Plasma Oscillations in a Periodic Potential: The One-Zone Theory

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Abstract
The collective description of electron interactions in the presence of a periodic potential is investigated. It is shown that there is a re-formulation of the problem which lends itself to a treatment closely resembling the free electron case. This treatment is carried through, and it is shown that the results are formally very similar to those for free electrons. For a parabolic band the main effect of the potential is to replace the electronic mass m by the effective mass m*. The present theory applies only to the electrons in one Brillouin zone, and cannot be used when there is substantial overlapping of the occupied levels of this zone.