EDGE STATES, AHARONOV-BOHM OSCILLATIONS, AND THERMODYNAMIC AND SPECTRAL PROPERTIES IN A 2-DIMENSIONAL ELECTRON-GAS WITH ANTIDOT

The thermodynamic and spectral properties of a two-dimensional electron gas with an antidot in a strong magnetic field, r(c) less than or equal to r(0), where r(c) is the cyclotron radius and to is the antidot effective radius, are studied via a solvable model with the antidot confinement potential U similar to 1/r(2). The edge states localized at the antidot boundary result in an Aharonov-Bohm-type oscillatory dependence of the magnetization as a function of the magnetic field flux through the antidot. These oscillations are superimposed on the de Haas-van Alphen oscillations. In the strong-field limit, <(h)over bar omega(c)> similar to epsilon(F), where omega(c) is the cyclotron frequency and Ep is the Fermi energy, the amplitude of the Aharonov-Bohm-type oscillations bf the magnetization due to the contribution of the lowest edge state is similar to mu(B)k(F)r(c) (mu(B) is the Bohr magneton and k(F) is the Fermi wave vector). When the magnetic field is decreased; higher edge states can contribute to the magnetization, leading to the appearance of a beating pattern in the Aharonov-Bohm oscillations. The role of temperature in suppressing the oscillatory contribution due to higher edge states is analyzed. Rapid oscillations of the magnetization as a function of the Aharonov-Bohm flux, occurring on a scale of a small fraction of the flux quantum hc/e, are demonstrated. The appearance of a manifold of nonequidistant frequencies in the magneto-optical-absorption spectrum, due to transitions between electronic edge states localized near the antidot boundary, is predicted.