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

Renebeth B Payod,Vasil A Saroka,Davide Grassano,Gil Nonato C Santos,Dmitry I Levshov,Olivia Pulci

doi:10.1038/s41467-019-13728-8

Abstract

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 2N+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.

Highlights

Development of on-chip integrated carbon-based optoelectronic nanocircuits requires fast and non-invasive structural characterization of their building blocks
Significant advancements in the synthesis of graphene ribbons with atomic precision have been observed in recent years[4,5], whereas a comprehensive progress has been achieved in production of monochiral carbon nanotubes[2,6,7]
None of these previous works have provided a proper comparison of the armchair GNRs (AGNRs) optical resonances with those of zigzag Single-walled carbon nanotubes (SWCNT), whereas such comparative analysis is highly desirable for a reliable optical nanodevice and nanocircuit engineering

Summary

Introduction

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. Significant advancements in the synthesis of graphene ribbons with atomic precision have been observed in recent years[4,5], whereas a comprehensive progress has been achieved in production of monochiral carbon nanotubes[2,6,7]. A standard way of presenting diameter dependence of SWCNT optical resonances polarized parallel to the tube axis is Kataura plot[8]. This plot has been both measured experimentally[9,17] and reproduced numerically in semi-empirical and ab-initio calculations[18,19,20]. Joint analysis of several previous studies attempting to compare zigzag

Methods

Results

Conclusion