Resonant coherent phonon spectroscopy of single-walled carbon nanotubes

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 the 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 mod2 nanotubes and found that our model provides satisfactory overall trends in the relative strengths of the coherent phonon signal both within and between different mod2 families. We also find that the coherent phonon intensities are considerably weaker in mod1 nanotubes in comparison with mod2 nanotubes, which is also in excellent agreement with experiment.