Relaxed cross-sections (a) of (10,0) carbon nanotubes with different degrees of flattness in (b) and (c). (d) and (e) plot the electronic band structures for a flattened (10,0) nanotube. The flatness is characterized by which is defined as , where is the original diameter of the nanotube and is the distance between two straight lines of the cross-section (adapted from [13]).