In work \cite{Kukhtaruk_UJP}, the studies of the interaction between a remote nanoparticle and a drifting 2DEG at relatively low frequencies, i.e. when the application of the “low-frequency” drift-diffusion approximation is valid, were started. In this work, we present the results of our researches of THz-frequency properties of hybrid systems in the “high-frequency” approximation for the electron motion in a 2DEG. We revealed collective oscillations of interacting nanoparticles and the 2DEG. In particular, we determined the frequencies of collective oscillations and their extra damping stemming from the interaction between the nanoparticle and plasmons. The damping character is similar to that of Landau damping. This system was demonstrated to become unstable under definite nonequilibrium conditions, i.e. there emerges an increase of collective oscillations in time induced by an electric current. The nanoparticle destroys the translational symmetry, and the system becomes non-uniform, which promotes the appearance of an instability, similarly to what takes place in non-uniform or spatially confined plasma \cite{f-length-1}.
The structure of the paper is as follows. In Section 2, the model of a hybrid system is discussed, and the basic equations are substantiated. In Section 3, the exact solutions of the equations are obtained, and their general properties are examined. In Section 4, the main attention is given to the stability/instability of a hybrid system under the condition of two-dimensional electron drift, the numerical results are presented, and the specific examples of nanoparticles and heterostructures with two-dimensional electrons are considered. The features of coordinated space-time charge waves are dealt in Section 5. The properties of the NP dipole moment, plasmon field, and emission by the hybrid system are studied in Section 6. Conclusions are presented in Section 7.