Plasma solitons in gated two-dimensional electron systems: Exactly solvable analytical model for the regime beyond weak nonlinearity

We analytically study plasma solitary waves, or solitons, in a two-dimensional electron system placed in close proximity to and between two ideal metallic gates. As a rule, solitons are described using a perturbative approach applicable only in the weak nonlinearity regime. In contrast, we analyze solitons considering a nonperturbative model. This framework enables an exact analytical description of the soliton shape. Moreover, it can be achieved in the regime beyond weak nonlinearity—when the concentration deviation due to the soliton is of the order of the equilibrium concentration. We determine the conditions required for a soliton to exist and derive the relationship between its amplitude, width, and velocity. We believe that our results obtained for the given model can provide valuable insight into the physics of nonlinear waves.

Figure 1

The exact spectrum of linear plasmons [Eq. (1)] (blue) compared against the approximations (gray and green) obtained, respectively, based on the expansion at $qd\ll 1$, and the model Green's function of the Poisson equation (4). The inset shows the schematic view of the 2DES setup under consideration.

Figure 2

The effective potential energy $W\left(\mathrm{\Phi }\right)$ (13) plotted for different values of the dimensionless soliton velocity (11), (a) $U=0.7$, (b) $U=1.6$, and (c) $U=2.4$. Solitons correspond to the finite solutions with zero energy that exist only for $1<U<2$, as indicated by the red line in (b).

Figure 3

The dimensionless soliton width $\mathrm{\Delta }X=\mathrm{\Delta }\xi /d$ extracted from the concentration dependency $n\left(X\right)$, plotted as a function of the velocity $U=u/v_p$ (11). Gray and green dashed lines denote the asymptotics (15) and (16), correspondingly. The width vanishes at $u/v_p=2$. The inset shows the soliton shape at $u/v_p=1.7$.