Electronic relaxation and coherent phonon dynamics in semiconducting single-walled carbon nanotubes with several chiralities

Abstract

Coherent phonon (CP) dynamics and electronic relaxation in single-walled carbon nanotubes (SWNTs) are investigated in femtosecond pump-probe experiments. Using a sensitive multichannel lock-in amplifier, chirality-specific electronic relaxation and vibrational dynamics are resolved in SWNT ensembles composed of several chiral systems without the need for selective isolation of the different species by purification. The dynamics of vibrational wave packets are studied based on oscillatory changes in the absorbance of the systems. Modulations corresponding to the radial breathing mode (RBM), observed in the time traces of the absorbance change for the four chiral systems (6,4), (6,5), (7,5), and (8,3), have been analyzed in detail. The vibrational modes of the CP spectra are identified from the two-dimensional distribution of probe photon energy versus Fourier frequency. Resonance conditions and mode frequencies lead to definite chirality assignments. Coherent RBM phonon generation is analyzed using the probe photon energy-dependent amplitude profiles as a result of the spectral shift induced by wave-packet motion on the potential surface. The present study clarifies that the observed probe photon energy dependence is due to both the imaginary and real parts of the third-order susceptibility, corresponding to Raman (and Raman-like) gain and loss processes and to molecular phase modulation, respectively. The imaginary part is the dominant contribution to the modulation in the difference absorbance. It shows probe photon energy dependence in the form of a difference in absorbed photon energy between the spectra that are shifted and unshifted with vibrational frequency. The size of the Huang-Rhys factors from the difference fitting to the (6,4), (6,5), and (8,3) systems are 0.26, 0.32, and 0.75, respectively. The trend of the factors originates in the stiffness differences of the SWNT structures. The real part depends on the derivative of the absorbed photon energy spectrum due to cross-phase modulation, resulting from the change in refractive index during the molecular vibrations. This process induces a probe spectral change, as evidenced by first-derivative fitting using a small number of data points of probe photon energies. The effective nonlinear refractive index for each chiral system is determined to range from 0.2 to $3.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ cm${}^{2}$/W.