  Degeneracy of discrete energy levels of finite-length, metallic single-wall
carbon nanotubes depends on type of nanotubes, boundary condition, length of
nanotubes and spin-orbit interaction. Metal-1 nanotubes, in which two
non-equivalent valleys in the Brillouin zone have different orbital angular
momenta with respect to the tube axis, exhibits nearly fourfold degeneracy and
small lift of the degeneracy by the spin-orbit interaction reflecting the
decoupling of two valleys in the eigenfunctions. In metal-2 nanotubes, in which
the two valleys have the same orbital angular momentum, vernier-scale-like
spectra appear for boundaries of orthogonal-shaped edge or cap-termination
reflecting the strong valley coupling and the asymmetric velocities of the
Dirac states. Lift of the fourfold degeneracy by parity splitting overcomes the
spin-orbit interaction in shorter nanotubes with a so-called minimal boundary.
Slowly decaying evanescent modes appear in the energy gap induced by the
curvature of nanotube surface. Effective one-dimensional model reveals the role
of boundary on the valley coupling in the eigenfunctions.
