Electronic spectra of commensurate and incommensurate DWNTs in parallel magnetic field

TL;DR

This paper investigates the electronic spectra of finite-length double-wall carbon nanotubes (DWNTs), considering intershell tunneling and magnetic field effects, revealing how chiralities influence spectrum modulations.

Contribution

It introduces selection rules for intershell coupling in DWNTs, enabling efficient spectrum calculations and analyzing magnetic field effects on electronic spectra.

Findings

Intershell coupling allows momentum state mixing in incommensurate DWNTs.

Magnetic fields induce spectrum modulations dependent on nanotube chiralities.

Selection rules simplify the calculation of electronic spectra.

Abstract

We study the electronic spectra of commensurate and incommensurate double-wall carbon nanotubes (DWNTs) of finite length. The coupling between nanotube shells is taken into account as an intershell electron tunneling. Selection rules for the intershell coupling are derived. Due to the finite size of the system, these rules do not represent exact conservation of the crystal momentum, but only an approximate one; therefore the coupling between longitudinal momentum states in incommensurate DWNTs becomes possible. The use of the selection rules allows a fast and efficient calculation of the electronic spectrum. In the presence of a magnetic field parallel to the DWNT axis we find spectrum modulations which depend on the chiralities of the shells.