(a) Schematics of graphene conical dispersion with doping
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Figure 1. (a) Schematics of graphene conical dispersion with doping. Intraband and interband optical transitions are indicated. (b) Geometry of the proposed multilayer metamaterial. The structure is made up of alternating graphene–silica–silicon layers, with total thickness L, much smaller than the wavelength of the THz beam. Each layer of graphene is doped by using an applied gate voltage Vg.
We propose an electrically tunable graphene-based metamaterial that shows a large nonlinear optical response at THz frequencies. The responsible nonlinearity comes from the intraband current, which we are able to calculate analytically. We demonstrate that the proposed metamaterial supports stable 2D spatial solitary waves. Our theoretical approach is not restricted to graphene, but can be applied to all materials exhibiting a conical dispersion supporting massless Dirac fermions.