Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-17T15:00:37.525Z Has data issue: false hasContentIssue false

Band-Gap Modulation and Kohn Anomalies in Two-Dimensional Graphite and Single-Wall Carbon Nanotubes

Published online by Cambridge University Press:  01 February 2011

Georgii Samsonidze
Affiliation:, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 77 Massachusetts Ave., Room 13-3021, Cambridge, MA, 02139, United States, 617-253-6860, 617-253-6827
Eduardo B. Barros
Affiliation:, Universidade Federal do Ceara, Fortaleza, 60455-760, Brazil
Hyungbin Son
Affiliation:, Massachusetts Institute of Technology, Cambridge, MA, 02139, United States
Riichiro Saito
Affiliation:, Tohoku University and CREST JST, Sendai, 980-8578, Japan
Gene Dresselhaus
Affiliation:, Massachusetts Institute of Technology, Cambridge, MA, 02139, United States
Mildred S. Dresselhaus
Affiliation:, Massachusetts Institute of Technology, Cambridge, MA, 02139, United States
Get access


The electron-phonon coupling in two-dimensional graphite (graphene sheet) and metallic single-wall carbon nanotubes (SWNTs) is analyzed. In the graphene sheet the G-band phonon mode induces oscillations of the Fermi points, while the G′-band phonon mode opens a dynamical (oscillating with the phonon frequency) band gap, and accordingly, both phonon modes exhibit Kohn anomalies. Similarly, truly metallic armchair SWNTs undergo Peierls transitions driven by the G- and G′-band phonon modes both of which open a dynamical band gap. In addition, the dynamical band gap induces a non-linear dependence of the phonon frequencies on the doping level and gives rise to strong anharmonic effects in the graphene sheet and metallic SWNTs.

Research Article
Copyright © Materials Research Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



1. Pimenta, M. A., Marucci, A., Empedocles, S., Bawendi, M., Hanlon, E. B., Rao, A. M., Eklund, P. C., Smalley, R. E., Dresselhaus, G., and Dresselhaus, M. S., Phys. Rev. B 58, R16016 (1998).10.1103/PhysRevB.58.R16016Google Scholar
2. Maultzsch, J., Reich, S., Thomsen, C., Requardt, H., and Ordejon, P., Phys. Rev. Lett. 92, 075501 (2004).Google Scholar
3. Dubay, O., Kresse, G., and Kuzmany, H., Phys. Rev. Lett. 88, 235506 (2002).Google Scholar
4. Piscanec, S., Lazzeri, M., Mauri, F., Ferrari, A. C., and Robertson, J., Phys. Rev. Lett. 93, 185503 (2004).Google Scholar
5. Tommasini, M., Di Donato, E., Castiglioni, C., and Zerbi, G., Chem. Phys. Lett. 414, 166 (2005).Google Scholar
6. Barnett, R., Demler, E., and Kaxiras, E., Phys. Rev. B 71, 035429 (2005).Google Scholar
7. Bohnen, K.-P., Heid, R., Liu, H. J., and Chan, C. T., Phys. Rev. Lett. 93, 245501 (2004).Google Scholar
8. Connétable, D., Rignanese, G.-M., Charlier, J.-C., and Blase, X., Phys. Rev. Lett. 94, 015503 (2005).Google Scholar
9. Popov, V. N. and Lambin, P., Phys. Rev. B 73, 085407 (2006).Google Scholar
10. Saito, R., Dresselhaus, G., and Dresselhaus, M. S., Physical properties of carbon nanotubes (Imperial College Press, 1998).Google Scholar
11. Saito, R., Grüneis, A., Samsonidze, G. G., Brar, V. W., Dresselhaus, G., Dresselhaus, M. S., Jorio, A., Cançado, L. G., Fantini, C., Pimenta, M. A., and Filho, A. G. Souza, New J. Phys. 5, 157 (2003).Google Scholar
12. Samsonidze, G. G., Photophysics of carbon nanotubes (PhD thesis, MIT, 2006).Google Scholar
13. Rafailov, P. M., Maultzsch, J., Thomsen, C., and Kataura, H., Phys. Rev. B 72, 045411 (2005).Google Scholar