Band structure and inter-tube optical transitions in double-walled carbon nanotubes

TL;DR

This paper investigates how interlayer coupling in double-walled carbon nanotubes can alter their electronic band structure, enabling new optical transitions and spectral features, which aids in structural identification.

Contribution

It demonstrates that interlayer coupling can induce unconventional inter-tube electronic transitions in specific DWCNTs, expanding understanding of their optical spectra.

Findings

Interlayer coupling modifies band structure in certain DWCNTs.

Additional peaks in optical spectra linked to inter-tube transitions.

Geometrical selection rules for inter-tube transitions derived.

Abstract

Usually, in optical spectra of double-walled carbon nanotubes (DWCNTs) weak van der Waals coupling between the layers leads only to a small shift of transition energies with respect to their values in pristine single-walled nanotubes. However, recent results have shown that the Rayleigh spectrum of the DWCNT (12,11)@(17,16) contains additional peaks. Using the tight binding approximation, we demonstrate that in specific DWCNTs the interlayer coupling can slightly modify the band structure of pristine nanotubes in such a way that the unconventional inter-tube electronic transitions become possible and additional peaks in the DWCNT optical spectrum appear. Using the known experimental data on 118 optical transitions in DWCNTs, in addition to the recently published case we reveal six more DWCNTs with inter-tube transitions and obtain geometrical selection rules permitting them. In few dozens of DWCNTs our approach yields the energies of electronic transitions close to the experimentally observed ones and may be useful for structural identification of this-type nanotubes.