Comptes Rendus
Condensed matter physics in the 21st century: The legacy of Jacques Friedel
Friedel oscillations in graphene-based systems probed by Scanning Tunneling Microscopy
[Oscillations de Friedel dans les systèmes à base de graphène, sondées par Microscopie à Effet Tunnel]
Comptes Rendus. Physique, Volume 17 (2016) no. 3-4, pp. 294-301.

Depuis 25 ans, les scientifiques utilisent la microscopie à effet tunnel afin de visualiser dans l'espace direct la réponse d'un gaz d'électron bidimensionnel à des impuretés de taille atomique. L'analyse des oscillations de Friedel générées autour de telles impuretés donne des informations précieuses sur le système 2D : propriétés de diffusion élastique, structure de bande, niveau de dopage et symétrie des états électroniques. Cet article est consacré à l'analyse par microscopie à effet tunnel des oscillations de Friedel dans le graphène, matériau 2D star de cette dernière décennie. En particulier, nous montrons comment cette technique permet d'accéder au pseudospin, un degré de liberté unique propre aux fermions de Dirac du graphène.

For the last 25 years, scientists have demonstrated the capabilities of Scanning Tunneling Microscopy (STM) to visualize in real space the response of a two-dimensional electron gas to atomic-scale impurities. The analysis of the Friedel oscillations surrounding the impurities yields valuable information regarding the elastic scattering properties, the band structure, the doping level and the symmetry of the electronic states in the two-dimensional host system. We will address in this article the use of this technique for probing the electronic properties of graphene, the star two-dimensional compound of the last decade. In particular, we will emphasize how this technique can be pushed up to unravel the electronic pseudospin, a distinctive degree of freedom of graphene's Dirac fermions.

Publié le :
DOI : 10.1016/j.crhy.2015.12.013
Keywords: Friedel oscillations, Graphene, Dirac fermions, Electronic pseudospin, Scanning tunneling microscopy
Mot clés : Oscillations de Friedel, Graphène, Fermions de Dirac, Pseudospin électronique, Microscope à effet tunnel

Pierre Mallet 1, 2 ; Iván Brihuega 3 ; Vladimir Cherkez 1, 2, 4 ; Jose Marìa Gómez-Rodríguez 3 ; Jean-Yves Veuillen 1, 2

1 Université Grenoble Alpes, Institut Néel, 38042 Grenoble, France
2 CNRS, Institut Néel, 38042 Grenoble, France
3 Departamento de Física de la Materia Condensada, Universidad Autonoma de Madrid, 28049 Madrid, Spain
4 LNCMI, CNRS–UJF–UPS–INSA, 25, rue des Martyrs, 38042 Grenoble, France
@article{CRPHYS_2016__17_3-4_294_0,
     author = {Pierre Mallet and Iv\'an Brihuega and Vladimir Cherkez and Jose Mar{\`\i}a G\'omez-Rodr{\'\i}guez and Jean-Yves Veuillen},
     title = {Friedel oscillations in graphene-based systems probed by {Scanning} {Tunneling} {Microscopy}},
     journal = {Comptes Rendus. Physique},
     pages = {294--301},
     publisher = {Elsevier},
     volume = {17},
     number = {3-4},
     year = {2016},
     doi = {10.1016/j.crhy.2015.12.013},
     language = {en},
}
TY  - JOUR
AU  - Pierre Mallet
AU  - Iván Brihuega
AU  - Vladimir Cherkez
AU  - Jose Marìa Gómez-Rodríguez
AU  - Jean-Yves Veuillen
TI  - Friedel oscillations in graphene-based systems probed by Scanning Tunneling Microscopy
JO  - Comptes Rendus. Physique
PY  - 2016
SP  - 294
EP  - 301
VL  - 17
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crhy.2015.12.013
LA  - en
ID  - CRPHYS_2016__17_3-4_294_0
ER  - 
%0 Journal Article
%A Pierre Mallet
%A Iván Brihuega
%A Vladimir Cherkez
%A Jose Marìa Gómez-Rodríguez
%A Jean-Yves Veuillen
%T Friedel oscillations in graphene-based systems probed by Scanning Tunneling Microscopy
%J Comptes Rendus. Physique
%D 2016
%P 294-301
%V 17
%N 3-4
%I Elsevier
%R 10.1016/j.crhy.2015.12.013
%G en
%F CRPHYS_2016__17_3-4_294_0
Pierre Mallet; Iván Brihuega; Vladimir Cherkez; Jose Marìa Gómez-Rodríguez; Jean-Yves Veuillen. Friedel oscillations in graphene-based systems probed by Scanning Tunneling Microscopy. Comptes Rendus. Physique, Volume 17 (2016) no. 3-4, pp. 294-301. doi : 10.1016/j.crhy.2015.12.013. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.12.013/

