Surface effects in the response of a polarisable lattice to an external field

Abstract

The authors consider surface effects in the response of a plane slab shaped sample of a simple cubic lattice of polarisable points with unit spacing to an applied constant external electric field E. In the bulk interior, with the polarisability alpha of a point less than a critical value alpha c=3/4 pi , the response is that of a plane slab of continuum dielectric with dielectric constant epsilon =(1+2x)/(1-x) with x= alpha / alpha c, the value alpha = alpha c corresponding to the usual polarisation catastrophe. If E is normal to the plane surface of the slab, there is almost no difference between the surface and the bulk interior. However if E is parallel to the plane surface then there are marked surface effects which can decay slowly as alpha becomes large. There is a second critical polarisability alpha c2 for this response which signals the onset of surface effects which propagate undiminished into the bulk of the lattice.