  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.
