Abstract
The model of electron gas situated on the two-dimensional continual cylindrical surface is suggested to describe a polaron in the single-walled nanotube made of polar material. The problem on weak-coupling polaron is solved using perturbation theory. Analytical expression for the polaron energy shift of the subband is found in the case of bulk phonon approximation and the case when longitudinal optical (LO) phonons are confined on the cylinder's surface. It is shown that in the second case the polaron effect is negligible.
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