  Semiconducting single-wall carbon nanotubes are classified into two types by
means of orbital angular momentum of valley state, which is useful to study
their low energy electronic properties in finite-length. The classification is
given by an integer $d$, which is the greatest common divisor of two integers
$n$ and $m$ specifying the chirality of nanotubes, by analyzing cutting lines.
For the case that $d$ is equal to or greater than four, two lowest subbands
from two valleys have different angular momenta with respect to the nanotube
axis. Reflecting the decoupling of two valleys, discrete energy levels in
finite-length nanotubes exhibit nearly fourfold degeneracy and its small lift
by the spin-orbit interaction. For the case that $d$ is less than or equal to
two, in which two lowest subbands from two valleys have the same angular
momentum, discrete levels exhibit lift of fourfold degeneracy reflecting the
coupling of two valleys. Especially, two valleys are strongly coupled when the
chirality is close to the armchair chirality. An effective one-dimensional
lattice model is derived by extracting states with relevant angular momentum,
which reveals the valley coupling in the eigenstates. A bulk-edge
correspondence, relationship between number of edge states and the winding
number calculated in the corresponding bulk system, is analytically shown by
using the argument principle, which enables us to estimate the number of edge
states from the bulk property. The number of edge states depends not only on
the chirality but also on the shape of boundary.
