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Register a new userValley polarization induced second harmonic generation in graphene
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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.
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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.
The electron transport of different conical valleys is investigated in graphene with extended line-defects. Intriguingly, the electron with a definite incident angle can be completely modulated into one conical valley by a resonator which consists of several paralleling line-defects. The related incident angle can be controlled easily by tuning the parameters of the resonator. Therefore, a controllable 100% valley polarization, as well as the detection of the valley polarization, can be realized conveniently by tuning the number of line-defects and the distance between two nearest neighbouring line-defects. This fascinating finding opens a way to realize the valley polarization by line-defects. With the advancement of experimental technologies, this resonator is promising to be realized and thus plays a key role in graphene valleytronics.
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.
Second harmonic generation (SHG) is a fundamental nonlinear optical phenomenon widely used both for experimental probes of materials and for application to optical devices. Even-order nonlinear optical responses including SHG generally require breaking of inversion symmetry, and thus have been utilized to study noncentrosymmetric materials. Here, we study theoretically the SHG in inversion-symmetric Dirac and Weyl semimetals under a DC current which breaks the inversion symmetry by creating a nonequilibrium steady state. Based on analytic and numerical calculations, we find that Dirac and Weyl semimetals exhibit strong SHG upon application of finite current. Our experimental estimation for a Dirac semimetal Cd$_3$As$_2$ and a magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$ suggests that the induced susceptibility $chi^{(2)}$ for practical applied current densities can reach $10^5~mathrm{pm}cdotmathrm{V}^{-1}$ with mid-IR or far-IR light. This value is 10$^2$-10$^4$ times larger than those of typical nonlinear optical materials. We also discuss experimental approaches to observe the current-induced SHG and comment on current-induced SHG in other topological semimetals in connection with recent experiments.
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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