Theoretical study of the vibrational edge modes in graphene nanoribbons

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 19, 2008, Pages

  Vandescuren, M ^a   Hermet, P ^a   Meunier, V ^b   Henrard, L ^a   Lambin, Ph ^a  

^a UNIVERSITY OF NAMUR   (Belgium)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56349166719     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.195401     Document Type: Article

References (39)

1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004). 10.1126/science.1102896
2. A. K. Geim and K. S. Novoselov, Nature Mater. 6, 183 (2007). 10.1038/nmat1849
3. M. I. Katsnelson, Mater. Today 10, 20 (2007). 10.1016/S1369-7021(06) 71788-6
4. L. Tapasztó, G. Dobrik, Ph. Lambin, and L. P. Biró, Nat. Nanotechnol. 3, 397 (2008). 10.1038/nnano.2008.149
5. Y. Zhang, Y. W. Tan, H. L. Stormer, and Ph. Kim, Nature (London) 438, 201 (2005). 10.1038/nature04235
6. D. A. Abanin, P. A. Lee, and L. S. Levitov, Phys. Rev. Lett. 96, 176803 (2006). 10.1103/PhysRevLett.96.176803
7. K. Nomura and A. H. MacDonald, Phys. Rev. Lett. 96, 256602 (2006). 10.1103/PhysRevLett.96.256602
8. S. Bhattacharjee and K. Sengupta, Phys. Rev. Lett. 97, 217001 (2006). 10.1103/PhysRevLett.97.217001
9. F. Miao, S. Wijeratne, Y. Zhang, U. C. Coskun, W. Bao, and C. N. Lau, Science 317, 1530 (2007). 10.1126/science.1144359
10. M. Fujita, K. Wakabayashi, K. Nakada, and K. Kusakabe, J. Phys. Soc. Jpn. 65, 1920 (1996). 10.1143/JPSJ.65.1920
11. K. I. Sasaki, J. Jiang, R. Saito, S. Onari, and Y. Tanaka, J. Phys. Soc. Jpn. 76, 033702 (2007). 10.1143/JPSJ.76.033702
12. M. Igami, M. Fujita, and S. Mizuno, Synth. Met. 103, 2576 (1999). 10.1016/S0379-6779(98)01073-X
13. T. Tanaka, A. Tajima, R. Mariizumi, M. Hosoda, R. Ohno, E. Rokuda, C. Oshima, and S. Otani, Solid State Commun. 123, 33 (2002). 10.1016/S0038-1098(02) 00186-2
14. T. Yamamoto, K. Watanabe, and K. Mii, Phys. Rev. B 70, 245402 (2004). 10.1103/PhysRevB.70.245402
15. D. W. Brenner, Phys. Rev. B 42, 9458 (1990). 10.1103/PhysRevB.42.9458
16. J. Zhou and J. Dong, Appl. Phys. Lett. 91, 173108 (2007). 10.1063/1.2800796
17. M. Yamada, Y. Yamakita, and K. Ohno, Phys. Rev. B 77, 054302 (2008). 10.1103/PhysRevB.77.054302
18. D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Nii, and S. B. Sinnott, J. Phys.: Condens. Matter 14, 783 (2002). 10.1088/0953-8984/14/4/312
19. O. Shenderova, V. Zhirnov, and D. W. Brenner, Crit. Rev. Solid State Mater. Sci. 27, 227 (2002). 10.1080/10408430208500497
20. D. Sanchez-Portal, P. Ordejon, E. Artacho, and J. M. Soler, Int. J. Quantum Chem. 65, 453 (1997). 10.1002/(SICI)1097-461X(1997)65:5<453::AID- QUA9>3.0.CO;2-V
21. J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). 10.1103/PhysRevB.23.5048
22. N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 (1991). 10.1103/PhysRevB.43.1993
23. E. Artacho, D. Sanchez-Portal, P. Ordejon, A. Garcia, and J. M. Soler, Phys. Status Solidi B 215, 809 (1999). 10.1002/(SICI)1521-3951(199909)215: 1<809::AID-PSSB809>3.0.CO;2-0
24. H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976). 10.1103/PhysRevB.13.5188
25. K. Parlinski, Z. Q. Li, and Y. Kawazoe, Phys. Rev. Lett. 78, 4063 (1997). 10.1103/PhysRevLett.78.4063
26. P. Hermet, J.-L. Bantignies, A. Rahmani, J.-L. Sauvajol, and M. R. Johnson, J. Phys.: Condens. Matter 16, 7385 (2004). 10.1088/0953-8984/16/41/018
27. It has been shown that LDA and generalized gradient approximation (GGA) give similar results for phonon computation of graphite. In particular phonon frequencies have been calculated to be lower by 2% in GGA than in LDA [L. Wirtz and A. Rubio, Solid State Commun. 131, 141 (2004)]. 10.1016/j.ssc.2004.04.042
28. J. Tersoff, Phys. Rev. Lett. 56, 632 (1986). 10.1103/PhysRevLett.56.632
29. J. Tersoff, Phys. Rev. Lett. 61, 2879 (1988). 10.1103/PhysRevLett.61.2879
30. R. Al-Jishi and G. Dresselhaus, Phys. Rev. B 26, 4514 (1982). 10.1103/PhysRevB.26.4514
31. C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950).
32. K. Sbai, A. Rahmani, H. Chadli, J.-L. Bantignies, P. Hermet, and J.-L. Sauvajol, J. Phys. Chem. B 110, 12388 (2006). 10.1021/jp0574504
33. H. Chadli, A. Rahmani, K. Sbai, P. Hermet, S. Rols, and J.-L. Sauvajol, Phys. Rev. B 74, 205412 (2006). 10.1103/PhysRevB.74.205412
34. R. Haydock, V. Heine, and M. J. Kelly, J. Phys. C 8, 2591 (1975). 10.1088/0022-3719/8/16/011
35. C. Benoit, E. Royer, and G. Poussigue, J. Phys.: Condens. Matter 4, 3125 (1992). 10.1088/0953-8984/4/12/010
36. Q. Ding, Q. Jiang, Z. Jin, and D. Tian, Fullerene Sci. Technol. 4, 31 (1996).
37. This comparison method has already been used with defects in carbon nanotubes. M. Vandescuren, H. Amara, R. Langlet, and Ph. Lambin, Carbon 45, 349 (2007). 10.1016/j.carbon.2006.09.018
38. The recursion method is useful as a global method providing an overall view on phonon modes and allowing comparisons of the intensities of the peaks in VDOS spectra. However, when very precise characterizations are needed, the diagonalization method is the only alternative.
39. The width of the ribbon is calculated without the C-H bond. Namely, it is the distance between the outmost carbons in the relaxed structure.