Observation of Excitons in One-Dimensional Metallic Single-Walled Carbon Nanotubes

Excitons are generally believed not to exist in metals because of strong screening by free carriers. Here we demonstrate that excitonic states can in fact be produced in metallic systems of a one-dimensional character. Using metallic single-walled carbon nanotubes as a model system, we show both experimentally and theoretically that electron-hole pairs form tightly bound excitons. The exciton binding energy of 50 meV, deduced from optical absorption spectra of individual metallic nanotubes, significantly exceeds that of excitons in most bulk semiconductors and agrees well with ab initio theoretical predictions.

Figure 1

(a) Scanning electron micrograph of a carbon nanotube suspended across the slit structure. (b) High-resolution transmission electron micrograph of a single-walled carbon nanotube. It is seen to be free of amorphous carbon.

Figure 2

Spectroscopic analysis of a given, individual SWNT by different optical techniques. (a) The Rayleigh scattering spectrum reveals an optical transition at 1.87 eV. The single peak is characteristic of an armchair metallic nanotube, and the transition energy indicates that it is a (21,21) nanotube. (b) Raman spectrum of the radial breathing mode. The Raman shift of $90{\mathrm{cm}}^{-1}$ corresponds to a diameter of 2.9 nm, consistent with the (21,21) assignment. (c) Raman spectrum of the $G$-mode feature. Its symmetric line shape and single peak also indicate an armchair nanotube.

Figure 3

Absorption spectra of individual SWNTs. (a) The (21,21) armchair metallic nanotube. The line shape cannot be described by a van Hove singularity within a picture of band-band transitions (black curve). The discrepancy is particularly marked for the spectral range within the dashed box where the experimental line shape is largely symmetric, characteristic of an excitonic transition. (b) The (16,15) semiconducting nanotube. The excitonic effect is much stronger in this semiconducting SWNT and the continuum band-band absorption feature seen in the high-energy tail of (a) is absent. The weak peak located 200 meV above the main resonance is attributed to a phonon side band [22, 23, 24, 25]. The absorption line shape is fit by two Lorentzian functions.

Figure 4

Detailed analysis of the absorption spectrum of the (21,21) metallic nanotube of Fig. 3a (red symbol). (a) Comparison with the experimental absorption feature of the (16,15) semiconducting SWNT of Fig. 3b (blue symbol), after a slight shift in energy and adjustment in strength. In the metallic nanotube, absorption from the continuum transitions is apparent in the high-energy wing. From the threshold of the continuum absorption (dashed line), we estimate an exciton binding energy of 50 meV. (b) Comparison of the theory (black solid line) for the optical transition in a metallic nanotube as described in the text. The predicted absorption can be decomposed into the dominant exciton contribution and a continuum contribution (green dashed lines).