Finite band-width corrections in the small-polaron theory

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Abstract
Linear superposition of coherent states is used in a variational calculation of the small polaron wavefunctions in the representation in which the Hamiltonian no longer contains the electron coordinates. It is shown that even in the case of very narrow bands the spatial extent of the self-trapped electronic state must be taken into account in the construction of the tight-binding polaron Bloch functions. Investigation of transport properties shows that the activation energy for the hopping motion diminishes relatively fast with increasing ratio of the rigid lattice band-width to the small-polaron binding energy. Explicit formulae for the variation of the activation energy have been derived for two cases: the interaction with optical phonons and the deformation-potential-type interaction with acoustic phonons.