Abstract
For surface plasmons on graphene in an arbitrary dielectric environment, combinations of the plasmon energy and frequency (adiabatic invariants) that are conserved during slow time-variations of the graphene free carrier density are obtained. The invariants allow one to find the plasmon energy changes directly from the frequency shift without solving a dynamic equation. The invariants have a different form in the cases of increasing and decreasing carrier density. In both cases, however, they predict that plasmon frequency shifting is accompanied by a decrease of the plasmon energy.
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