Friedel oscillations at the Dirac-cone-merging point in anisotropic graphene

TL;DR

This paper investigates the unique Friedel oscillations caused by impurities in anisotropic graphene at the Dirac-cone-merging point, revealing asymmetrical patterns and unconventional decay behaviors through analytical and numerical methods.

Contribution

It provides the first detailed analysis of Friedel oscillations at the Dirac-cone-merging point in anisotropic graphene using both T-matrix and tight-binding techniques.

Findings

Friedel oscillations exhibit strong asymmetry.

Oscillations decay with an inverse square-root law.

Results from different methods are in excellent agreement.

Abstract

We study the Friedel oscillations induced by a localized impurity in anisotropic graphene. We focus on the limit when the two inequivalent Dirac points merge. We find that in this limit the Friedel oscillations manifest very peculiar features, such as a strong asymmetry and an atypical inverse square-root decay. Our calculations are performed using both a T-matrix approximation and a tight-binding exact diagonalization technique. They allow us to obtain numerically the local density of states as a function of energy and position, as well as an analytical form of the Friedel oscillations in the continuum limit. The two techniques yield results that are in excellent agreement, confirming the accuracy of such methods to approach this problem.