Hydrodynamic electron transport and nonlinear waves in graphene

We derive the system of hydrodynamic equations governing the collective motion of massless fermions in graphene. The obtained equations demonstrate the lack of Galilean and Lorentz invariance and contain a variety of nonlinear terms due to the quasirelativistic nature of carriers. Using these equations, we show the possibility of soliton formation in an electron plasma of gated graphene. The quasirelativistic effects set an upper limit for soliton amplitude, which marks graphene out of conventional semiconductors. The mentioned noninvariance of the equations is revealed in spectra of plasma waves in the presence of steady flow, which no longer obey the Doppler shift. The feasibility of plasma-wave excitation by direct current in graphene channels is also discussed.

Figure 1

Dependence of soliton amplitude $\delta n_{max}/n_0$ on its velocity $(u_0-s_0)/v_F$ at different velocities of plasma waves, $s_0$. The dashed black line indicates the boundary of soliton existence. The profiles of solitary waves obtained from numerical integration of Eq. (25) are plotted in the insets.

Figure 2

Dependencies of plasma-wave velocities $s_{\pm }$ in the presence of steady flow on the flow velocity $u_0$.

Figure 3

Dependence of wave increment ${\omega }_1^{\prime \prime }$ on flow velocity $u_0$ at different values of Fermi energy.