Simplified theory of the acoustic surface plasmons at the two-dimentional electron gas

In the two-dimensional electron gas (2DEG), the system can be polarized by metal ions on the 2D surface, resulting in screening of Coulomb interaction between electrons. We calculate the 2D screened Coulomb interaction in Thomas–Fermi approximation and find that both electron–hole (e–h) and collective excitations occurring in the 2DEG can be described with the use of effective dielectric function, in the random-phase approximation (RPA). In this paper we show that the mode proportional to in-plane momentum, called acoustic surface plasmon (ASP), can appear in long-wavelength limit. We calculate ASP dispersion and determine the critical wave number and frequency for the ASP decay into e–h pair, and the velocity of ASP. Our result agrees qualitatively with previous ones in tendency.