Wide-range optical studies on various single-walled carbon nanotubes: the 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/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 DFT calculations, the difference increasing with decreasing diameter. This difference can be assigned to electron-hole interactions.Comment: 9 pages, 8 figures, to be published in Physical Review B, supplemental material attached v2: Figures 1, 7 and 8 replaced, minor changes to text; v3: Figures 3, 4 and 5 replaced, minor changes to tex