Friedel oscillations around a short range scatterer

The case of graphene

A. Virosztek, Ádám Bácsi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We review the basic theory of Friedel oscillations around a well localized impurity using Green's function technique in Born approximation. After a pedagogical presentation of the case of free electrons in various dimensions, we turn our attention to graphene, which is described by a tight-binding scheme. Utilizing the localized nature of the atomic wavefunctions we calculate the change in the electronic density due to the impurity, and identify, in addition to the slowly decaying long wavelength oscillations, a short wavelength pattern as well. The latter, being of opposite sign on the two sublattices of graphene, may cancel the leading inverse square envelope of the long wavelength oscillations, if a probe with resolution worse than a few unit cells is used. We corroborate these findings by exact diagonalization results on a 21×21 unit cell graphene sheet.

Original languageEnglish
Pages (from-to)691-697
Number of pages7
JournalJournal of Superconductivity and Novel Magnetism
Volume25
Issue number3
DOIs
Publication statusPublished - Apr 2012

Fingerprint

Graphite
Graphene
graphene
Wavelength
oscillations
scattering
wavelengths
Impurities
Born approximation
impurities
Wave functions
cells
Green's function
sublattices
free electrons
envelopes
Green's functions
Electrons
probes
electronics

Keywords

  • Friedel oscillations
  • Graphene

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Friedel oscillations around a short range scatterer : The case of graphene. / Virosztek, A.; Bácsi, Ádám.

In: Journal of Superconductivity and Novel Magnetism, Vol. 25, No. 3, 04.2012, p. 691-697.

Research output: Contribution to journalArticle

@article{0ca1ea3c4d044f24891f401f8a8c1810,
title = "Friedel oscillations around a short range scatterer: The case of graphene",
abstract = "We review the basic theory of Friedel oscillations around a well localized impurity using Green's function technique in Born approximation. After a pedagogical presentation of the case of free electrons in various dimensions, we turn our attention to graphene, which is described by a tight-binding scheme. Utilizing the localized nature of the atomic wavefunctions we calculate the change in the electronic density due to the impurity, and identify, in addition to the slowly decaying long wavelength oscillations, a short wavelength pattern as well. The latter, being of opposite sign on the two sublattices of graphene, may cancel the leading inverse square envelope of the long wavelength oscillations, if a probe with resolution worse than a few unit cells is used. We corroborate these findings by exact diagonalization results on a 21×21 unit cell graphene sheet.",
keywords = "Friedel oscillations, Graphene",
author = "A. Virosztek and {\'A}d{\'a}m B{\'a}csi",
year = "2012",
month = "4",
doi = "10.1007/s10948-012-1436-1",
language = "English",
volume = "25",
pages = "691--697",
journal = "Journal of Superconductivity and Novel Magnetism",
issn = "1557-1939",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Friedel oscillations around a short range scatterer

T2 - The case of graphene

AU - Virosztek, A.

AU - Bácsi, Ádám

PY - 2012/4

Y1 - 2012/4

N2 - We review the basic theory of Friedel oscillations around a well localized impurity using Green's function technique in Born approximation. After a pedagogical presentation of the case of free electrons in various dimensions, we turn our attention to graphene, which is described by a tight-binding scheme. Utilizing the localized nature of the atomic wavefunctions we calculate the change in the electronic density due to the impurity, and identify, in addition to the slowly decaying long wavelength oscillations, a short wavelength pattern as well. The latter, being of opposite sign on the two sublattices of graphene, may cancel the leading inverse square envelope of the long wavelength oscillations, if a probe with resolution worse than a few unit cells is used. We corroborate these findings by exact diagonalization results on a 21×21 unit cell graphene sheet.

AB - We review the basic theory of Friedel oscillations around a well localized impurity using Green's function technique in Born approximation. After a pedagogical presentation of the case of free electrons in various dimensions, we turn our attention to graphene, which is described by a tight-binding scheme. Utilizing the localized nature of the atomic wavefunctions we calculate the change in the electronic density due to the impurity, and identify, in addition to the slowly decaying long wavelength oscillations, a short wavelength pattern as well. The latter, being of opposite sign on the two sublattices of graphene, may cancel the leading inverse square envelope of the long wavelength oscillations, if a probe with resolution worse than a few unit cells is used. We corroborate these findings by exact diagonalization results on a 21×21 unit cell graphene sheet.

KW - Friedel oscillations

KW - Graphene

UR - http://www.scopus.com/inward/record.url?scp=84860767829&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860767829&partnerID=8YFLogxK

U2 - 10.1007/s10948-012-1436-1

DO - 10.1007/s10948-012-1436-1

M3 - Article

VL - 25

SP - 691

EP - 697

JO - Journal of Superconductivity and Novel Magnetism

JF - Journal of Superconductivity and Novel Magnetism

SN - 1557-1939

IS - 3

ER -