Interpretation of the linear coefficient of surface-plasmon dispersion

Abstract

Microscopic theory predicts that the fluctuating charge of free-electron-metal surface plasmons will lie in the tail of the metallic electron gas, and that, as a consequence, the linear coefficient of surface-plasmon dispersion will be negative. The latter prediction is interpreted here using the virial theorem. At larger wave vectors the more rapidly attenuating electric field associated with a fluctuating charge that lies outside the bulk of a metal will move fewer electrons. The virial theorem relates this fact to a lower frequency. Were the fluctuating charge to lie inside a metal, then more of its electric field would move electrons as the field attenuation became more rapid. This, according to the virial theorem, would imply a positive dispersion coefficient.