Donor binding energy under magnetic field with different radii and parabolic bottom potential

Within the framework of the effective mass approximation we analyze a variation of the ground state energy of the off-axis neutral donor in a GaAs/Ga_1-xAl_xAs cylindrical nanotube with a parabolic bottom potential under a uniform magnetic field directed along the symmetry axis. By using a variational principle and the functional derivative procedure, we derive a one-dimensional differential equation for the envelope function, which we solve numerically by using of the trigonometric sweep method. To take into account the mixing of the low lying subbands, we express the wave function as a product of the combination of 1s and 2p_x,y wave functions with an unknown envelope function that depends only on electron-ion separation. Results of the calculation of the ground state binding energy dependencies on the distance from the donor position to the axis and on the strength of the external magnetic field parabolic bottom potentials are presented. It is shown that the effect of the subband mixing for off-axis donors in the nanotube is considerable.