Collective π -electronic excitations in BN double-walled nanotubes

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 3, 2008, Pages

  Margulis, Vl A ^a   Muryumin, E E ^a   Gaiduk, E A ^a  

^a OGAREV MORDOVIA STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47349115302     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.035415     Document Type: Article

References (39)

1. A. Rubio, J. L. Corkill, and M. L. Cohen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.5081 49, 5081 (1994).
2. A. Loiseau, F. Willaime, N. Demoncy, G. Hug, and H. Pascard, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.4737 76, 4737 (1996).
3. M. Terauchi, M. Tanaka, T. Matsumoto, and Y. Saito, J. Electron Microsc. 47, 319 (1998). 0022-0744
4. M. Kociak, L. Henrard, O. Stéphan, K. Suenaga, and C. Colliex, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.13936 61, 13936 (2000).
5. G. G. Fuentes, E. Borowiak-Palen, T. Pichler, X. Liu, A. Graff, G. Behr, R. J. Kalenczuk, M. Knupfer, and J. Fink, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.035429 67, 035429 (2003).
6. R. Arenal, O. Stéphan, M. Kociak, D. Taverna, A. Loiseau, and C. Colliex, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.127601 95, 127601 (2005).
7. Vl. A. Margulis, E. E. Muryumin, and E. A. Gaiduk, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.77.035425 77, 035425 (2008).
8. H. Ehrenreich and M. H. Cohen, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.115.786 115, 786 (1959).
9. M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund, Science of Fullerenes and Carbon Nanotubes (Academic, San Diego, 1996)
10. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College, London, 1998).
11. J. Cumings and A. Zettl, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/S0009-2614(99)01277-4 316, 211 (2000).
12. M. Terrones, J. M. Romo-Herrera, E. Cruz-Silva, F. López-Urias, E. M. noz Sandoval, J. J. Velázquez-Salazar, H. Terrones, Y. Bando, and D. Golberg, Mater. Today MTOUAN 1369-7021 10.1016/S1369-7021(07)70077-9 10, 30 (2007).
13. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (Dover, New York, 2003).
14. H. Bruus and K. Flesberg, Many-Body Quantum Theory in Condensed Matter Physics (Oxford University Press, Oxford, 2004).
15. D. Pines, Elementary Excitations in Solids (Benjamin, New York, 1963)
16. D. Pines and P. Nozières, The Theory of Quantum Liquids (Addison-Wesley, New York, 1989).
17. M. Terauchi, M. Tanaka, K. Suzuki, A. Ogino, and K. Kimura, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/S0009-2614(00)00637-0 324, 359 (2000).
18. R. S. Lee, J. Gavillet, M. Lamy de la Chapelle, A. Loiseau, J. L. Cochon, D. Pigache, J. Thibault, and F. Willaime, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.121405 64, 121405 (R) (2001).
19. G. Y. Guo and J. C. Lin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.165402 71, 165402 (2005).
20. S. Okada, S. Saito, and A. Oshiyama, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.165410 65, 165410 (2002).
21. T. M. Schmidt, R. J. Baierle, P. Piquini, and A. Fazzio, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.113407 67, 113407 (2003).
22. H. J. Xiang, J. Yang, J. G. Hou, and Q. Zhu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.035427 68, 035427 (2003).
23. X. Blase, A. Rubio, S. G. Louie, and M. L. Cohen, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/28/5/007 28, 335 (1994).
24. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodinamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).
25. C.-H. Park, C. D. Spataru, and S. G. Louie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.126105 96, 126105 (2006).
26. L. Wirtz, A. Marini, and A. Rubio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.126104 96, 126104 (2006).
27. A. G. Marinopoulos, L. Wirtz, A. Marini, V. Olevano, A. Rubio, and L. Reining, Appl. Phys. A: Mater. Sci. Process. APAMFC 0947-8396 10.1007/s00339-003-2467-z 78, 1157 (2004).
28. R. Perez and W. Que, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/18/12/004 18, 3197 (2006).
29. Vl. A. Margulis, E. A. Gaiduk, E. E. Muryumin, O. V. Boyarkina, and L. V. Fomina, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.245419 74, 245419 (2006).
30. J. S. Lauret, R. Arenal, F. Ducastelle, A. Loiseau, M. Cau, B. Attal-Tretout, and E. Rosencher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.037405 94, 037405 (2005).
31. J. Wang, V. K. Kayastha, Y. K. Yap, Z. Fan, J. G. Lu, Z. Pan, I. N. Ivanov, A. A. Puretzky, and D. B. Geohegan, Nano Lett. NALEFD 1530-6984 10.1021/nl051859n 5, 2528 (2005).
32. G. Y. Guo, S. Ishibashi, T. Tamura, and K. Terakura, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.245403 75, 245403 (2007).
33. Note that this feature is not a unique property of only the collective excitations in BN-NTs. For metals (such as sodium), the occurence of the specific interband collective electronic modes, the so-called zone-boundary collective modes, which, unlike conventional plasmonic modes, do not exist at small values of the wave vector, was pointed out by E-Ni Foo and J. J. Hopfield, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.173.635 173, 635 (1968) a long time ago. However, as a matter of fact, such modes are experimentally observed only in noble and transition metals. In alkali metals, the peaks of the energy-loss function, associated with those modes, manifest themselves only in experiments on monocrystals
34. [see, e.g., C. H. Chen and J. Silcox, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.16.4246 16, 4246 (1977)], having thereby very small intensity as compared to that of the main plasmon-resonance peak.
35. Obviously, as q increases our theoretical results become less reliable because the RPA, which we have rilied on in this paper, is applicable, strictly speaking, only if q kBZ, i.e., at a small transfer momentum. We believe, however, that the results obtained should be qualitatively valid even as q approaches the one-dimensional-Brillouin-zone edge of the nanotube. What may militate in favor of this latter is the excelent agreement between the RPA theory [E. H. Hwang and S. Das Sarma, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.165409 64, 165409 (2001)] and the experiment
36. [M. A. Eriksson, A. Pinczuk, B. S. Dennis, C. F. Hirjibehedin, S. H. Simon, L. N. Pfeiffer, and K. W. West, Physica E (Amsterdam) PELNFM 1386-9477 10.1016/S1386-9477(99)00075-2 6, 165 (2000)] on collective excitations in GaAs quantum wells at very low carrier densities and very large wave vectors. The above-mentioned statement is also strongly supported by a theoretical analysis of the dynamic response of a one- dimensional quantum-wire electron system
37. [S. Das Sarma and E. H. Hwang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.1936 54, 1936 (1996)], which convincingly proves that the RPA description of plasmon dispersion works better in one-dimensional systems than in two- and three-dimensional ones.
38. Recently, M. H. Upton, R. F. Klie, J. P. Hill, T. Gog, D. Casa, W. Ku, Y. Zhu, M. F. Sfeir, J. Misewich, G. Eres, and D. Lowndes, arXiv:cond-mat/0611151 (unpublished) have arrived at the same conclusion in the case of CNTs, carrying out momentum-resolved EELS measurements on a number of isolated double-walled CNTs, as well as on samples of aligned multiwalled and aligned few-walled CNTs.
39. It is worthwhile to note, however, that, as is known by experience accumulated over the years in many-particle physics, a more involved approach does not necessarily lead to better results. A notable example of such a situation is the theory of the collective excitations in a low-density two-dimensional electron system, developed by Hwang and Das Sarma (see Ref.). The calculation of the plasmon dispersion, carried out by those authors, shows that the RPA offers much better agreement with the experiment, cited in Ref., as compared to its "improved" version including local-field corrections arising from correlation effects.