Semiconductor nanotube in the field of uniformly charged ring: Additional quantization in the form of one-dimensional hydrogen-type levels

The single-particle states in a cylindrical nanotube placed in the field of charged ring are considered theoretically in the effective-mass approximation. The electrostatic field of charged ring creates an additional quantum well the symmetry axes of system. It is shown, that this quantum well can be described as one-dimensional modified Coulomb-like potential By using a variation-method the wave functions and energy levels of the first two states of charge carriers in the well were obtained. The interband and intraband electro-optical transitions in the tube are also considered.