Comptes Rendus
Exploring the electronic band structure of individual carbon nanotubes under 60 T
[Étude de la structure de bande électronique de nanotubes de carbone isolés sous 60 T]
Comptes Rendus. Physique, Volume 10 (2009) no. 4, pp. 268-282.

Les nano-sciences, et plus particulièrement la nano-physique, constituent un champ d'investigations aux défis expérimentaux multiples incluant la synthèse, l'adressage (par exemple, optique ou électrique), l'étude et l'exploitation des propriétés physiques remarquables des nano-objets individuels. Les nano-matériaux carbonés (hybridation sp2) concentrent aujourd'hui une attention toute particulière ; en effet, les nanotubes de carbone, le graphène et plus récemment encore les nano-rubans de graphène pourraient constituer d'ici peu des briques élémentaires de la micro-électronique du futur. Mais en premier lieu, il convient d'insister sur la compréhension des mécanismes de transport de charges lorsque ces nano-objets sont utilisés comme élément actif du canal drain–source soumis à un potentiel de grille, ou bien comme élément passif pour l'interconnection. Dans cet article, nous présenterons l'intérêt de conduire des expériences où les nano-objets individuels sont soumis à un environnement extrême : l'application de champs magnétiques très intenses et l'utilisation des très basses températures. Nous montrerons que des champs magnétiques de plusieurs dizaines de teslas, associés à un contrôle du dopage électrostatique, modifient singulièrement la structure de bande électronique d'un nanotube de carbone et permettent ainsi de sonder les états électroniques et les spécificités des régimes de conduction associés aux dimensions réduites. Plusieurs exemples seront abordés. Lorsque le champ magnétique est appliqué parallèlement à l'axe du tube, un quantum de flux magnétique pénétrant la section du nanotube engendre une modulation géante de la conductance (de type Aharonov–Bohm), contrôlée par la présence de barrières Schottky dont le profil varie sous champ magnétique. Dans une configuration où le champ magnétique est perpendiculaire à l'axe, ce dernier rompt naturellement la symétrie de révolution et des états de Landau non-conventionels se développent sous fort champ magnétique. En utilisant la sensibilité d'une cavité Fabry–Pérot constituée d'un nanotube de carbone agissant comme un guide d'ondes électronique, il apparaît que les états résonants de la cavité dépendent du champ magnétique transverse. Leurs dépendances révèlent la formation du premier état de Landau à énergie nulle. Ces expériences soulignent l'efficacité des expériences de magnéto-conductance sous champ magnétique intense pour sonder les propriétés électroniques des nano-matériaux individuels à base de carbone.

Nano-sciences, and in particular nano-physics, constitute a fascinating world of investigations where the experimental challenges are to synthesize, to address (for instance optically or electrically) to explore and promote the remarkable physical properties of new nano-materials. Somehow, one of the most promising realization of nano-sciences lies in carbon-based nano-materials with sp2 covalent bonds. In particular, carbon nanotubes, graphene and more recently ultra-narrow graphene nano-ribbons are envisioned as elementary bricks of the future of nano-electronics. However, prior to such an achievement, the first steps consist in understanding their fundamental electronic properties when they constitute the drain–source channel of a gated device or inter-connexion elements. In this article, we present the richness of challenging experiments combining single-object measurements with an extreme magnetic environment. We demonstrate that an applied magnetic field (B), along with a control of the electrostatic doping, drastically modifies the electronic band structure of a carbon nanotube based transistor. Several examples will be addressed in this presentation. When B is applied parallel to the tube axis, a quantum flux threading the tube induces a giant Aharonov–Bohm conductance modulation mediated by Schottky barriers whose profile is magnetic field dependent. In the perpendicular configuration, the applied magnetic field breaks the revolution symmetry along the circumference and non-conventional Landau states develop in the high field regime. By playing with a carbon nanotube based electronic Fabry–Perot resonator, the field dependence of the resonant states of the cavity reveals the onset of the first Landau state at zero energy. These experiments enlighten the outstanding efficiency of magneto-conductance experiments to probe the electronic properties of carbon based nano-materials.

