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 inter-shell electron tunneling. Selection rules for the inter-shell 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 that depend on the chiralities of the shells.
Highlights
Due to their unusual physical properties, cf. e.g. [1, 2], carbon nanotubes have become promising building blocks for nanotechnology applications and have attracted a lot of attention since their discovery
In a commensurate (5,5)@(10,10) double-wall carbon nanotubes (DWNTs) the band structure obtained with this method agrees with that obtained by the partial real-space method described in section 3.5, down to the fine details of the subband crossings near the Fermi level
When this method is applied to the DWNTs in the parallel magnetic field, we observe complex geometrical patterns developing in the density of states (DOS) of the nanotubes
Summary
Due to their unusual physical properties, cf. e.g. [1, 2], carbon nanotubes have become promising building blocks for nanotechnology applications and have attracted a lot of attention since their discovery. In [25] the authors consider a long DWNT and calculate the intershell resistance, as coming only from the Coulomb drag, i.e. neglecting the inter-shell tunneling They find selection rules for the coupling between momentum states in different shells. The tunneling coupling between shells of a DWNT modifies the spectra of the individual shells, introducing numerous avoided crossings, which in turn result in the depletion of the density of states (DOS) in one or more regions of the spectrum [39] In small fields this region lies close to the bottom of the valence band, but when the magnetic field increases, the influence of the intershell coupling is visible in higher energy ranges.
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