2N+4-rule and an atlas of bulk optical resonances of zigzag graphene nanoribbons

Development of on-chip integrated carbon-based optoelectronic nanocircuits requires fast and non-invasive structural characterization of their building blocks. Recent advances in synthesis of single wall carbon nanotubes and graphene nanoribbons allow for their use as atomically precise building blocks. However, while cataloged experimental data are available for the structural characterization of carbon nanotubes, such an atlas is absent for graphene nanoribbons. Here we theoretically investigate the optical absorption resonances of armchair carbon nanotubes and zigzag graphene nanoribbons continuously spanning the tube (ribbon) transverse sizes from 0.5(0.4) nm to 8.1(12.8) nm. We show that the linear mapping is guaranteed between the tube and ribbon bulk resonance when the number of atoms in the tube unit cell is 2 N+ 4 , where N is the number of atoms in the ribbon unit cell. Thus, an atlas of carbon nanotubes optical transitions can be mapped to an atlas of zigzag graphene nanoribbons

Ab initio study of absorption resonance correlations between nanotubes and nanoribbons of graphene and hexagonal boron nitride

Density functional theory calculations are performed for the electronic band structures and optical absorption spectra of the zigzag nanoribbons and armchair nanotubes of graphene and hexagonal boron nitride as well as hybrid tubular structures obtained by embedding two dimer lines of B and N atoms into an armchair nanotube. Linear correlation coefficient analysis is carried out to quantitatively investigate relations between energies of absorption resonances in these tube-ribbon pairs. Despite the large disparity in the energy band gaps of some of these structures, our results show a high degree of correlation (r > 0.85 with >95% confidence level) between them