  Using femtosecond pump-probe spectroscopy with pulse shaping techniques, one
can generate and detect coherent phonons in chirality-specific semiconducting
single-walled carbon nanotubes. The signals are resonantly enhanced when the
pump photon energy coincides with an interband exciton resonance, and analysis
of such data provides a wealth of information on the chirality-dependence of
light absorption, phonon generation, and phonon-induced band structure
modulations. To explain our experimental results, we have developed a
microscopic theory for the generation and detection of coherent phonons in
single-walled carbon nanotubes using a tight-binding model for the electronic
states and a valence force field model for the phonons. We find that the
coherent phonon amplitudes satisfy a driven oscillator equation with the
driving term depending on photoexcited carrier density. We compared our
theoretical results with experimental results on mod 2 nanotubes and found that
our model provides satisfactory overall trends in the relative strengths of the
coherent phonon signal both within and between different mod 2 families. We
also find that the coherent phonon intensities are considerably weaker in mod 1
nanotubes in comparison with mod~2 nanotubes, which is also in excellent
agreement with experiment.
