Sanders, G.D., Nugraha, A.R.T., Sato, K., et al.. "Theory of coherent phonons in carbon nanotubes and graphene nanoribbons." Journal of Physics: Condensed Matter, 25, (2013) IOP Publishing: 144201. http://dx.doi.org/10.1088/0953-8984/25/14/144201.
We survey our recent theoretical studies on the generation and detection of coherent radial
breathing mode (RBM) phonons in single-walled carbon nanotubes and coherent radial
breathing like mode (RBLM) phonons in graphene nanoribbons. We present a microscopic
theory for the electronic states, phonon modes, optical matrix elements and electronﾖphonon
interaction matrix elements that allows us to calculate the coherent phonon spectrum. An
extended tight-binding (ETB) model has been used for the electronic structure and a valence
force field (VFF) model has been used for the phonon modes. The coherent phonon
amplitudes satisfy a driven oscillator equation with the driving term depending on the
photoexcited carrier density. We discuss the dependence of the coherent phonon spectrum on
the nanotube chirality and type, and also on the graphene nanoribbon mod number and class
(armchair versus zigzag). We compare these results with a simpler effective mass theory
where reasonable agreement with the main features of the coherent phonon spectrum is found.
In particular, the effective mass theory helps us to understand the initial phase of the coherent
phonon oscillations for a given nanotube chirality and type. We compare these results to two
different experiments for nanotubes: (i) micelle suspended tubes and (ii) aligned nanotube
films. In the case of graphene nanoribbons, there are no experimental observations to date. We
also discuss, based on the evaluation of the electronﾖphonon interaction matrix elements, the
initial phase of the coherent phonon amplitude and its dependence on the chirality and type.
Finally, we discuss previously unpublished results for coherent phonon amplitudes in zigzag
nanoribbons obtained using an effective mass theory.
Theory of coherent phonons in carbon nanotubes and graphene nanoribbons
National Science Foundation
U.S. Department of Energy
Journal of Physics: Condensed Matter
Richard E. Smalley Institute for Nanoscale Science and Technology
OISE-0968405 (National Science Foundation)
DEFG02-06ER46308 (U.S. Department of Energy)
C-1509 (Welch Foundation)