Many-body method for infinite nonperiodic systems

Abstract

A method to implement the many-body Green function formalism in the GW approximation for infinite nonperiodic systems is presented. It is suitable to treat systems of known "asymptotic" properties which enter as boundary conditions, while the effects of the lower symmetry are restricted to regions of finite volume. For example, it can be applied to surfaces or localized impurities. We illustrate the method with a study of the surface of semi-infinite jellium. We report the dielectric function, the effective potential, and the electronic self-energy discussing the effects produced by the screening and by the charge density profile near the surface.

An effective potential of electron-electron interaction in semi-infinite jellium

“…As follows from this figure, there is observed a qualitative agreement between the results of our calculations and the results of the work [6]. However, the effective potential in the work [6] decreases faster to zero and there is no oscillation. In our opinion, the collective effects being insufficiently taken into account are responsible for this situation.…”

“…It is shown that numerical results for g [6] correspond to the mirror electron scattering approximation for g (25).…”

“…Effective potential of electron-electron interaction is a solution of the integral equation (see, for example, [6,7])…”

“…These figures show that the effective potential obtained by numerical solution of the integral equation (10) oscillates (solid line) and the neglect of electron scattering along the normal to the surface leads to the absence of the effective potential oscillations along the normal while there are oscillations in the plane parallel to the surface (see figures 3a,b,d). Figure 5 presents a comparison of the numerical solution of the integral equation (10), the results of the work [6] and Coulomb potential. As follows from this figure, there is observed a qualitative agreement between the results of our calculations and the results of the work [6].…”

“…Figure 5 presents a comparison of the numerical solution of the integral equation (10), the results of the work [6] and Coulomb potential. As follows from this figure, there is observed a qualitative agreement between the results of our calculations and the results of the work [6]. However, the effective potential in the work [6] decreases faster to zero and there is no oscillation.…”