Amplified-reflection plasmon instabilities in grating-gate plasmonic   crystals
  We identify a possible mechanism of the plasmon instabilities in periodically gated two-dimensional electron systems with a modulated electron density (plasmonic crystals) under direct current. The instability occurs due to the amplified reflection of the small density perturbations from the gated/ungated boundaries under the proper phase matching conditions between the crystal unit cells. Based on the transfer-matrix formalism, we derive the generic dispersion equation for the travelling plasmons in these structures. Its solution in the hydrodynamic limit shows that the threshold drift velocity for the instability can be tuned below the plasmon phase and carrier saturation velocities, and the plasmon increment can exceed the collisional damping rate typical to III-V semiconductors at 77 K and graphene at room temperature. 
Aleksandr S. Petrov, Dmitry Svintsov, Victor Ryzhii and Michael S.   Shur
cond-mat.mes-hall