Anomalous charge oscillations in the dynamical response of metals

In recent calculations of optical response at a metal surface, an unusual set of oscillations have been found in the induced charge density. These oscillations only appear when a crystal potential is included in the calculation. They propagate deep into the bulk, but are incommensurate with the lattice. We illustrate the occurrence of such oscillations in simple systems, and discuss their origin. For more general cases, we find that the amplitude of the oscillations is sensitive to the amount of spatial variation in directions parallel to the surface of either the crystal potential or the probing field. We also discuss the challenge of detecting this phenomenon experimentally.