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Symmetry‐adapted tight‐binding calculations of the phonon dispersion and the resonant Raman intensity of the totally symmetric phonons of single‐walled carbon nanotubes
Author(s) -
Popov Valentin N.,
Lambin Philippe
Publication year - 2006
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200669105
Subject(s) - phonon , raman spectroscopy , carbon nanotube , condensed matter physics , radius , translational symmetry , materials science , nanotube , dispersion (optics) , intensity (physics) , tight binding , symmetry (geometry) , molecular physics , physics , nanotechnology , electronic structure , quantum mechanics , geometry , computer security , mathematics , computer science
Abstract The atomistic calculations of the physical properties of perfect single‐walled carbon nanotubes based on the use of the translational symmetry of the nanotubes face increasing computational difficulties for most of the presently synthesized nanotubes, which have up to a few thousand atoms in the unit cell. This difficulty can be circumvented by use of the helical symmetry of the nanotubes. We present the results of such symmetry‐adapted tight‐binding calculations of the phonon dispersion and resonant Raman intensity of the totally symmetric A 1 phonons of several hundred nanotubes. In particular, we show that 1) the frequencies and the resonant Raman intensity of the RBM and the G‐band modes show radius and chirality dependence and family patterns, 2) the strong electron – A 1 (LO) phonon interactions in metallic nanotubes lead to Kohn anomalies of the phonon branches and to their softening at the zone‐center, 3) the G‐band consists of a subband due to A 1 (LO) phonons of semiconducting tubes centered at ≈1593 cm –1 , a subband of A 1 (TO) phonons at ≈1570 cm –1 , and a subband of A 1 (LO) phonons of metallic tubes at ≈1540 cm –1 . The latter prediction confirms previous theoretical results but disagrees with the assignment of the G‐band features adopted by other authors. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)