Comptes Rendus
L'effet hall quantique fractionnaire/The fractional quantum hall effect
Quantum Hall effect, chiral Luttinger liquids and fractional charges
[Effet Hall quantique, liquides de Luttinger et charges fractionnaires]
Comptes Rendus. Physique, Volume 3 (2002) no. 6, pp. 717-732.

Nous présentons une revue de quelques propriétés élémentaires de l'Effet Hall Quantique Fractionnaire et plus particulièrement des états de bord. Les aspects liquides chiraux de Luttinger des états de bords sont abordés et sondés expérimentalement par des mesures de transport. Les expériences de bruit de grenaille qui permettent de sonder la charge des quasiparticules sont aussi discutées.

We review some basic properties of the Fractional Quantum Hall Effect and particularly address the physics of the edge states. The chiral Luttinger liquid properties of the edges are discussed and probed experimentally using transport measurements. Shot noise measurements, which allow determination of the quasiparticle charge are also discussed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0705(02)01375-0
Keywords: quantum Hall effect, fractional charge, Luttinger liquids, 2D electron gas
Mot clés : effet Hall quantique, charge fractionnaire, liquide de Luttinger, gaz d'électrons bidimensionnel
Patrice Roche 1 ; V. Rodriguez 1 ; D.Christian Glattli 1, 2

1 Service de physique de l'etat condensé, CEA Saclay, 91191, Gif-sur-Yvette, France
2 Laboratoire de physique de la matière condensée, École normale supérieure, 24, rue Lhomond, 75231 Paris, France
@article{CRPHYS_2002__3_6_717_0,
     author = {Patrice Roche and V. Rodriguez and D.Christian Glattli},
     title = {Quantum {Hall} effect, chiral {Luttinger} liquids and fractional charges},
     journal = {Comptes Rendus. Physique},
     pages = {717--732},
     publisher = {Elsevier},
     volume = {3},
     number = {6},
     year = {2002},
     doi = {10.1016/S1631-0705(02)01375-0},
     language = {en},
}
TY  - JOUR
AU  - Patrice Roche
AU  - V. Rodriguez
AU  - D.Christian Glattli
TI  - Quantum Hall effect, chiral Luttinger liquids and fractional charges
JO  - Comptes Rendus. Physique
PY  - 2002
SP  - 717
EP  - 732
VL  - 3
IS  - 6
PB  - Elsevier
DO  - 10.1016/S1631-0705(02)01375-0
LA  - en
ID  - CRPHYS_2002__3_6_717_0
ER  - 
%0 Journal Article
%A Patrice Roche
%A V. Rodriguez
%A D.Christian Glattli
%T Quantum Hall effect, chiral Luttinger liquids and fractional charges
%J Comptes Rendus. Physique
%D 2002
%P 717-732
%V 3
%N 6
%I Elsevier
%R 10.1016/S1631-0705(02)01375-0
%G en
%F CRPHYS_2002__3_6_717_0
Patrice Roche; V. Rodriguez; D.Christian Glattli. Quantum Hall effect, chiral Luttinger liquids and fractional charges. Comptes Rendus. Physique, Volume 3 (2002) no. 6, pp. 717-732. doi : 10.1016/S1631-0705(02)01375-0. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/S1631-0705(02)01375-0/

[1] K. von Klitzing; G. Dorda; M. Pepper Phys. Rev. Lett., 45 (1980), p. 494

[2] D. Tsui; H. Stromer; A. Gossard Phys. Rev. Lett., 48 (1982), p. 1599

[3] R.B. Laughlin Phys. Rev. Lett., 50 (1983), p. 1395

[4] J.M. Leynaas; L. Myrheim Nuovo Cimento B, 37 (1977), p. 1

[5] S.R. Renn; D.P. Arovas Phys. Rev. B, 51 (1995), p. 16832

[6] S. Ouvry Phys. Rev. D, 50 (1994), p. 5296

[7] S. Wu Phys. Rev. Lett., 73 (1994), p. 922

[8] J. Jain Phys. Rev. Lett., 63 (1989), p. 199

[9] S.C. Zhang; H. Hansson; S. Kivelson Phys. Rev. Lett., 62 (1989), p. 82

[10] D.-H. Lee; S.-C. Zhang Phys. Rev. Lett., 66 (1991), p. 1220

[11] S.C. Zhang Int. J. Mod. Phys. B, 6 (1992), p. 25

[12] S.L. Sondhi; A. Karlhede; S.A. Kivelson; E.H. Rezayi Phys. Rev. B, 47 (1993), p. 16419

[13] S.M. Girvin Topological Aspects of Low Dimensional Systems, NATO ASI, Les Houches Summer School (A. Comtet; T. Jolicoeur; S. Ouvry; F. David, eds.), Springer, 1999, pp. 551-570

[14] The Quantum Hall Effect (R.E. Prange; S.M. Girvin, eds.), Springer-Verlag, New York, 1987

[15] A.H. Mac Donald Mesoscopic Quantum Physics (E. Akkermans; G. Montambaux; J.L. Pichard; J. Zinn-Justin, eds.), Elsevier, Amsterdam, 1994

[16] Perspectives in Quantum Hall Effects (S.D. Sarma; A. Pinczuk, eds.), Wiley, New York, 1997

[17] Topological Aspects of Low Dimensional Systems, NATO ASI, Les Houches Summer School (A. Comtet; T. Jolicoeur; S. Ouvry; F. David, eds.), Springer, 1999, pp. 551-570

