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 electro n gas with an antidot in a strong magnetic field, r(c) less than or eq ual 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 co nfinement potential U similar to 1/r(2). The edge states localized at the antidot boundary result in an Aharonov-Bohm-type oscillatory depen dence of the magnetization as a function of the magnetic field flux th rough 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 os cillations 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 th e appearance of a beating pattern in the Aharonov-Bohm oscillations. T he role of temperature in suppressing the oscillatory contribution due to higher edge states is analyzed. Rapid oscillations of the magnetiz ation 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 appe arance of a manifold of nonequidistant frequencies in the magneto-opti cal-absorption spectrum, due to transitions between electronic edge st ates localized near the antidot boundary, is predicted.