## (a) Plot of the analytical intraband current *j*_{2D}(ψ) (blue solid line), its hyperbolic tangent approximation (black dash–dotted line) and its relativistic approximation (red dashed line)

**Figure 2.** (a) Plot of the analytical intraband current *j*_{2D}(ψ) (blue solid line), its hyperbolic tangent approximation (black dash–dotted line) and its relativistic approximation (red dashed line). (b)–(d) Plots of analytical intraband current *j*_{2D}(*t*) when ψ(*t*) = ψ_{0}sech(*t*/*t*_{0})cos(5*t*/*t*_{0}) (blue solid line), for ψ_{0} = 0.2, 1 and 3 respectively, corresponding to the three black dots in (a). The same curves but using the tanh and the relativistic approximations are also shown by the black dash–dotted and the red dashed lines, respectively.

**Abstract**

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.