Surface polarons near rough surfaces

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Abstract
The theory of surface polarons near a rough polar crystal surface is presented. The effective Hamiltonian of the polaron is derived using the Lee-Low-Pines unitary transformation technique and considering the electron moving in the instantaneous field of the optical phonons. The image potential of the polaron arising from the interaction with both the longitudinal-optical and surface-optical phonons is obtained from the theory, while the image potential associated with the polarizations, which have much higher ‘‘vibrational’’ frequencies than those of optical phonons, is added to the theory using its electrostatic limit. The numerical calculations for the image potential of the polaron and its effective mass are carried out for a stepped ZnO surface for both cases of the polaron being inside and outside the crystal. The results show that the surface roughness will cause great changes in the polaron effective potential and introduce anisotropy in the polaron effective mass, which we expect may cause changes in the surface-polaron energy, its cyclotron-resonance frequency, and localizations of the surface polaron in the plane parallel to the rough surface.