Effect of a single impurity on the local density of states in monolayer and bilayer graphene

TL;DR

This paper investigates how a single impurity affects the local density of states in monolayer and bilayer graphene using the T-matrix approximation, revealing distinct oscillation behaviors and Fourier transform patterns.

Contribution

It provides a detailed analysis of impurity-induced oscillations in graphene layers, highlighting differences between monolayer and bilayer structures.

Findings

Monolayer graphene exhibits inverse-square and inverse law Friedel oscillations.

Fourier transform shows filled circle and empty contours in monolayer graphene.

Bilayer graphene shows inverse law oscillations for both types.

Abstract

We use the T-matrix approximation to analyze the effect of a localized impurity on the local density of states in mono- and bilayer graphene. For monolayer graphene the Friedel oscillations generated by intranodal scattering obey an inverse-square law, while the internodal ones obey an inverse law. In the Fourier transform this translates into a filled circle of high intensity in the center of the Brillouin zone, and empty circular contours around its corners. For bilayer graphene both types of oscillations obey an inverse law.