Hidden correlation between absorption peaks in achiral carbon nanotubes and nanoribbons

Abstract

In this paper we study the effect of absorption peak correlation in finite length carbon nanotubes and graphene nanoribbons. It is shown, in the orthogonal π-orbital tight-binding model with the nearest neighbor approximation, that if the ribbon width is a half of the tube circumference the effect takes place for all achiral ribbons (zigzag, armchair and bearded), and corresponding tubes, starting from lengths of about 30 nm. This correlation should be useful in designing nanoribbon-based optoelectronics devices fully integrated into a single layer of graphene.

Ab Initio Study of Absorption Resonance Correlations between Nanotubes and Nanoribbons of Graphene and Hexagonal Boron Nitride

“…The linear correlation coefficient between the absorption peaks of CNT(10,10) and ZGNR(9) is calculated to be equal to 0.9740, which means that the two structures have a very high correlation of peaks with a confidence level > 95 %. Hence, the predicted hidden correlation between GNR and CNT associated to van Hove singularities from the tight-binding model [21,23] persists in the DFT QE numerical calculations.…”

“…The CNT(10,10), which has been thoroughly studied both theoretically [25] and experimentally [26], is used as a reference in this study. Likewise, the infinitely long zigzag graphene nanoribbon (ZGNR) is set to width index w = 9 since ZGNR(9) and CNT(10,10) can form a "tube-ribbon" pair as predicted in previous studies [21,23]. Boron nitride tuberibbon pairs are investigated by comparisons of h-BNNT(6,6) and h-BNNT(7,7) to h-BNZNR with w = 6 or to ZGNR (5).…”

“…Previous tight-binding studies have shown manifestations of hidden correlation on the absorption resonances between of graphene nanoribbons and their corresponding tubes [21][22][23]. Although the selection rules for the optical transitions in GNRs and CNTs are generally different, the absorption resonances can be aligned when the width of the nanoribbon is half to the circumference of the nanotube [21,[23][24].…”

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

“…Joint analysis of several previous studies attempting to compare zigzag SWCNTs and AGNRs indicates that Kataura plots for these ribbons could be the replica of that plot for zigzag SWCNTs. As shown within the tight-binding model, the electronic energy bands of zigzag SWCNT duplicate the bands of the AGNR when , where is the chiral or diameter index of the tube and is the width index of the ribbon 39,40 . Similar correspondence takes place for the optical transition matrix elements 41,42 , leading to a perfect alignment of the single-electron optical absorption peaks of some SWCNTs and corresponding AGNRs 40 .…”

“…As shown within the tight-binding model, the electronic energy bands of zigzag SWCNT duplicate the bands of the AGNR when , where is the chiral or diameter index of the tube and is the width index of the ribbon 39,40 . Similar correspondence takes place for the optical transition matrix elements 41,42 , leading to a perfect alignment of the single-electron optical absorption peaks of some SWCNTs and corresponding AGNRs 40 . Moreover, this alignment should not be disordered by excitonic effects since Loudon’s model provide the same exciton binding energy for two structures of the same transverse size 43 .…”