses in graphene, even at very high doping levels. The quadratic response of gapped graphene is also strongly enhanced by doping, even for systems with small gaps such as commensurate structures of graphene on SiC. The nonlinear response of bilayer graphene is significantly richer, combining the resonances that stem from doping with its intrinsic strong low-energy resonances.