Full Symmetry of Single- and Multi-wall Nanotubes

TL;DR

This paper determines the complete symmetry groups of all single- and multi-wall carbon nanotubes, revealing new symmetry properties and their implications for electronic, phononic, and tensor characteristics.

Contribution

It provides the full symmetry classification for all nanotubes, extending previous results and enabling detailed analysis of their physical properties.

Findings

Symmetry groups for all nanotubes are fully characterized.

Enlarged symmetry groups for single-wall nanotubes compared to previous literature.

Multiple symmetry types for multi-wall nanotubes depending on their structure.

Abstract

The full symmetry groups for all single- and multi-wall carbon nanotubes are found. As for the single-wall tubes, the symmetries form nonabelian nonsymorphic line groups, enlarging the groups reported in literature. In the multi-wall case, any type of the line and the axial point groups can be obtained, depending on single-wall constituents and their relative position. Several other consequences are discussed: quantum numbers and related selection rules, electronic and phonon bands, and their degeneracy, application to tensor properties.