Nonequilibrium plasmons with gain in graphene

Graphene supports strongly confined transverse-magnetic sheet plasmons whose spectral characteristics depend on the energetic distribution of Dirac particles. The question arises whether plasmons can become amplified when graphene is pumped into a state of inversion. In establishing a theory for the dynamic nonequilibrium polarizability, we are able to determine the exact complex-frequency plasmon dispersion of photoinverted graphene and study the impact of doping, collision loss, and temperature on the plasmon gain spectrum. We calculate the spontaneous emission spectra and carrier recombination rates self-consistently and compare the results with approximations based on Fermi’s golden rule. Our results show that amplification of plasmons is possible under realistic conditions but inevitably competes with ultrafast spontaneous emission, which, for intrinsic graphene, is a factor of 5 faster than previously estimated. This work casts new light on the nature of nonequilibrium plasmons and may aid the experimental realization of active plasmonic devices based on graphene.