Publié le :
DOI : 10.1016/j.crhy.2009.05.005
Keywords: Carbon nanotubes, High magnetic field, Electronic conductivity
Mot clés : Nanotubes de carbone, Champ magnétique intense, Conductivité électronique

Sébastien Nanot 1 ; Walter Escoffier 1 ; Benjamin Lassagne 1 ; Jean-Marc Broto 1 ; Bertrand Raquet 1

1 Laboratoire national des champs magnétiques intenses UPR3228, CNRS, INSA, UPS, université de Toulouse, 143, avenue de Rangueil, 31400 Toulouse, France
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Sébastien Nanot; Walter Escoffier; Benjamin Lassagne; Jean-Marc Broto; Bertrand Raquet. Exploring the electronic band structure of individual carbon nanotubes under 60 T. Comptes Rendus. Physique, Volume 10 (2009) no. 4, pp. 268-282. doi : 10.1016/j.crhy.2009.05.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2009.05.005/

[1] Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications (G.D.A. Jorio; G. Dresselhaus; M.S. Dresselhaus, eds.), Springer, 2008

[2] J.C. Charlier; X. Blase; S. Roche Electronic and transport properties of nanotubes, Rev. Mod. Phys., Volume 79 (2007), p. 677

[3] H.I. Jørgensen; K. Grove-Rasmussen; T. Novitny; K. Flensberg; P.E. Lindelof Electron transport in single-wall carbon nanotube weak links in the Fabry–Perot regime, Phys. Rev. Lett., Volume 96 (2007), p. 207003

[4] W. Liang; M. Bockrath; D. Bozovic; J.H. Hafner; M. Tinkham; H. Park Fabry–Perot interference in a nanotube electron waveguide, Nature, Volume 411 (2001), p. 665

[5] J. Nygard; D.H. Cobden; P.E. Lindelof Kondo physics in carbon nanotubes, Nature, Volume 408 (2000), p. 342

[6] P. Jarillo-Herrero; S. Sapmaz; C. Dekker; L.P. Kouwenhoven; H.S.J. van der Zant Electron–hole symmetry in semiconducting carbon nanotube quantum dot, Nature, Volume 429 (2004), p. 389

[7] P.L. McEune; M. Bockrath; D.H. Cobden; Y.-G. Yoon; S.G. Louie Disorder, pseudospins and backscattering in carbon nanotubes, Phys. Rev. Lett., Volume 83 (1999), p. 5098

[8] H. Suzuura; T. Ando; Z. Yao; C.L. Kane; C. Dekker Phonons and electron–phonon in carbon nanotubes, Phys. Rev. B, Volume 65 (2002), p. 235412

[9] Z. Yao; C.L. Kane; C. Dekker High field electrical transport in single-wall carbon nanotubes, Phys. Rev. Lett., Volume 84 (2000), p. 2941

[10] S. Roche; J. Jiang; L.E.F. Foa Torres; R. Saito Charge transport in carbon nanotubes: quantum effects of electron–phonon coupling, J. Phys.: Condens. Matter, Volume 19 (2007), p. 183203

[11] S. Wang; M. Grifoni Helicity and electron-correlation effects on transport properties of double-walled carbon nanotubes, Phys. Rev. Lett., Volume 95 (2005), p. 266802

[12] F. Triozon; S. Roche; A. Rubio; D. Mayou Electrical transport in carbon nanotubes: Role of disorder and helical symmetries, Phys. Rev. B, Volume 69 (2004), p. 121410

[13] B. Bourlon; C. Miko; L. Forro; D.C. Glattli; A. Bachtold Determination of the intershell conductance in multiwalled carbon nanotubes, Phys. Rev. Lett., Volume 93 (2004), p. 176806

[14] P. Jarillo-Herrero; J. Kong; H.S.J. van der Zant; C. Dekker; L.P. Kouwenhoven; S. de Franceschi Electronic transport spectroscopy of carbon nanotubes in a magnetic field, Phys. Rev. Lett., Volume 94 (2005), p. 156802

[15] S. Moriyama; T. Fuse; M. Suzuki; Y. Aoyagi; K. Ishibashi Four-electron shell structures and an intercating two-electron system in carbon nanotube quantum dots, Phys. Rev. Lett., Volume 94 (2005), p. 186806

[16] K. Kuemmeth; S. Ilani; D.C. Ralph; P.L. McEuen Coupling of spin and orbital motion of electrons in carbon nanotubes, Nature, Volume 452 (2008), p. 448

