Hydrodynamic model for 2D degenerate free-electron gas for arbitrary frequencies

Abstract

Following Halevi's procedure for 3D degenerate free-electron gas (3D-DEG), we investigate the response function in the hydrodynamic model (HM) for 2D-DEG confined in low dimensional systems when collisions are included. For small wavevectors we found from the two-dimensional Boltzmann-Mermin model a useful expression for the HM complex stiffness parameter of the nonlocal dielectric function~$\beta $, which is $\beta ^{2}= [\left( (% 3\omega /4) +i(\nu /2)\right) /(\omega +i\nu )]v_{F}^{2}$, where $% \omega $ and $\nu $ are the circular and collisional frequencies and $v_{F}$ is the Fermi velocity.