Phonons are calculated for single wall carbon nanotubes. Eigenvalues and eigenvectors are presented for armchair and zig-zag tubes. The model contains just three adjustable spring constants: two for first and second nearest neighbor directed bonds, and a third for radial bond-bending interactions. There are four low frequency modes at long wavelength: a longitudinal acoustical, a torsional mode, and two flexure modes.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Aug 2004|
Bibliographical noteFunding Information:
We are grateful for research support from NSF Grant No. DMR-03-04178.