Local Energy Gap in Deformed Carbon Nanotubes

The effects of graphite surface geometrical deformation on the dynamics of conducting electrons are investigated theoretically. The analysis is performed within the framework of a deformation-induced gauge field and corresponding deformation-induced magnetic field. It is shown that the latter gives a local energy gap along the axis of a deformed nanotube. We compare our energy gap results with experimental data on energy gaps in nanotubes and peapods. We also discuss the mixing of two Fermi points and construct a general model of low energy dynamics, including a short-range deformation of the graphite sheet. This model is equivalent to the Weyl equation in {\it U}(1) Abelian and {\it SU}(2) non-Abelian deformation-induced gauge fields.