Electronic states of the cap structure in the carbon nanotube

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Abstract
The cap of a carbon nanotube is characterized by six five-membered rings called disclinations. Its electronic structure is studied by the simple tight-binding models for a monolayer nanotube. The method of the development map is used to systematically define the atomistic structures of the cap. The topological feature of the bond network is determined by the configuration of the six five-membered rings. The effects of such topological features on electronic structure are elucidated by the model in which the hopping integrals and the site energies are taken to be common at every atom. Though there are neither disorder of the potential nor that of the coordination number, some localized states emerge around the cap. The wave function and the energy eigenvalue can be obtained analytically for simpler cases. These results show explicitly that the localized states are formed by an analytic continuation of the wave number from the real number space to the complex number space. Some of them are near the Fermi level and coexist with the extended states in the same energy. The effects of magnetic field parallel to the tube axis are also discussed.