[18] T. Ando; A.B. Fowler; F. Stern Rev. Mod. Phys., 54 (1982), p. 437

[19] Molecular Beam Epitaxy (A. Cho, ed.), AIP Press, Woodbury, New York, 1994

[20] T. Ando; Y. Matsumoto; Y. Uemura J. Phys. Soc. Japan, 39 (1975), p. 279

[21] P. Streda; L. Smrcka Phys. Stat. Solidi B, 70 (1975), p. 537

[22] M. Buettiker Phys. Rev. B, 38 (1988), p. 9375

[23] R.J. Haug et al. Phys. Rev. Lett., 61 (1988), p. 2797

[24] D.B. Chklovskii; B.I. Shklovskii; L.I. Glazman Phys. Rev. B, 46 (1992), p. 4026

[25] C.W.J. Beenakker Phys. Rev Lett., 64 (1990), p. 216

[26] A.H. MacDonald Phys. Rev. Lett., 64 (1990), p. 220

[27] H. Schulz Fermi liquids and non-Fermi liquids (E. Akkermans; G. Montambaux; J.L. Pichard; J. Zinn-Justin, eds.), Mesoscopic Quantum Physics, Proceedings of the Les Houches Summer School of Theoretical Physics, Session LXI, Springer-Verlag, 1994

[28] X.G. Wen Phys. Rev. B, 43 (1991), p. 11025

[29] X.G. Wen Phys. Rev. Lett., 64 (1990), p. 2206

[30] X.G. Wen Phys. Rev. B, 44 (1991), p. 5708

[31] X.G. Wen Int. J. Mod. Phys. B, 6 (1992), p. 1711

[32] J.M. Luttinger J. Math. Phys., 4 (1963), p. 1154

[33] S. Tomonaga Prog. Theor. Phys. (Kyoto), 5 (1950), p. 544

[34] C.L. Kane; M.P.A. Fisher Phys. Rev. B, 46 (1992), p. 15233

[35] C.L. Kane; M.P.A. Fisher Phys. Rev. Lett., 68 (1992), p. 1220

[36] C.L. Kane; M.P.A. Fisher Phys. Rev. B, 51 (1995), p. 13449

[37] A.V. Shytov; L.S. Levitov; B.I. Halperin Phys. Rev. Lett., 80 (1998), p. 141

[38] L.S. Levitov; A.V. Shytov; B.I. Halperin Phys. Rev. B, 64 (2001), p. 075322

[39] A.M. Chang; L.N. Pfeiffer; K.W. West Phys. Rev. Lett., 77 (1996), p. 2538

[40] M. Grayson; D.C. Tsui; L.N. Pfeiffer; K.W. West; A.M. Chang Phys. Rev. Lett., 80 (1998), p. 1062

[41] A.M. Chang; M.K. Wu; J.C.C. Chi; L.N. Pfeiffer; K.W. West Phys. Rev. Lett., 87 (2001), p. 2538

[42] A.M. Chang C.R. Physique, 3 (2002), pp. 677-684

[43] F.P. Milliken; C.P. Umbach; R.A. Webb Solid State Commun., 97 (1996), p. 309

[44] P. Fendley; A.W.W. Ludwig; H. Saleur Phys. Rev. Lett., 74 (1995), p. 3005

[45] P. Fendley; H. Saleur Phys. Rev. B, 54 (1996), p. 10845

[46] H. Saleur C.R. Physique, 3 (2002), pp. 685-695

[47] K. Moon; S.M. Girvin Phys. Rev B, 54 (1996), p. 4448

[48] K. Imura; N. Nagaosa Solid State Commun., 103 (1997), p. 663

[49] L.P. Pryadko; E. Shimshoni; A. Auerbach Phys. Rev. B, 61 (2000), p. 10929

[50] G.B. Lesovik Pis'ma Zh. Eksp. Teor. Fiz., 49 (1989), p. 513 [JETP Lett. 49 (1989) 592]

[51] M. Reznikov et al. Phys. Rev. Lett., 18 (1995), p. 3340

[52] A. Kumar et al. Phys. Rev. Lett., 76 (1996), p. 2778

[53] W. Schottky Ann. Phys. (Leipzig), 57 (1918), p. 541

[54] C.L. Kane; M.P.A. Fisher Phys. Rev. Lett., 72 (1994), p. 724

[55] C.de C. Chamon; D.E. Freed; X.G. Wen Phys. Rev. B, 51 (1995), p. 2363

[56] Th. Martin; R. Landauer Phys. Rev. B, 45 (1992), p. 1742

[57] Th. Martin; R. Landauer Physica B, 175 (1991), p. 167

[58] L. Saminadayar; D.C. Glattli; Y. Jin; B. Etienne Phys. Rev. Let., 79 (1997), p. 2526 | arXiv

[59] R. de-Picciotto et al. Nature, 389 (1997), p. 162 | arXiv

[60] M. Reznikov; R. de-Picciotto; T.G. Griffiths; M. Heiblum Nature, 399 (1999), p. 238

[61] R. de-Picciotto | arXiv

Cité par Sources :

Commentaires - Politique


Ces articles pourraient vous intéresser

Edge states tunneling in the fractional quantum Hall effect: integrability and transport

Hubert Saleur

C. R. Phys (2002)


Fractional statistics, Hanbury-Brown and Twiss correlations and the quantum Hall effect

Rodolphe Guyon; Thierry Martin; Inès Safi; ...

C. R. Phys (2002)