Analysis of band-gap formation in squashed armchair carbon nanotubes

The electronic properties of deformed armchair carbon nanotubes are modeled using constraint free density functional tight binding molecular dynamics simulations. Independent from CNT diameter, deforming path can be divided into three regimes. In the first regime, the nanotube deforms with negligible force. In the second one, there is significantly more resistance to deforming with the force being $\sim 40\text{–}100\mathrm{nN}∕\mathrm{per}$ CNT unit cell. In the last regime, the CNT loses its hexagonal structure resulting in force drop-off followed by substantial force enhancement upon deforming. We compute the change in band gap as a function of deforming 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 deforming, large $\pi \text{−}\sigma$ 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 zero band gap. (iv) All armchair nanotubes become metallic in the third regime of deforming. Finally, we discuss both differences and similarities obtained from the tight binding and density functional approaches.