However, several conundrums surround their bizarre electrical conductivity behaviour, not least the issue of bandgap measurements and how these relate to the size and structure of semiconducting SWNTs.

Researchers have succeeded in making a wide variety of SWNTs of different internal diameters, lengths, and chirality, all of which are being tested in many different ways. One important facet of the carbon SWNT is that they might also provide scientists with a useful model system for observing physical effects constrained to the simplified realm of one dimension. Moreover, the ability to bundle the nanotubes together then adds the possibility of studying many-body interactions, such as strong electron to electron phenomena, inside each distinct 1D object.
Researchers in France [Rousset et al., Nature Mater (2010) DOI: 10.1038/NMAT2624] were puzzled by pioneering electronic structure calculations and scanning tunnelling spectroscopy (STS) experiments in comparison with optical experiments published recently. SWNTs can exist as either metals or semiconductors depending on their diameter and helicity. Surprisingly, they also seem to have an equivalent energy gap to those calculated for optical transitions which is not consistent with the recent findings regarding excitons in two-photon absorption experiments.
The French team has now carried out an experimental STS study of the bandgap of semiconducting SWNTs to explain this puzzle. They looked at nanotube bundles, produced using an arc discharge method that were deposited on a gold substrate. Such a system gave the team the unique opportunity to measure bandgaps of single isolated nanotubes, as well as those in direct contact with the gold substrate or at any "elevation" above the substrate depending on the position of a particular SWNT within the bundle.
The study revealed there to be a continuous transition from the gap reduced by a screening effect due to the gold substrate to the intrinsic gap dominated by many-body interactions. In other words, the equivalence of STS bandgap measurements in earlier electronic and optical experiments is most likely not to be due to SWNT diameter and helicity but to the effect of substrate and position of the particular SWNT in the bundle.
With this revelation SWNT research can move forward once more, albeit with a slightly different tack. "Knowledge of the electronic bandgap values of carbon nanotubes and many-body effects in these structures is a crucial issue for their potential integration in functional devices," the team concludes.