Longitudinal and transverse dielectric functions of a two-dimensional electron system: Inclusion of exchange correlations

Abstract

The calculation of the longitudinal dielectric function for a two-dimensional electron system is of importance in discussing the properties of electrons in semiconductor-insulator sandwiches and those confined to the surface of liquid helium. We present here a calculation of this function when exchange processes are included. A variational solution to the vertex equation is used to solve the integral equation. We also compute the plasmon dispersion and the static dielectric function in powers of the wave vector, by solving the appropriate vertex equation exactly in these limits. The latter is important in a theory of gradient expansion for the inhomogeneous counterpart of this two-dimensional system. This may be used in the calculation of the band structure of such systems. We also calculate the transverse dielectric function in the same scheme. From these two, we deduce the orbital susceptibility of the system. As in three dimensions, we find that screening of the electron interactions is essential to give finite values for the orbital susceptibility and the coefficient of the gradient expansion term in the theory of inhomogeneous systems.