[17] B. Stojetz; C. Miko; L. Forró; Ch. Strunk Effect of band structure on quantum interference in multiwalled carbon nanotubes, Phys. Rev. Lett., Volume 94 (2005), p. 186802

[18] B.L. Al'tshuler; A.G. Aronov; B.Z. Spivak; D.Yu. Sharvin; Yu.V. Sharvin Observation of the Aharonov–Bohm effect in hollow metal cylinders, JETP Lett., Volume 35 (1982), p. 588

[19] R.A. Webb; S. Washburn; C.P. Umbach; R.B. Laibowitz Observation of h/e Aharonov–Bohm oscillations in normal-metal rings, Phys. Rev. Lett., Volume 54 (1985), p. 2696

[20] S. Zaric; G.N. Ostojic; J. Kono; J. Shaver; V.C. Moore; M.S. Strano; R.H. Hauge; R.E. Smalley; X. Wei Orbital signatures of the Aharonov–Bohm phase in single-wall carbon nanotubes, Science, Volume 304 (2004), p. 1129

[21] G. Fedorov; B. Lassagne; M. Sagnes; B. Raquet; J.-M. Broto; F. Triozon; S. Roche Gate-dependent magnetoresistance phenomena in carbon nanotubes, Phys. Rev. Lett., Volume 94 (2005), p. 066801

[22] R.C. Ashoori Electrons in artificial atoms, Nature, Volume 379 (1996), p. 413

[23] D. Vignolles; D. Smirnov; G. Rikken; B. Raquet; H. Rakoto; C. Proust; M. Nardone; J. Léotin; F. Lecouturier; M. Goiran; O. Drachenko; J.M. Broto; L. Brossard; A. Audouard Low Temperature Physics at the Laboratoire National des Champs Magnétiques Pulsés in Toulouse, J. Low Temp. Phys., Volume 131 (2003), p. 97

[24] R. Kubo The fluctuation–dissipation theorem, Rep. Prog. Phys., Volume 29 (1966), p. 255

[25] A. Fujiwara; K. Tomiyama; H. Suematsu; M. Yumura; K. Uchida Quantum interference of electrons in multiwall carbon nanotubes, Phys. Rev. B, Volume 60 (1999), p. 13492

[26] J.O. Lee; J.-R. Kim; J.-J. Kim; J. Kim; N. Kim; J.W. Park; K.-H. Yoo; K.-H. Park Magnetoresistance and differential conductance in multiwalled carbon nanotubes, Phys. Rev. B, Volume 61 (2000), p. 16362

[27] C. Schönenberger; A. Bachtold Comment on magnetoresistance and differential conductance in multiwalled carbon nanotubes, Phys. Rev. B, Volume 64 (2001), p. 157401

[28] A. Bachtold; Ch. Strunk; J.-P. Salvetat; J.-M. Bonard; L. Forró; T. Nussbaumer; Ch. Schönenberger Aharonov–Bohm oscillations in carbon nanotubes, Nature, Volume 397 (1999), p. 673

[29] A.G. Aronov; Yu.V. Sharvin Magnetic flux effects in disordered conductors, Rev. Mod. Phys., Volume 59 (1987), p. 755

[30] J.-M. Bonard; T. Stora; J.-P. Salvetat; F. Maier; T. Stockli; C. Duschl; L. Forro; W.A. de Heer; A. Chatelain Purification and size-selection of carbon nanotubes, Adv. Mater., Volume 9 (1997), p. 827

[31] H. Ajiki; T. Ando Electronic states of carbon nanotubes, J. Phys. Soc. Jpn., Volume 62 (1993), p. 1255

[32] H. Ajiki; T. Ando Energy bands of carbon nanotubes in magnetic fields, J. Phys. Soc. Jpn., Volume 65 (1996), p. 505

[33] Y. Aharonov; D. Bohm Significance of electromagnetic potentials in the quantum theory, Phys. Rev., Volume 115 (1959), p. 485

[34] S. Roche; G. Dresselhaus; M.S. Dresselhaus; R. Saito Aharonov–Bohm spectral features and coherence lengths in carbon nanotubes, Phys. Rev. B, Volume 62 (2000), p. 16092

[35] F.L. Shyu; C.P. Chang; R.B. Chen; C.W. Chiu; M.F. Lin Magnetoelectronic and optical properties of carbon nanotubes, Phys. Rev. B, Volume 67 (2003), p. 045405

