Ultrafast Dynamics of Delocalized and Localized Electrons in Carbon Nanotubes

We report on the dynamics of the dielectric function of single-wall carbon nanotubes in the 10–30 THz frequency range after ultrafast laser excitation. The absence of a distinct free-carrier response is attributed to the photogeneration of strongly bound excitons in the tubes with large energy gaps. We find a feature of enhanced transmission caused by the blocking of optical transitions in small-gap tubes. The rapid decay of a featureless background with pronounced dichroism is associated with the increased absorption of spatially localized charge carriers before thermalization is completed.

Figure 1

(a) THz electric field $E^0(t)$ transmitted through the unexcited sample and the pump-induced change $\Delta E_{\tau }(t)$ at $\tau =0.1\mathrm{ps}$ after excitation. (b) Dielectric function of unexcited NTs.

Figure 2

(a) Excitonic levels of a large-gap NT together with a visible pump pulse resonantly exciting the $E_2$ band. (b) Single-electron density of states of a small-gap NT with a magnification of the small band gap. Wiggled arrows mark transitions induced by the visible pump and the THz probe photons, respectively. The various gray scales represent different electronic occupation numbers.

Figure 3

(a) Pump-induced changes of the NTs’ dielectric function at several pump-probe delays $\tau$. In the imaginary part, absorption and bleaching are labeled $A$ and $B$, respectively. (b) As a reference, the pump-induced changes of the dielectric function of highly oriented pyrolytic graphite at $\tau =0.1\mathrm{ps}$ after excitation with comparable strength as in the NT measurements [21]. Note the different scales of the ordinates. (c) Measured $\Delta {\epsilon }_{\tau }(\omega )$ of NTs at $\tau =0.5\mathrm{ps}$ together with a fit according to Eq. (1) (dashed line) and an extended fit including the spectral feature at 15 THz (solid line; see text).

Figure 4

(a) Temporal decay of $\mathrm{Im}\Delta {\epsilon }_{\tau }$ at 10 THz (feature $B$) and 26 THz (feature $A$). The decay of $B$ is well described by a single exponential with a time constant of 1 ps, whereas the decay of $A$ is fitted best to a double exponential with time constants of 0.2 and 1 ps, respectively. (b) Temporal dynamics of the pump-induced dichroism of both features $A$ and $B$.