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Register a new userDoping Induced Second Harmonic Generation in Centrosymmetric Graphene from Quadrupole Response
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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.
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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 polarization in graphene is still a challenge. Here, we develop a theory of the second optical harmonic generation in graphene and show that this effect can be used to measure the degree and sign of the valley polarization. We show that, at the normal incidence of radiation, the second harmonic generation stems from imbalance of carrier populations in the valleys. The effect has a specific polarization dependence reflecting the trigonal symmetry of electron valley and is resonantly enhanced if the energy of incident photons is close to the Fermi energy.
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). We report a red shift and an order of magnitude enhancement of the SHG resonance with growing gap, or alternatively, reduced electro-chemical potential.
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 from the quantum geometric tensor and the quantum geometric connection in systems with finite Fermi surfaces and disorder. In addition to the injection, shift, and anomalous currents we find two new contributions, which we term double resonant and higher-order pole contributions. Our findings can be tested in state-of-the-art devices in WTe2 (time-reversal symmetric system) and in CuMnAs (parity-time reversal symmetric systems).
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 layer of graphene disposed on an insulating hexagonal Boron Nitride (hBN) and Silicon Carbide (SiC) substrates. The considered systems are described by a non-interacting tight-binding model with a mass term, which describes a non-equivalence of two sublattices of graphene when the latter is placed on a substrate. The resulting SHG signal linearly depends on the degree of the inversion symmetry breaking (value of the mass term) and reveals several resonances associated with the band gap, van Hove singularity, and band width. The difficulty in distinguishing between SHG signals coming from the considered heterostrusture and environment (insulating substrate) can be avoided applying a homogeneous magnetic field. The latter creates Landau levels in the energy spectrum and leads to multiple resonances in the SHG spectrum. Position of these resonances explicitly depends on the value of the mass term. We show that at energies below the band-gap of the substrate the SHG signal from the massive graphene becomes resonant at physically relevant values of the applied magnetic field, while the SHG response from the environment stays off-resonant.
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 the valley polarization created, e.g., by polarized light and, thus, can be used for a development of ultrafast valleytronics in graphene.
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