**Figure 3.** (a) Soliton profiles of the fundamental mode (*n* = 0) and two higher order modes (*n* = 1 and *n* = 2) as a function of dimensionless radius *R*, for *q* = −0.7. (b) Same as (a), but for *q* = −0.1. (c), (d) 3D plots of the fundamental and the second-order soliton of (a), (b), 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.