Abstract
The nonlocal conductivity tensor for a semi-infinite electron gas bounded by a finite-step potential is studied, both numerically and analytically, within the random-phase approximation. The tensor component normal to the surface is compared with the corresponding nonlocal conductivity tensor of the bulk, or homogeneous, electron gas with a view to isolating the "optical" surface region, i.e., the region near the surface in which the two functions differ. It is shown that the slow asymptotic decay of the two functions makes it impossible to define an unambiguous optical surface region at low frequencies below the photoemission threshold. It is also shown by direct numerical comparison that the width of the surface region is strongly frequency dependent. The significance of these conclusions in terms of theoretical approaches to the study of optical reflectance from metal surfaces is discussed.
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