Hofstadter butterflies of carbon nanotubes: Pseudofractality of the magnetoelectronic spectrum

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 16, 2006, Pages

  Nemec, Norbert ^a   Cuniberti, Gianaurelio ^a  

^a UNIVERSITY OF REGENSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750361534     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.165411     Document Type: Article

References (73)

1. D. R. Hofstadter, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.14.2239 14, 2239 (1976).
2. S. Iijima, Nature (London) NATUAS 0028-0836 10.1038/354056a0 354, 56 (1991).
3. A. Oberlin, M. Endo, and T. Koyama, J. Cryst. Growth JCRGAE 0022-0248 10.1016/0022-0248(76)90115-9 32, 335 (1976).
4. M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund, Science of Fullerenes and Carbon Nanotubes (Academic Press, San Diego, 1996).
5. R. Saito, Physical Properties of Carbon Nanotubes (World Scientific Publishing Company, London, 1998).
6. S. Reich, C. Thomsen, and J. Maultzsch, Carbon Nanotubes: Basic Concepts and Physical Properties (Wiley-VCH, Weinheim, 2004).
7. E. Thune and C. Strunk, Quantum Transport in Carbon Nanotubes, Lecture Notes in Physics Vol. 680 (Springer, Berlin, 2005), pp. 351-380.
8. H. W. C. Postma, T. Teepen, Z. Yao, M. Grifoni, and C. Dekker, Science SCIEAS 0036-8075 10.1126/science.293.5535.1576 293, 76 (2001).
9. S. Frank, P. Poncharal, Z. L. Wang, and W. A. de Heer, Science SCIEAS 0036-8075 10.1126/science.280.5370.1744 280, 1744 (1998).
10. F. Wang, G. Dukovic, L. E. Brus, and T. F. Heinz, Science SCIEAS 0036-8075 10.1126/science.1110265 308, 838 (2005).
11. H. Ajiki and T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.62.1255 62, 1255 (1993).
12. S. Zaric, G. N. Ostojic, J. Kono, J. Shaver, V. C. Moore, M. S. Strano, R. H. Hauge, R. E. Smalley, and X. Wei, Science SCIEAS 0036-8075 10.1126/science.1096524 304, 1129 (2004).
13. A. Bachtold, C. Strunk, J.-P. Salvetat, J.-M. Bonard, L. Forró, T. Nussbaumer, and C. Schönenberger, Nature (London) NATUAS 0028-0836 10.1038/17755 397, 673 (1998).
14. E. D. Minot, Y. Yaish, V. Sazonova, and P. L. McEuen, Nature (London) NATUAS 0028-0836 10.1038/nature02425 428, 536 (2004).
15. H. Ajiki and T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.62.2470 62, 2470 (1993).
16. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50.14698 50, 14698 (1994).
17. H. Ajiki and T. Ando, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.65.505 65, 505 (1995).
18. S. Roche and R. Saito, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.246803 87, 246803 (2001).
19. G. Fedorov, B. Lassagne, M. Sagnes, B. Raquet, J.-M. Broto, F. Triozon, S. Roche, and E. Flahaut, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 94.066801 94, 066801 (2005).
20. Y.-W. Son, J. Ihm, M. L. Cohen, S. G. Louie, and H. J. Choi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.225002 95, 216602 (2005).
21. S. Roche, G. Dresselhaus, M. S. Dresselhaus, and R. Saito, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.16092 62, 16092 (2000).
22. B. Stojetz, C. Miko, L. Forró, and C. Strunk, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.186802 94, 186802 (2005).
23. B. Stojetz, S. Roche, C. Miko, F. Triozon, L. Forró, and C. Strunk, cond-mat/0607034 (unpublished).
24. R. Rammal, J. Phys. (Paris) JOPQAG 0302-0738 46, 1345 (1985).
25. C. Kreft and R. Seiler, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.531681 37, 5207 (1996).
26. T. G. Pedersen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.245104 68, 245104 (2003).
27. D. Osadchy and J. E. Avron, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1412464 42, 5665 (2001).
28. Y. Iye, E. Kuramochi, M. Hara, A. Endo, and S. Katsumoto, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.144524 70, 144524 (2004).
29. J. Brüning, V. V. Demidov, and V. A. Geyler, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.033202 69, 033202 (2004).
30. J. G. Analytis, S. J. Blundell, and A. Ardavan, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1615568 72, 613 (2004).
31. C. Zhou, M. Berciu, and R. N. Bhatt, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.125310 71, 125310 (2005).
32. C. Albrecht, J. H. Smet, K. von Klitzing, D. Weiss, V. Umansky, and H. Schweizer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.147 86, 147 (2001).
33. F. Herlach, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/62/6/201 62, 859 (1999).
34. R. Peierls, Z. Phys. ZEPYAA 0044-3328 80, 763 (1933).
