Hydrodynamic Effects in Interacting Fermi Electron Jets

We theoretically study hydrodynamic phenomena originating from electron-electron collisions in a two-dimensional Fermi system. We demonstrate that an electron beam sweeping past an aperture creates a pumping effect, attracting carriers from this aperture. This pumping effect originates from the specific electric potential distribution induced by the injected electrons. In the regions near the main stream of injected electrons, a positive potential is induced by the injected electrons. Thus, the normally repulsive Coulomb interaction leads to an attractive force in the Fermi system. This quantum pumping mechanism in a Fermi system differs qualitatively from the Bernoulli pumping effect in classical liquids. We also discuss possible experimental realizations.

Figure 1

(a) Momentum relaxation and electron-electron mean free paths, $l_p$ and $l_{ee}$, as a function of temperature. The parameter $l_p$ is obtained from mobility measurements on a GaAs$/$AlGaAs heterostructure at the 2DES density $4.8\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ [12]. $l_{ee}$ is calculated using Eq. (14) from Ref. 10. (b) Geometry of the system with an injected electron beam. (c) Schematic of two symmetric jets in a two-dimensional plasma.

Figure 2

Calculated nonequilibrium electron density as a function of the in-plane coordinates.

Figure 3

Schematic of a hydrodynamic pump in a mesoscopically patterned 2DES. The streamlines and density distribution are shown schematically. The detector serves as a probe for the potential near the main beam of electrons. Inset: The induced voltage at point $A$ with coordinates $(x_A,y_A)$ as a function of temperature; $N=10$; 2DES $\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}=4.8\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$, $d=400\AA$, $a_0^{*}=100\AA$, and $ϵ=12.5$.

Figure 4

Calculated nonequilibrium electron density as a function of the $x$ coordinate in the one-dimensional system. Inset: Schematic of a hydrodynamic pump utilizing a one-dimensional channel with an injecting barrier and a detector aperture.