Енергетичний спектр електрона в еліптичній напівпровідниковій нанотрубці

Abstract

The electron energy spectrum in elliptic semiconductor nanotubes is investigated within the effective mass approximation. In elliptic coordinates, there is obtained a solution of Shroedinger equation based on the Mathieu functions. The dependencies of the electron size quantization spectrum on the sizes and the shape of the nanotube are calculated. It is shown that the ellipticity of the nanotube leads to the breakage of the degeneration quasiparticle energy spectrum.The energy dependencies of odd and even electron states on the focus distance are of nonmonotonous character. In the limiting case of the degeneracy of elliptic nanotubes into circle ones the quasiparticle energy spectrum coincides with the corresponding quasiparticle spectrum in cylindrical nanosystems.