Many-body method for infinite nonperiodic systems

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.

Figure 1

Values of ${\epsilon }^{-1}(z_1,z_2)-\delta (z_1-z_2)$ for different inverting regions $V_{\epsilon }=[L_B,L_V]$. Here, $r_s=2.07a_0$, $\omega =0$, and $k_{\Vert }=0.2k_F$, $k_F$ being the Fermi wave vector.

Figure 2

Contour levels of $W_0(z_1,z_2,k_{\Vert },\omega )-v(\mid z_1-z_2\mid ,k_{\Vert })$ in the $z_1,z_2$ plane. Thick curves: semi-infinite jellium. Thin curves: HEG of equal density. Here $r_s=2.07a_0$, $\omega =0$, and $k_{\Vert }=0.2k_F$.

Figure 3

Effective and bare Coulomb interaction near the jellium surface for points aligned on the normal. Here $\omega =0$. $r_s=2.07a_0$.

Figure 4

Self-energy ${\Sigma }_{\mathrm{XC}}(z_1,z_2,k_{\Vert },\omega )$ for $r_s=2.07a_0$, $k_{\Vert }=0$, and $\omega =\mu$. Inset: model in Ref. 20.