Theory of electromagnetic response and collective excitations in antidots.

Abstract

The theory of collective excitations in a single antidot and in a system of interacting antidots is presented. The problem is solved within the framework of classical electrodynamics neglecting the nonlocal and retardation effects. It is shown that the spectrum of collective excitations in a single antidot consists of two branches. The first mode coincides with the single-particle cyclotron resonance \ensuremath{\omega}=${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$; the second one is the edge magnetoplasmon (EMP) mode. The EMP mode has the vanishing damping (in the collisionless approximation) only at \ensuremath{\omega}${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$. At \ensuremath{\omega}>${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ it decays on account of emission of two-dimensional (2D) bulk magnetoplasmons to the surrounding 2D medium. The induced electric potential and charge density of the EMP mode have the form of outgoing cylindrical waves at \ensuremath{\omega}>${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$. As a consequence, the interantidot interaction cannot be neglected in an array of antidots at \ensuremath{\omega}>${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$. Collective excitations in an array of interacting antidots are considered in the modified-dipole and effective-medium approximations. The results obtained explain the main features of the antidot excitation spectrum observed in recent experiments.