Analysis of band-gap formation in squashed arm-chair CNT
  The electronic properties of squashed arm-chair carbon nanotubes are modeled using constraint free density functional tight binding molecular dynamics simulations. Independent from CNT diameter, squashing path can be divided into {\it three} regimes. In the first regime, the nanotube deforms with negligible force. In the second one, there is significantly more resistance to squashing with the force being $\sim 40-100$ nN/per CNT unit cell. In the last regime, the CNT looses its hexagonal structure resulting in force drop-off followed by substantial force enhancement upon squashing. We compute the change in band-gap as a function of squashing and our main results are: (i) A band-gap initially opens due to interaction between atoms at the top and bottom sides of CNT. The $\pi-$orbital approximation is successful in modeling the band-gap opening at this stage. (ii) In the second regime of squashing, large $\pi-\sigma$ interaction at the edges becomes important, which can lead to band-gap oscillation. (iii) Contrary to a common perception, nanotubes with broken mirror symmetry can have {\it zero} band-gap. (iv) All armchair nanotubes become metallic in the third regime of squashing. Finally, we discuss both differences and similarities obtained from the tight binding and density functional approaches. 
H. Mehrez, A. Svizhenko, M. P.Anantram, M. Elstner, and T. Frauenheim