Adiabatic invariants for surface plasmons on temporally dynamic graphene

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.