Please see the answers below:

https://www.researchgate.net/post/What_could_be_the_band_gap_of_multi_walled_carbon_nanotubes

Single walled nanotubes can be metallic or semiconducting, and the band gap of the latter depends on chirality.

Here is a starting point

https://en.wikipedia.org/wiki/Optical_properties_of_carbon_nanotubes

Article Optical properties of single-wall carbon nanotubes

Hugh J Byrne already posted the Kataura plot which gives the theoretical n-m-bandgap relation. There is also an empiric refinement to that work:

Article Dependence of Optical Transition Energies on Structure for S...

I think it is difficult to use carbon nano tube for solar cell because it's band gap fall between(0.8-1 eV) that mean in near IR region

Isam M. Ibrahim : the usage of CNTs for solar cells is actually a highly investigated topic, see e.g.

Article The Role of Nanotubes in Carbon Nanotube–Silicon Solar Cells