This is a graphic supplied by Bruce Weisman of Rice University showing a suspension of carbon nanotubes isolated within micelles. When the tubes are excited by visible light (the beam in the graphic) they fluoresce in the near infrared. Comparison of the excitation and emission frequencies provides a powerful probe of the electronic excitations of individual carbon nanotubes.
The electronic structure of a carbon nanotube can be described approximately by the mapping of the electronic states of a graphene sheet on to the surface of a cylinder. This generates
a family of azimuthally quantized subbands that propagate freely along the tube direction. Fluorescence spectroscopy
is providing a closer look at the electronic excitations of individual carbon nanotubes, and indicating how this model must be extended to describe the electronic spectra.
Carbon nanotubes are formed by seamlessly wrapping a graphene sheet into the form of a cylinder. There are an infinite number of possible wrappings, each corresponding to folding along a different translation vector of the graphene sheet. It has been appreciated for some time that the electronic properties of the tube depend sensitively on this wrapping; nearby structures can exhibit conducting or semiconducting behavior. Because of this structural variation, spectroscopy on an ensemble of tubes is complicated by the coexistence of many inequivalent structures. Recently the Rice group carried out optical measurements on an ensemble of single walled carbon nanotubes that are isolated in micelles. The absorption spectra are complex and consist of many overlapping absoption bands each due to a different wrapped structure in the ensemble.
These tubes also fluoresce in the near infrared. By monitoring the efficiency for the fluorescence at a single frequency as a function of the excitation frequency, Weisman and coworkers were able to develop a two dimensional spectroscopy to identify the excitation spectra of individual tubes. A plot from their work is shown on the right. The discrete peaks in a plot of the excitation wavelength as a function of the emission wavelength are due to the quantization of the possible wrapped tube structures and can be assigned to the excitations of specific tubes.
This two dimensional spectroscopy is providing a powerful new window on the electronic excitations of carbon nanotubes, and indicates that the conventional zone folding description of the electronic structures needs to be extended to account for the observed electronic spectra. For example the observed absorption features are systematically "blue shifted" (i.e. they occur at higher energy) than predicted by wrapping the graphene bands onto the nanotube. Closer inspection shows that the ratios of the energies of the observed subband absorption edges are inconsistent with a zone folded prediction for the electronic bands.
These discrepancies highlight the importance of incorporating the effects of the electron-electron interaction in theory for the nanotube electronic properties. For the optical excitations this has been emphasized previously in the work of Ando (see the reference below) who explored the effects of excitonic binding of the photoexcited electron and hole on a carbon nanotube. We are further studying the consequences of the electron electron interactions for the excitation spectrum of carbon nanotubes by exploiting special features of the interacting problem that occur in one and two dimensions.
S. Bachilo, M.S. Strano, C. Kittrell, R.H. Hauge, R.E. Smalley and R. Bruce Weisman, "Structure Assigned Optical Spectra of Single Walled Carbon Nanotubes" Science 298, 2361 (2002)
T. Ando "Excitons in Carbon Nanotubes" J. Phys. Soc. Japan 66, 1066 (2001)
C.L. Kane and E.J. Mele "Ratio Problem in Carbon Nanotube Fluorescence Spectrosopy" Physical Review Letters90, 207401 (2003); and to be published.