Acoustic Plasmon Focusing in Graphene with an Applied Current.*

Nonreciprocity in the plasmonic spectrum opens fundamentally new possibilities in the field of plasmonics. Here we present a theory of the nonreciprocity induced in the acoustic plasmon spectrum of a graphene-dielectric-metal system with an applied current bias. We show that the bias induces a redshift (blueshift) of the plasmonic spectrum whose wave vector is antiparallel (parallel) to the direction of the applied current. While such an effect has been discussed previously for the conventional plasmon in graphene, we show that the acoustic plasmon exhibits a focusing effect that does not occur in the conventional plasmon. We find that at large enough currents a significant portion of the plasmonic spectrum is effectively damped out, focusing the plasmon along the direction of the applied current. We argue that the source of this focusing effect is crossing of the redshifted branch into the particle-hole continuum. We present analytical and numerical results, and discuss the experimental conditions necessary to observe such an effect.