Surface-polaron first-order phase-transition-like behavior

A simple unitary-transformation formalism, successfully applied to the bulk polaron problem, is used in order to investigate the ground-state properties of an electron near a surface of a semi-infinite material and interacting with the surface optical modes. The method has the advantage of being applicable to the whole range of the electron---surface-phonon coupling. A first-order phase-transition---like behavior from the quasifree to the self-trapping electron state as the coupling constant exceeds a certain critical value is observed. The characteristic features of this phase transition such as rapid changes of the ground-state energy, the effective mass, the mean number of surface phonons in the cloud around the electron, and the spatial localization of the electron perpendicular to the surface at the critical coupling constant, are seen. In the present calculation, the coupling of the electron to the bulk excitation modes is not treated.