Feynman-Haken path-integral approach for the two-dimensional surface optical polaron bound to a Coulomb impurity

The problem of an electron confined to a purely two-dimensional surface of a polar semiconductor interacting with the surface optical phonons and a surface Coulomb impurity is investigated in the framework of the Feynman-Haken path-integral formalism. The ground-state energy is obtained in the weak- and strong-coupling limits by using the harmonic-oscillator and the hydrogenic effective potentials. A new dimensional scaling relation is proposed which holds only in the case of the harmonic-oscillator effective potential, and which, in the limit of vanishing impurity binding, reduces to the free-polaron scaling relation.