Resonant magnetopolarons in semiconductor nanotube

It is presented the results of theoretical study of the magnetopolaron effect for nanotubes (NT) of the finite length. It was established the possibility of the resonant coupling between the discrete energy levels of the electrons with the different numbers of the size quantization, which correspond to the movement of electrons around the circumference of NT in a longitudinal magnetic field. As an interaction that creates a resonant electron-phonon coupling are used the interaction of the electrons with the bulk longitudinal optical (LO) phonons. By using the perturbation theory for degenerate states, it was calculated the energy of usual double and triple magnetopolarons. Numerical calculations of the energy splitting of the double magnetopolaron depending on the length and diameter of the NT were fulfilled for GaAs. It was found that the energy splitting is inversely to the square root of the NT length and decreases slightly with increasing diameter of the NT