35. L. V. Hove, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.89.1189 89, 1189 (1953).
36. S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, U.K., 2005).
37. G. Cuniberti, F. Großmann, and R. Gutiérrez, The Role of Contacts in Molecular Electronics (Springer, Berlin, 2002), Vol. 42, pp. 133-149.
38. D. S. Fisher and P. A. Lee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.23.6851 23, 6851 (1981).
39. S. Krompiewski, J. Martinek, and J. Barnaś, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.073412 66, 073412 (2002).
40. S. Krompiewski, R. Gutiérrez, and G. Cuniberti, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.155423 69, 155423 (2004).
41. V. Moldoveanu, A. Aldea, A. Manolescu, and M. Niţ̌, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.63.045301 63, 045301 (2001).
42. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature (London) NATUAS 0028-0836 10.1038/nature04233 438, 197 (2005).
43. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature (London) NATUAS 0028-0836 10.1038/nature04235 438, 201 (2005).
44. C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, Science SCIEAS 0036-8075 10.1126/science.1125925 312, 1191 (2006).
45. H.-W. Lee and D. S. Novikov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.155402 68, 155402 (2003).
46. Y. Zheng and T. Ando, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65. 245420 65, 245420 (2002).
47. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 61.2015 61, 2015 (1988).
48. J. E. Müller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 68.385 68, 385 (1992).
49. V. A. Margulis and M. A. Pyataev, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.075312 72, 075312 (2005).
50. D. V. Zav'yalov, S. V. Kryuchkov, and N. E. Meshcheryakova, Phys. Solid State PSOSED 1063-7834 10.1134/1.1946875 47, 1169 (2005).
51. K. Handrich, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.161308 72, 161308 (R) (2005).
52. A. Krakovsky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.8469 53, 8469 (1996).
53. J. Yi, M. Porto, and G. Cuniberti, in Encyclopedia of Nanoscience and Nanotechnology, edited by, H. S. Nalwa, (American Scientific Publishers, Stevenson Ranch, CA, 2004), Vol. 5, pp. 607-617.
54. E. Perfetto, J. González, F. Guinea, S. Bellucci, and P. Onorato, cond-mat/0604046 (unpublished).
55. S. Zaric, G. N. Ostojic, J. Shaver, J. Kono, O. Portugall, P. H. Frings, G. L. J. A. Rikken, M. Furis, S. A. Crooker, X. Wei, V. C. Moore, R. H. Hauge, and R. E. Smalley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96. 016406 96, 016406 (2006).
56. J. Kono (private communication).
57. J. L. Hutchisona, N. A. Kiselev, E. P. Krinichnayac, A. V. Krestininc, R. O. Loutfyd, A. P. Morawskyc, V. E. Muradyanc, E. D. Obraztsovae, J. Sloanf, S. V. Terekhove, and D. N. Zakharovc, Carbon CRBNAH 0008-6223 10.1016/S0008- 6223(00)00187-1 39, 761 (2001).
58. T. Sugai, H. Yoshida, T. Shimada, T. Okazaki, and H. Shinohara, Nano Lett. NALEFD 1530-6984 10.1021/nl034183+ 3, 769 (2003).
59. Y. H. Ho, G. W. Ho, S. J. Wu, and M. F. Lin, J. Vac. Sci. Technol. B JVTBD9 0734-211X 10.1116/1.2188409 24, 1098 (2006).
60. P. Lambin, J. Charlier, and J. Michenaud, Electronic Structure of Coaxial Carbon Tubules (World Scientific, Singapore, 1994), pp. 130-134.
61. S. Roche, F. Triozon, A. Rubio, and D. Mayou, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.121401 64, 121401 (R) (2001).
62. P. G. Harper, Proc. Phys. Soc., London, Sect. A PPSAAM 0370-1298 10.1088/0370-1298/68/10/304 68, 874 (1955).
63. N. Nemec and G. Cuniberti (unpublished).
64. M. P. López Sancho, J. M. López Sancho, and J. Rubio, J. Phys. F: Met. Phys. JPFMAT 0305-4608 10.1088/0305-4608/15/4/009 15, 851 (1985).
65. N. Bezroukov, First Monday 4, 10 (1999).
66. Python Reference Manual, edited by, G. van Rossum, and, F. Drake, (PythonLabs, VA, 2001), http://www.python. org.
67. D. Ascher, P. Dubois, K. Hinsen, J. Hugunin, and T. Oliphant, computer code NUMERICAL PYTHON 2001, http://www.numpy.org.
68. T. E. Oliphant, Guide to NumPy (Trelgol Publishing, Spanish Fork, UT, 2006), http://www.numpy.org.
69. E. Jones, computer code SCIPY, 2001, http://www.scipy. org.
70. F. Altet, I. Vilata, S. Prater, V. Mas, T. Hedley, A. Valentino, and J. Whitaker, computer code PYTABLES, 2002, http://www.pytables.org.
71. P. Barrett, J. Hunter, and P. Greenfield, in Astronomical Data Analysis Software & Systems XIV. (2004), http://matplotlib. sourceforge. net
72. Computer code INKSCAPE, 2003, http://www.inkscape.org
73. J. van der Hoeven, Cah. Gutenberg 39-40, 39 (2001).