Effect of spatial dispersion on the spectrum of inter - edge magnetoplasmons in the two - dimensional hetero - geneous system

Effect of spatial dispersion on the spectrum of inter-edge magnetoplasmons in the two-dimensional heterogeneous system. 1 Abstract The present paper is devoted to the theoretical study of the spectrum of low-frequency electronic density oscillations (plasmon waves) running along the boundary of two contacting two-dimensional electronic systems in the perpendicular magnetic field. For the first time, such waves were predicted in the Institute of Radio-engineering and Electronics of RAS (V.A. Volkov, S.A. Mikhailov, 1992), studied experimentally in the papers of foreign investigations and called inter-edge magnetoplasmons (IEMP). In a specific case when the two-dimensional system is finite and has the half-plane shape, the internal boundary becomes external and these plasmons go over into the well-known edge magnetoplasmons. The existing theory of edge and inter-edge magnetoplasmons is built with the neglect of spatial dispersion of the conductivity. The dispersion becomes essential when the electric potential changes significantly over the radius of the electron Larmor orbit or cyclotron radius R c. Here we attempt to derive and analyze the IEMP dispersion equation involving spatial dispersion of conductivity. The approximations are made as follows. The inner boundary is assumed to be a straight line at which the electron concentration changes weakly but stepwise. The same refers to all components of the tensor magnetoconductivity. The jump of the diagonal conductivity is considered small compared with that of the Hall magnetoconductivity. The latter is neglected everywhere with the exception of cutting nonphysical divergencies. We neglect the spatial dispersion of the Hall conductivity. The IEMP frequency is small compared with the cyclotron frequency. Finally, we solve a linearized system of quasi hydrodynamic equations of electron motion in the self-consistent field describing small fluctuations of concentration, potential, and current with the neglect of retardation. The main result is the following. The existence of the spatial dispersion results in analogue of the so-called geometric resonance in the shortwave limit. The IEMP frequency as a function of wave vector oscillates with the period determined by a ratio of electron cyclotron radius to the plasmon wavelength. For long wavelengths, the IEMP dispersion curve coincides with the known result.