Properties of Image-Potential-Induced Surface States of Insulators

The strongly repulsive interaction between electrons and He or Ne atoms, or ${\mathrm{H}}_2$ molecules, gives rise to the existence of electronic states localized near a condensed medium consisting of such units. The attractive image potential binds the electrons weakly near the surface; the binding energy ranges from 0.4 meV for liquid ${\mathrm{He}}^3$ to 22 meV for solid ${\mathrm{D}}_2$. Motion parallel to the surface is nearly free-electron—like. An exploration of the interaction between electrons and oscillations of the medium's surface reveals a breakdown in perturbation theory which may be remedied by correct treatment of long-wavelength oscillations. A determination is made of the temperature-dependent mobility of electrons for fields parallel to the surface. We find that the surface waves scatter more for the liquid than for the solid. A transition occurs in the mobility as the temperature increases to a point where scattering by atoms of the vapor becomes dominant over other mechanisms. A second transition occurs when the electron in the vapor becomes localized in the bubble state, and the present treatment loses its validity.