[1] A.K. Geim Science, 324 (2009), p. 1530

[2] A. Ferrari et al. Nanoscale, 7 (2015), p. 4598

[3] P.R. Wallace Phys. Rev., 71 (1947), p. 622

[4] A.H. Castro Neto; F.N.M.R. Peres; K.S. Novoselov; A. Geim Rev. Mod., 81 (2009), p. 109

[5] M.I. Katsnelson; K.S. Novoselov; A.K. Geim Nat. Phys., 2 (2006), p. 620

[6] S.V. Morozov et al. Phys. Rev. Lett., 100 (2008)

[7] J.-H. Chen et al. Nat. Nanotechnol., 3 (2008), p. 206

[8] A.S. Mayorov et al. Nano Lett., 11 (2011), p. 2396

[9] K.S. Novoselov; A.K. Geim; S.V. Morozov; D. Jiang; Y. Zhang; S.V. Dubonos; I.V. Grigorieva; A.A. Firsov Science, 306 (2004), p. 666

[10] K.S. Novoselov et al. Nature, 438 (2005), p. 197

[11] Y.B. Zhang; Y.-W. Tan; H.L. Stormer; P. Kim Nature, 438 (2005), p. 201

[12] E. McCann et al. Phys. Rev. Lett., 97 (2006)

[13] V.I. Fal'ko et al. Solid State Commun., 143 (2007), p. 33

[14] X. Wu; X. Li; Z. Song; C. Berger; W.A. de Heer Phys. Rev. Lett., 98 (2007)

[15] F.V. Tikhonenko; A.A. Kozikov; A.K. Savchenko; R.V. Gorbachev Phys. Rev. Lett., 103 (2009)

[16] A.F. Young; Ph. Kim Nat. Phys., 5 (2009), p. 222

[17] N. Stander; B. Huard; D. Goldhaber-Gordon Phys. Rev. Lett., 102 (2009)

[18] J. Friedel Suppl. Nuovo Cim., 2 (1958), p. 287

[19] T. Ando; T. Nakanishi; R. Saito J. Phys. Soc. Jpn., 67 (1998), p. 1704

[20] V.V. Cheianov; V.I. Fal'ko Phys. Rev. Lett., 97 (2006) (In this publication, it is shown that the charge density modulations have a 1/r3 decay, accordingly to the 1/r2 decay of the LDOS)

[21] E. Mariani; L.I. Glazman; A. Kamenev; F. von Oppen Phys. Rev. B, 76 (2007)

[22] C. Bena Phys. Rev. Lett., 100 (2008)

[23] T. Pereg-Barnea; A.H. MacDonald Phys. Rev. B, 78 (2008)

[24] C. Bena Phys. Rev. B, 79 (2009)

[25] N.M.R. Peres; L. Yang; S.W. Tsai New J. Phys., 11 (2009)

[26] A. Bacsi; A. Virosztek Phys. Rev. B, 82 (2010)

[27] M.F. Crommie; C.P. Lutz; D.M. Eigler Nature, 363 (1993), p. 524

[28] Y. Hasegawa; Ph. Avouris Phys. Rev. Lett., 71 (1993), p. 1071

[29] I. Brihuega et al. Phys. Rev. Lett., 101 (2008)

[30] P. Mallet et al. Phys. Rev. B, 86 (2012)

[31] G. Binnig; H. Rohrer Helv. Phys. Acta, 55 (1982), p. 726

[32] J. Tersoff; D.R. Hamann Phys. Rev. Lett., 50 (1983), p. 1998

[33] J.M. Ziman Principles of the Theory of Solids, Cambridge University Press, 1972

[34] N.W. Ashcroft; N. David Mermin Solid State Physics, Oxford University Press, Oxford, UK, 1987 (HRW International edn. chapter 17)

