We have developed a theory for the generation and detection of coherent phonons in carbon based nanotstructures such as single walled nanotubes (SWNTs), graphene, and graphene nanoribbons. Coherent phonons are generated via the deformation potential electron/hole-phonon interaction with ultrafast photo-excited carriers. They modulate the reflectance or absorption of an optical probe pules on a THz time scale and might be useful for optical modulators. In our theory the electronic states are treated in a third nearest neighbor extended tight binding formalism which gives a good description of the states over the entire Brillouin zone while the phonon states are treated using valence force field models which include bond stretching, in-plane and out-of-plane bond bending, and bond twisting interactions up to fourth neighbor distances. We compare our theory to experiments for the low frequency radial breathing mode (RBM) in micelle suspended single-walled nanotubes (SWNTs). The analysis of such data provides a wealth of information on the dynamics and interplay of photons, phonons and electrons in these carbon based nanostructures.
Graphene and carbon nanotubes provide a variety of new opportunities for fundamental and applied research. Here, we describe results of our recent terahertz and ultrafast studies of carriers and phonons in these materials. Time-domain terahertz spectroscopy is a powerful method for determining the basic properties of charge carriers in a non-contact manner. We show how one can modulate the transmission of terahertz waves through graphene by gating and how one can improve the modulation performance by combining graphene with apertures and gratings. In carbon nanotubes, we demonstrate that the terahertz response is dominated by plasmon oscillations, which are enhanced by collective antenna effects when the nanotubes are aligned. Finally, ultrafast spectroscopy of carbon nanotubes allow us to excite and probe coherent phonons, both in the low-energy radial breathing mode and high-energy G-mode, which are strongly coupled with excitonic interband transitions.