Friedel oscillations in a two-dimensional electron gas and monolayer graphene with a non-Coulomb impurity potential

TL;DR

This paper investigates how non-Coulomb impurity potentials affect Friedel oscillations in 2D electron gases and monolayer graphene, revealing that the oscillation phase remains unchanged while amplitude varies with the potential's non-Coulomb parameter.

Contribution

It introduces a model for impurity potentials with a non-Coulomb form and analyzes their impact on Friedel oscillations in 2D systems and graphene, extending understanding beyond Coulomb interactions.

Findings

Phase of oscillations unaffected by non-Coulomb parameter at large distances

Amplitude of oscillations depends on the non-Coulomb parameter

Results recover Coulomb potential case when parameter equals one

Abstract

We study Friedel oscillations in a two-dimensional non-interacting electron gas and in a monolayer graphene in the presence of a single impurity. The potential generated by the impurity is modeled using a non-Coulomb interaction ($\sim r^{-\eta}$). The charge carrier density deviation as a function of distance from the impurity is calculated within the linear response theory. Our results show that, in both a two-dimensional non-interacting electron gas and graphene, the phase of charge carrier density oscillations remains unaffected by the parameter $\eta$, which characterizes the non-Coulomb nature of the interaction, at large distances from the impurity. The parameter $\eta$ influences only the amplitude of the oscillations in this regime. The results for an impurity modeled by Coulomb-like potential ($\eta = 1$) are recovered in both cases.