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. 
Lei Liu, C.S. Jayanthi, H. Guo, and S.Y. Wu