Electron waves in chemically substituted graphene

TL;DR

This paper provides exact analytical and numerical insights into how chemical substitutional impurities affect electronic spectra and Friedel oscillations in graphene, highlighting interference effects detectable by STM.

Contribution

It introduces a comprehensive T-matrix formalism to analyze impurity effects in graphene, accounting for changes in on-site potential and hopping amplitudes, including hopping disorder effects.

Findings

Hopping disorder introduces additional interference terms.

Impurity effects can be observed via scanning tunneling microscopy.

Analytical and numerical results agree on impurity-induced spectral features.

Abstract

We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential as well as in the hopping amplitude. We employ a T-matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity that can be understood in terms of bound, semi-bound, and unbound processes for the Dirac electrons. These interference effects can be detected by scanning tunneling microscopy.