[36] U.C. Coskun; T.-C. Wei; S. Vishveshwara; P.-M. Goldbart; A. Bezryadin h/e magnetic flux modulation of the energy gap in nanotube quantum dots, Science, Volume 304 (2004), p. 1132

[37] J. Cao; Q. Wang; M. Rolandi; H. Dai Aharonov–Bohm interference and beating in single-walled carbon nanotube interferometers, Phys. Rev. Lett., Volume 93 (2004), p. 216803

[38] B. Lassagne; J.-P. Cleuziou; S. Nanot; W. Escoffier; R. Avriller; S. Roche; L. Forró; B. Raquet; J.-M. Broto Aharonov–Bohm conductance modulation in ballistic carbon nanotubes, Phys. Rev. Lett., Volume 98 (2007), p. 176802

[39] V. Derycke; R. Martel; J. Appenzeller; Ph. Avouris Controlling doping and carrier injection in carbon nanotube transistors, Appl. Phys. Lett., Volume 80 (2002), p. 2773

[40] G. Fedorov; A. Tselev; D. Jimenez; S. Latil; N.G. Kalugin; P. Barbara; D. Smirnov; S. Roche Magnetically induced field effect in carbon nanotube devices, Nano Lett., Volume 7 (2007), p. 960

[41] S. Heinze; J. Tersoff; R. Martel; V. Derycke; J. Appenzeller; Ph. Avouris Carbon nanotubes as Schottky barrier transistors, Phys. Rev. Lett., Volume 89 (2002), p. 106801

[42] C. Strunk; B. Stojetz; S. Roche Quantum interference in multiwall carbon nanotubes, Semicond. Sci. Technol., Volume 21 (2006), p. S38

[43] E.D. Minot; Y. Yaish; V. Sazonova; P.L. McEuen Determination of electron orbital magnetic moments in carbon nanotubes, Nature, Volume 428 (2004), p. 536

[44] S. Datta Electronic Transport in Mesoscopic System, Cambridge University Press, 1998

[45] K.S. Novoselov; A.K. Geim; S.V. Morozov; D. Jiang; M.I. Katsnelson; I.V. Grigorieva; S.D. Dubonos; A.A. Firsov Two-dimensional gas of massless Dirac fermions in graphene, Nature, Volume 438 (2005), p. 197

[46] Y. Zhang; Y.-W. Tan; H.L. Stormer; P. Kim Experimental observation of the quantum Hall effect and Berry's phase in graphene, Nature, Volume 438 (2005), p. 201

[47] E. Perfetto; J. Gonzalez; F. Guinea; S. Bellucci; P. Onorato Quantum Hall effect in carbon nanotubes and curved graphene strips, Phys. Rev. B, Volume 76 (2007), p. 125430

[48] R. Saito; G. Dresselhaus; M.S. Dresselhaus Magnetic energy bands of carbon nanotubes, Phys. Rev. B, Volume 50 (1994), p. 14698

[49] H.-W. Lee; D.S. Novikov Supersymmetry in carbon nanotubes in a transverse magnetic field, Phys. Rev. B, Volume 68 (2003), p. 155402

[50] N. Nemec; G. Cuniberti Hofstadter butterflies of carbon nanotubes: pseudofractality of the magnetoelectronic spectrum, Phys. Rev. B, Volume 74 (2006), p. 165411

[51] R. Avriller; S. Roche; F. Triozon; X. Blase; S. Latil Low dimensional quantum transport properties of chemically disordered carbon nanotubes: from weak to strong localisation regimes, Mod. Phys. Lett. B, Volume 21 (2007), p. 1955

[52] R. Avriller; S. Latil; F. Triozon; X. Blase; S. Roche Chemical disorder strength in carbon nanotubes: magnetic tuning of quantum transport regimes, Phys. Rev. B, Volume 74 (2006), p. 121406(R)

[53] B. Raquet; R. Avriller; B. Lassagne; S. Nanot; W. Escoffier; J.-M. Broto; S. Roche Onset of the Landau level formation in carbon nanotubes-based electronic Fabry–Perot resonators, Phys. Rev. Lett., Volume 101 (2008), p. 046803

[54] S. Nanot, R. Avriller, W. Escoffier, J.-M. Broto, S. Roche, B. Raquet, Propagative Landau states in multiwall carbon nanotubes, submitted for publication

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