Phonon-induced dephasing in single-wall carbon nanotubes

We report on original nonlinear spectral hole-burning experiments in ensembles of single-wall carbon nanotubes. We have measured the temperature dependence of the excitonic homogeneous linewidth from 5 K up to room temperature. We show that the phonon-induced broadening in the weak coupling regime predominantly consists in pure dephasing. We present theoretical calculations of the exciton scattering rate due to phonon absorption within a one-dimensional framework for both excitons and phonons. We obtain a fair agreement with our experimental data and we discuss the specific properties of the exciton-phonon coupling in single-wall carbon nanotubes.

Figure 1

(Left axis) Differential transmission $\Delta T/T$ (squares) of the probe laser as a function of energy with a pump laser of 4 kW cm${}^{-2}$ at 0.8 eV for three different temperatures: 5, 75, and 250 K (the two upper curves are shifted for a better visibility). System response function (solid line) of the nonlinear spectral hole-burning setup. (Right axis) Optical density spectrum (dotted line) obtained by linear absorption spectroscopy of the carbon nanotubes gelatine sample. Inset: optical density spectrum on a larger scale.

Figure 2

Temperature dependence of the excitonic homogeneous linewidth: data (squares), theoretical fits (red solid line). The dashed red line indicates ${\Gamma }_0+\tilde{a}T$ where $\tilde{a}T$ is the temperature dependence of the population relaxation rate from Ref. 26. Inset: same display on a larger temperature range.