Screening of a single impurity and Friedel oscillations in Fermi liquids

TL;DR

This paper numerically investigates how electron interactions affect Friedel oscillations and screening around a single impurity in one- and two-dimensional Fermi liquids, revealing damping and localization effects.

Contribution

It introduces a self-energy approach obeying Luttinger's theorem to study interaction effects on impurity screening and oscillations in lattice electrons.

Findings

Oscillation amplitude decreases with interaction strength in 1D.

Screening charge is suppressed by interactions.

Surface oscillations become more localized in 2D with increasing interactions.

Abstract

We numerically study Friedel Oscillations and screening effect around a single impurity in one- and two-dimensional interacting lattice electrons. The interaction between electrons is accounted for by using a momentum independent self-energy obeying the Luttinger theorem. It is observed in one-dimensional systems that the amplitude of oscillations is systematically damped with increasing the interaction while the period remains unchanged. The variation of screening charge with the impurity potential is discussed. We see that the screening charge is suppressed by the interactions. In case of two-dimensional systems the surface oscillations around the impurity are more localized with increasing the interactions.