Direct Observation of Dark Excitons in Micelle-Wrapped Single-Wall Carbon Nanotubes

We have performed electroabsorption spectroscopy on micelle-wrapped single-wall carbon nanotubes. In semiconducting nanotubes, many oscillating structures composed of the increase and decrease of absorption are observed in the spectra in the region of the first and second absorption bands, $E_{11}$ and $E_{22}$. The spectral shape is reproduced mainly by the second-derivative curve of the absorption spectrum, which indicates the presence of nearly degenerate bright and dark excitonic states.

Figure 1

Schematics of continuum bands and the exciton levels in single-wall carbon nanotubes. One (broken) of the three dark excitons is two-photon allowed states and the others (dotted) are two-photon forbidden ones. The positions of the states are not exact.

Figure 2

(a),(d) Absorption spectra of micelle-wrapped SWNT embedded in gelatin films measured at room temperature. Comparison of EA signals [(c) and (f)] with the first and second-derivative curves ((b) and (e)) of absorption spectra [(a) and (d)]. The possible chiral indices are also shown (round brackets: $E_{11}$ peaks; square brackets: $E_{22}$). The valley and peak positions in the EA spectra are labeled in (c) and (f) and indicated by vertical broken lines.

Figure 3

Electric-field dependence of the EA spectra in the (a) $E_{11}$ and (b) $E_{22}$ regions. (c) The peak intensities of signals at several labeled peaks are plotted as a function of the electric field. The lines with a slope of 2 are a guide to the eye. The labels are the same as those of Fig. 2.

Figure 4

Simulated spectra based on three discrete level models composed of the ground state, the bright state fixed at 1.00 eV, and a two-photon state. (a) Absorption spectrum. The damping energy is 5 meV. (b) The first and second-derivative spectra of absorption. (c) EA spectra.