Effect of screening on the phonon-polaron states in diluted magnetic semiconductor nanotubes

We calculate the effect of screening on the weakly coupled Fröhlich polaron binding energy of the ground state and the polaron contribution to the mass for the lowest spin-down subband of the conduction band in diluted magnetic semiconductor nanotubes. Expressions for the polaron energy and the polaron contribution to the effective mass are obtained as functions of the magnetic field and the radius of the nanotube, taking into account the screening effect as well as virtual transitions from the ground state with n = 0 to size-quantized subbands with n′ = 1, 2, …, 10. Numerical calculations show that screening reduces the polaron binding energy and polaron contribution to the effective mass by about 35% and 25%, respectively, for a magnetic field of 0.1 T. Screening reduces the polaron binding energy of the ground state by approximately 30%-15% and also reduces the polaron contribution to the effective mass by 25%-10% when the nanotube radius is increased by 10-40 nm.