Retardation effect on absorption of microwave radiation in disk with 2D electron gas

Plasmons in 2D disk have been studied since 1985 [1] and recently were intensively discussed in graphene structures. However most works were done in quasielectrostatic or non-retarded regime, when the size of the sample is much smaller than the wavelength of the exciting electromagnetic field. Here we develop a theory of resonant absorption of microwave radiation in two-dimensional electronic systems in the form of a disk when the radiation wavelength is less than or comparable to the radius of the disk. The problem is solved in a self-consistent approximation. We use the Drude model for conductivity of the system. The absorption peak in the dependence of the absorption power on the frequency corresponds to the excitation of plasma waves, while the linewidth of the peak corresponds to the plasmon damping. We find analytical corrections due to retardation for the fundamental (dipole) and the axisymmetric (quadrupole) modes. The frequency of the axisymmetric mode depends on the electromagnetic retardation rather weakly since the plasma oscillations have zero dipole moment [2]. The damping of the modes strongly depend on the ratio between the radiative and collisional decay. In the absence of collisions, the radiative decay rate of axisymmetric mode is mainly determined by the quadrupole moment for the mode. However, even for small retardation the linewidth of the resonances is not merely the sum of two decays since it contain additional terms. This work was supported by the Russian Science Foundation (project no. 16-12-10411).