Stopping Power Modulation by Pump Waves of Charged Particles Moving above Two-Dimensional Electron Gases

The perturbation electron density and stopping power caused by the movement of charged particles above two-dimensional quantum electron gases (2DQEG) have been studied in numerous works using the quantum hydrodynamic (QHD) theory. In this paper, the QHD is modified by introducing the two-dimensional electron exchange-correlation potential at high density $V_{xc2\text{DH}}$ and the pump wave modulations. Based on the modified QHD, the perturbation electron density and stopping power are calculated for pump waves with various parameters. The results show that the stopping power values are more accurate after considering $V_{xc2\text{DH}}$ . Under the modulation of pump waves with the wavelength from $0.1\text{nm}$ to $0.1\text{cm}$ , the perturbation electron density of 2DQEG and the stopping power of charged particles show periodic changes. Under the modulation of pump waves with $\lambda =1.76\times {10}^{-4}$ cm and ${\mathrm{\Phi }}_0=2\times {10}^{10}e/{\lambda }_f$ , the average stopping power with respect to the time phase $\theta$ becomes negative, which means that the charged particles will gain energy and can be accelerated. This is a new phenomenon in the fields of 2DQEG and of great significance in surface physics and surface modification in nanoelectronic devices with beam matter interactions.