Broken Symmetry, Boundary Conditions, and Band Gap Oscillations in Finite Single Wall Nanotubes

We have shown how the interplay between the broken symmetry associated with the finite single-wall nanotubes (SWNT) and the boundary conditions affects the electronic properties of SWNTs in a profound way. For finite SWNTs (p,q) characterized by p=k+l,q=k-l,p-q=2l,l=0,1...,k, and k=1,2..., we found that the band gaps of finite SWNTs belonging to a certain k exhibit similar well-defined oscillating patterns but with diminishing amplitudes from the armchair (l=0) to the zigzag (l=k) SWNTs. These profound changes hold intiguing implications in the potential utilization of these finite NTs as the basic component of molecular scale devices.