[35] F. Stern Phys. Rev. Lett., 18 (1967), p. 546

[36] M.F. Crommie; C.P. Lutz; D.M. Eigler Science, 262 (1993), p. 218

[37] F. Reinert; G. Nicolay; S. Schmidt; D. Ehm; S. Hüfner Phys. Rev. B, 63 (2001)

[38] L. Petersen et al. Phys. Rev. B, 57 (1998)

[39] L. Petersen; Ph. Hoffmann; E.W. Plummer; F. Besenbaecher J. Electron Spectrosc. Relat. Phenom., 109 (2000), p. 97

[40] Ph. Hofmann; B.G. Briner; M. Doering; H.-P. Rust; E.W. Plummer; A.M. Bradshaw Phys. Rev. Lett., 79 (1997), p. 265

[41] K. Mc Elroy et al. Nature, 422 (2003), p. 592

[42] Q.H. Wang; D.H. Lee Phys. Rev. B, 67 (2003)

[43] F. Vonau et al. Phys. Rev. Lett., 95 (2005)

[44] K. Mc Elroy et al. Phys. Rev. Lett., 96 (2006)

[45] L. Simon; C. Bena; F. Vonau; M. Cranney; D. Aubel J. Phys. D, Appl. Phys., 44 (2011), p. 464010

[46] L. Petersen; L. Bürgi; H. Brune; F. Besenbacher; K. Kern Surf. Sci., 443 (1999), p. 154

[47] J.I. Pascual et al. Phys. Rev. Lett., 93 (2004)

[48] P. Mallet et al. Phys. Rev. B, 76 (2007)

[49] F. Varchon et al. Phys. Rev. Lett., 99 (2007)

[50] F. Varchon; P. Mallet; J.Y. Veuillen; L. Magaud Phys. Rev. B, 77 (2008)

[51] A. Bostwick; T. Ohta; T. Seyller; K. Horn; E. Rotenberg Nat. Phys., 3 (2007), p. 36

[52] S.Y. Zhou et al. Nat. Mater., 6 (2007), p. 770

[53] T. Ohta et al. Phys. Rev. Lett., 98 (2007)

[54] G.M. Rutter; J.N. Crain; N.P. Guisinger; T. Li; P.N. First; J.A. Stroscio Science, 317 (2007), p. 219

[55] L. Simon; C. Bena; F. Vonau; D. Aubel; H. Nasrallah; M. Habar; J.C. Peruchetti Eur. Phys. J. B, 69 (2009), p. 351

[56] H. Yang; A.J. Mayne; M. Boucherit; G. Comtet; G. Dujardin Nano Lett., 10 (2010), p. 943

[57] M. Ye et al. Eur. Phys. J. B, 75 (2010), p. 31

[58] H.A. Mizes; J.S. Foster Science, 244 (1989), p. 559

[59] P. Ruffieux; O. Gröning; P. Schwaller; L. Schlapbach; P. Gröning Phys. Rev. Lett., 84 (2000), p. 4910

[60] P. Ruffieux et al. Phys. Rev. B, 71 (2005)

[61] M.M. Ugeda; I. Brihuega; F. Guinea; J.M. Gomez-Rodriguez Phys. Rev. Lett., 104 (2010)

[62] M.M. Ugeda et al. Phys. Rev. Lett., 107 (2011)

[63] J.M.B. Lopes dos Santos; N.M.R. Peres; A.H. Castro Neto Phys. Rev. Lett., 99 (2007)

[64] G. Trambly de Laissardiére; D. Mayou; L. Magaud Nano Lett., 10 (2010), p. 804

[65] M. Sprinkle et al. Phys. Rev. Lett., 103 (2009)

[66] G. Li; A. Luican; J.M.B. Lopes dos Santos; A.H. Castro Neto; A. Reina; J. Kong; E.Y. Andrei Nat. Phys., 6 (2009), p. 109

[67] I. Brihuega et al. Phys. Rev. Lett., 109 (2012)

[68] F. Varchon; P. Mallet; L. Magaud; J.-Y. Veuillen Phys. Rev. B, 77 (2008)

[69] A. Mahmood; P. Mallet; J.Y. Veuillen Nanotechnology, 23 (2012)

[70] I. Horcas et al. Rev. Sci. Instrum., 78 (2007)

Cité par Sources :

Commentaires - Politique