  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.

Mesoscale and Nanoscale Physics