Plasma Wave Instabilities in Non-Equilibrium Graphene

TL;DR

This paper investigates plasma wave instabilities in non-equilibrium graphene with electron injection, identifying conditions for unstable charge-density waves and comparing these to parabolic band systems.

Contribution

It introduces an analysis of two-stream instabilities in non-equilibrium graphene, detailing the unstable wavevector range and growth rates, and comparing with parabolic band systems.

Findings

Unstable charge-density waves can grow in non-equilibrium graphene.

Instability depends on wavevector orientation, absent for parallel or perpendicular directions.

The maximum growth rate angle increases with wavevector magnitude.

Abstract

We study two-stream instabilities in a non-equilibrium system in which a stream of electrons is injected into doped graphene. As with equivalent non-equilibrium parabolic band systems, we find that the graphene systems can support unstable charge-density waves whose amplitudes grow with time. We determine the range of wavevector $\boldsymbol{q}$ that are unstable, and their growth rates. We find no instability for waves with wavevectors parallel or perpendicular to the direction of the injected carriers. We find that, within the small wavevector approximation, the angle between $\boldsymbol{q}$ and the direction of the injected electrons that maximizes the growth rate increases with increasing $\boldsymbol{|q|}$. We compare the range and strength of the instability in graphene to that of two and three dimensional parabolic band systems.