Image-Potential-Induced Surface Bands in Insulators

We find that whenever the bottom of the conduction band of an insulator lies at positive energy, the image potential gives rise to bands of surface states. We present lower limits for binding energies of electrons to the surface of liquid and solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, Ne, ${\mathrm{H}}_2$, and ${\mathrm{D}}_2$. Interaction between electrons and surface phonons (solids) or ripplons (liquids) increases the binding. We argue that these states may have in fact been observed in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.