Electron self-energy in two dimensions

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Abstract
We have carried out an extensive investigation of the frequency-dependent quasiparticle Coulomb self-energy of a two-dimensional electron gas for various values of the electronic density. Our analysis reveals a richly structured self-energy, a feature that we attribute to the existence in two dimensions of a low-lying collective-excitation spectrum. From the self-energy we have extracted and studied the effective mass, the spectral density, the wave-function renormalization factor, and the momentum-space occupation number. Our approach is based on Hedin’s GW approximation and the effective interaction due to Kukkonen and Overhauser. One of the purposes of the present work is to investigate for the first time the many-body effects associated with charge- and spin-fluctuation-induced vertex corrections, which we have included by a suitable choice of the Hubbard-type many-body local fields appearing in the effective interaction. The present study shows that the unjustified neglect of these effects can lead to a seriously inaccurate estimate of various quantities of interest. The validity of the familiar on-shell approximation is also discussed. For simplicity, we have carried out our calculations at zero temperature and have taken advantage of the plasma-pole scheme.