  We point out an apparently overlooked consequence of the boundary conditions
obeyed by the electric displacement vector at air-metal interfaces: the
continuity of the normal component combined with the quantum mechanical
penetration of the electron gas in the air implies the existence of a surface
on which the dielectric function vanishes. This, in turn, leads to an
enhancement of the normal component of the total electric field. We study this
effect for a planar metal surface, with the inhomogenous electron density
accounted for by a Jellium model. We also illustrate the effect for equilateral
triangular nanoislands via numerical solutions of the appropriate Maxwell
equations, and show that the field enhancement is several orders of magnitude
larger than what the conventional theory predicts.
