Abstract
Quantized energy levels and electronic wave functions of all shortened metallic carbon nanotubes are treated in a unified way under the tight-binding approximation by using the helical and rotational symmetries of the nanotubes and a quantum box boundary condition. Unlike infinite-length metallic nanotubes having universal energy dispersion relations near the Fermi level, the dispersion relations of finite-length ones can be classified into two kinds and their energy levels can be tailored by the length and diameter of the nanotube. Along a helical line or a line along the nanotube axis, the wave functions near the Fermi level appear periodic or keep constants. The standing-wave functions for an arbitrary metallic nanotube are also derived, from which an experimental method is suggested for measuring the chiral angle.
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