Introduction

Physical phenomena in the terahertz (THz) spectral range are intensively studied, which is associated with the fundamental importance of new terahertz physics, as well as with a considerable number of feasible applications. In particular, many researches aim at constructing new sources and detectors of THz radiation.
In this context, of great interest are the researches of semiconductor heterostructures with quantum wells (QWs), in which collective oscillations of a two-dimensional electron gas (2DEG), i.e. plasmons, can be excited. The frequencies of plasmon oscillations belong to the THz spectral range. In a homogeneous 2DEG, plasmons are stable, i.e. their oscillations attenuate in time owing to the electron scattering by various crystal defects and by means of the known mechanism of Landau damping. Various methods were proposed in order to achieve the instability and obtain oscillation-growth effects intended to be used for the amplification and the generation of THz radiation. Among those, a possibility of the instability excitation owing to the electron drift in an electric field \cite{rev-1, rev-2, Wilkins}, various variants of two-beam instability \cite{Wilkins, Gribnikov}, and others were examined. However, for such instabilities to be realized in a spatially uniform plasma, very high drift velocities, which are difficult to be obtained experimentally, are required. The situation essentially changes in spatially non-uniform or finite systems \cite{f-length-1}. For example, as was shown in works \cite{Dyakonov}, if special types of contacts are applied to a quantum well with a finite length, the electron system becomes unstable already at moderate drift velocities of electrons. This instability has been studied experimentally \cite{Knap-2004,Knap-2005,Knap-2008}.
Another class of objects, which are active in the THz spectral range, includes quantum dots \cite{Demel_1990, old-QDs-1, old-QDs-2, old-QDs-3}, molecules and some molecular compounds \cite{Yu_2004, Maistrenko_1999, Balu_1999}, shallow impurity centers \cite{Burghoon_1994, Kalkman_1996, Allen_2005}, and so forth. For brevity, let us call such “zero-dimensional” objects as nanoparticles (NPs).
Hybrid systems consisting of nanoparticles and heterostructures with free electrons constitute a new type of heterodimensional objects, which should demonstrate essentially new properties and effects. In particular, if the oscillation frequencies of zero-dimensional NPs and two-dimensional plasmons are in the THz spectral range, hybrid systems may reveal new properties at extremely high frequencies. Therefore, the study of the interaction between such NPs and plasmons under equilibrium and nonequilibrium conditions seems well-timed.