Unique properties of plasmons in two-dimensional electron systems (2DESs) have been studied for many years. Existing theoretical approaches allow for analytical study of the properties of ungated and gated plasmons in two fundamental, ideal cases -the 2DES in dielectric environment and under an infinite metallic gate, respectively. However, it is for the first time that we introduce an analytical theory of the interaction of gated and ungated plasmons in partly gated 2DES. Generally, a finitewidth gate is formed by a metallic strip placed over an infinite plane hosting 2D electrons. Our solution, in particular, describes the propagating plasmon modes with their charge density having N nodes under the gate. In this regard, a new mode with N = 0 has been found in addition to the gapped modes with N = 1, 2, ... previously derived from numerical calculations. Unexpectedly, this fundamental plasmon mode has been found to differ substantially from the rest. In fact, it is characterised by gapless square root dispersion and represents a hybrid of gated and ungated plasmons. In contrast to the higher modes, the currents and lateral fields of the fundamental mode are localized mainly to the outside area in the vicinity of the gate. Heretofore, such a 'near-gate plasmon' has never been considered.

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We report on a contribution to the microwave response of a two-dimensional electron system in a magnetic field which originates from excitation of virtual Bernstein modes. These collective modes emerge as a result of interaction between the usual magnetoplasmon mode and cyclotron resonance harmonics. The electrons are found to experience a strongly enhanced radiation field when its frequency falls in a gap of the Bernstein modes spectrum. This field can give rise to nonlinear effects, one of which, the parametric cyclotron resonance, is discussed. We argue that this resonance leads to a plasma instability in the ultraclean system. The instability-induced heating is responsible for the giant photoresistivity spike recently observed in the vicinity of the second cyclotron resonance harmonic.PACS numbers: 73.21. Fg, 73.20.Mf, 73.43.Qt, 72.30.+q Plasma oscillations are well known; their study began about a century ago by Langmuir and Tonks. These oscillations are mostly investigated in two different types of systems: low-density nondegenerate gas plasma [1] and the degenerate plasma of solids [2]. In the latter case plasma excitations are often referred to as plasmons. A characteristic feature of the solid state systems is that the motion of particles can be easily restricted in one or more directions and thus low-dimensional systems can be created. Properties of plasmons in these systems differ dramatically from those in the three-dimensional (3D) systems. For instance, the plasmon dispersion law in a twodimensional (2D) electron system (ES) can be written as ω (2) p (q) = 2πn s e 2 q/κm, where n s is 2D electron concentration, κ is the surrounding dielectric constant, m is electron effective mass, and q is the 2D wave vector of the plasmon. The spectrum of 2D plasmons is gapless and strongly depends on q in contrast to the dispersionless spectrum of the 3D plasmon ω (3) p (q) = 4πn 3D e 2 /κm, where n 3D is the electron concentration of 3DES.Recently an ultrastrong radiation-plasmon coupling in 2DES in magnetic field has been observed [3,4]. Plasma oscillation in the perpendicular magnetic field B is called the upper hybrid mode in gas plasma or the magnetoplasmon mode in solid state plasma. The dispersion relation of the excitation is as follows:where ω c = eB/mc is the electron cyclotron frequency, and ω (i)p is the plasmon frequency in a 3D (i = 3) or 2D (i = 2) system in the absence of a magnetic field.Plasma oscillations determined by Eq. (1) can interact with cyclotron resonance harmonics due to finite value of qR c , where R c = v F /ω c is the electron cyclotron radius, and v F is the Fermi velocity (in the case of degenerate plasma). This interaction splits mode (1) into the so-called Bernstein modes. In 2DES these modes, see Consider the influence of the Bernstein modes on the screening of incident radiation by magnetoplasmons in 2DES. If a wave vector of radiation q is nonzero and the radiation frequency Ω lies in one of the gaps, see Fig. 1(b), then real magnetoplasma modes are not excited but elect...