Carbon Nanotubes

SWCNT can be defined by its diameter and chiral angle. The chiral angle can range from 0 to 30 degrees. However, more conveniently, a pair of indices (n, m) is used instead. The indices refer to equally long unit vectors at 60° angles to each other across a single 6-member carbon ring. When |m – n| = 3k (k is integer), the tube is metallic; but if |m – n| = 3k ± 1, the tube is semiconducting.
The nanotube diameter d is related to m and n as: \begin{equation} d =\frac{a}{\pi}\sqrt{(n^2+nm+m^2)} \end{equation}

A first approach to calculate the transition energy is defined as \begin{equation} E_{sc,m} =2i\frac{\gamma_0 a_{c-c}}{d} \end{equation} where i=1 for $S{11}$, i=2 for $S{22}$ and i=3 for $M{11}$, $\gamma0=2.9eV$ is the nearest neighbout carbon-carbon interaction energy and $a_{c-c}=0.144$ is the nearest neighbour carbon-carbon distance. (*"Optical absorption spectroscopy and properties of single walled carbon nanotubes at high temperature")