Twisted Helical shaped Graphene Nano-Ribbons: Role of Symmetries and Passivation

The Hydrogen and Fluorine planar armchairs graphene nanoribbons (H and F AGNRs), subjected to twist deformation within fixed periodic boundary conditions, eventually morph to a helical conformations are investigated at few tractable points. Unlike structural properties, no effect of symmetries on mechanical properties is observed, though passivation does have a significant effect on mechanical as well as on electrical properties. Hookes law for severely twisted AGNRs indicates the high elasticity of H-AGNRs whereas the F-AGNRs shows plasticity after threshold torsional strain. Torsional stress($E_{\theta}$) is approximated from the variation in total energy(${\Delta}E$) with square of torsional strain(${\theta}^4 {\Sigma}^4$). Further, the effect of passivation on the electronic properties of helical conformations with different torsional strain is decisive in metal-to-semimetal and semimetal-to-metal transition. The band gap response of narrow GNRs N=6, 7 and 8, within a fixed cell under sever twisting arranged itself in two group as (i) monotonously increasing for q=0,2 and (ii) decreasing for q=1, here q=mod(N,3) in effective strain space (${\theta}^2 {\Sigma}^2$). This trend has also been observed for Fluorine passivated AGNRs, though band gap of N=7 F-AGNRs drops from 0.95eV to 0.05eV at extreme torsional strain forming Dirac cone at K allows dissipation less transport for longer wavelength electrons.