  We study here polaron (soliton) states of electrons or holes in a model
describing carbon-type nanotubes. In the Hamiltonian of the system we take into
account the electron-phonon interaction that arises from the deformation
dependencies of both the on-site and the hopping interaction energies. Using an
adiabatic approximation, we derive the equations for self-trapped electron
states in zigzag nanotubes. We find the ground states of an electron in such a
system and show that the polaron states can have different symmetries depending
on the strength of the electron-phonon coupling. Namely, at relatively weak
coupling the polarons possess quasi-one-dimensional (quasi-1D) properties and
have an azimuthal symmetry. When the coupling constant exceeds some critical
value, the azimuthal symmetry breaks down and the polaron spreads out in more
than one dimension.
  We also study polarons that are formed by the electrons in the conducting
band (or by holes in the valence band) in semiconducting carbon nanotubes. We
show that their properties are more complex than those of quasi-1D ground state
polarons. In particular, polarons in semiconducting carbon nanotubes possess an
inner structure: being self-trapped along the nanotube axis they exhibit some
modulations around the nanotube.
