Empirical model for optical transitions in inner semiconducting tubes of double wall carbon nanotubes

The inter-wall distance, average diameter, and chirality of the constituent nanotubes play a significant role in determining the electronic structure of double wall carbon nanotubes (DWNTs). In DWNTs, the inner tube possesses a special status, granted by the outer tube, which acts as a shield. Here, we proposed an empirical model for estimating the different optical transitions of inner semiconducting tubes (ISCTs) of DWNTs from the chirality of the constituent single wall carbon nanotubes when the outer tube can be semiconducting or metallic. So far, there have been no well-known theoretical or empirical models to estimate the optical transitions of ISCTs of DWNTs except first principles simulations. The proposed model relates the optical transitions of ISCTs of DWNTs with the chirality of the inner tube and the average diameter of DWNTs. The relation is used to calculate the optical transitions of a number of ISCTs of DWNTs, and the result was found to be in good agreement with the recent experimental reports. The proposed relation can help understand the electronic behavior of DWNTs in terms of their structural parameters and can help in identifying the chirality of unknown DWNTs from its electronic properties.