# Doping Induced Second Harmonic Generation in Centrosymmetric Graphene from Quadrupole Response

## TL;DR

This paper reports a doping-induced second harmonic generation in centrosymmetric graphene, arising from an electric-quadrupole response, with tunability via carrier doping and potential for novel optoelectronic applications.

## Contribution

It demonstrates a novel electric-quadrupole SHG in graphene, enabled by optical dressing, expanding nonlinear optics in centrosymmetric 2D materials.

## Key findings

- Strong SHG observed in doped graphene
- SHG tunable by carrier doping and chemical potential
- SHG peaks at Fermi edge resonances

## Abstract

For centrosymmetric materials such as monolayer graphene, no optical second harmonic generation (SHG) is generally expected because it is forbidden under the electric-dipole approximation. Yet we observed a strong, doping induced SHG from graphene, with its highest strength comparable to the electric-dipole allowed SHG in non-centrosymmetric 2D materials. This novel SHG has the nature of an electric-quadrupole response, arising from the effective breaking of inversion symmetry by optical dressing with an in-plane photon wave vector. More remarkably, the SHG is widely tuned by carrier doping or chemical potential, being sharply enhanced at Fermi edge resonances, but vanishing at the charge neutral point that manifests the electron-hole symmetry of massless Dirac Fermions. The striking behavior in graphene, which should also arise in graphene-like Dirac materials, expands the scope of nonlinear optics, and holds the promise of novel optoelectronic and photonic applications.

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Source: https://tomesphere.com/paper/1812.11306