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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.
The valley degeneracy of electron states in graphene stimulates intensive research of valley-related optical and transport phenomena. While many proposals on how to manipulate valley states have been put forward, experimental access to the valley pol
The second-order nonlinear optical susceptibility $Pi^{(2)}$ for second harmonic generation is calculated for gapped graphene. The linear and second-order nonlinear plasmon excitations are investigated in context of second harmonic generation (SHG).
Quantum geometry of the electron wave function plays a significant role in the linear and non-linear responses of crystalline materials. Here, we study quantum geometry induced second harmonic generation. We identify non-linear responses stemming fro
An optical Second-Harmonic Generation (SHG) allows to probe various structural and symmetry-related properties of materials, since it is sensitive to the inversion symmetry breaking in the system. Here, we investigate the SHG response from a single l
Valley polarization in graphene breaks inversion symmetry and therefore leads to second-harmonic generation. We present a complete theory of this effect within a single-particle approximation. It is shown that this may be a sensitive tool to measure