Wide-range optical studies on various single-walled carbon nanotubes: Origin of the low-energy gap

We present wide-range (3 meV-6 eV) optical studies on freestanding transparent carbon nanotube films, made from nanotubes with different diameter distributions. In the far-infrared region, we found a low-energy gap in all samples investigated. By a detailed analysis we determined the average diameters of both the semiconducting and metallic species from the near-infrared and visible features of the spectra. Having thus established the dependence of the gap value on the mean diameter, we find that the frequency of the low-energy gap is increasing with increasing curvature. Our results strongly support the explanation of the low-frequency feature as arising from a curvature-induced gap instead of effective-medium effects. Comparing our results with other theoretical and experimental low-energy gap values, we find that optical measurements yield a systematically lower gap than tunneling spectroscopy and density functional theory calculations, the difference increasing with decreasing diameter. This difference can be assigned to electron-hole interactions.