Edge states, Aharonov-Bohm oscillations, and thermodynamic and spectral properties in a two-dimensional electron gas with an antidot.

Abstract

The thermodynamic and spectral properties of a two-dimensional electron gas with an antidot in a strong magnetic field, ${\mathit{r}}_{\mathit{c}}$\ensuremath{\le}${\mathit{r}}_{0}$, where ${\mathit{r}}_{\mathit{c}}$ is the cyclotron radius and ${\mathit{r}}_{0}$ is the antidot effective radius, are studied via a solvable model with the antidot confinement potential U\ensuremath{\sim}1/${\mathit{r}}^{2}$. 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, \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$\ensuremath{\sim}${\mathrm{\ensuremath{\epsilon}}}_{\mathit{F}}$, where ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ is the cyclotron frequency and ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{F}}$ is the Fermi energy, the amplitude of the Aharonov-Bohm-type oscillations of the magnetization due to the contribution of the lowest edge state is \ensuremath{\sim}${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$${\mathit{k}}_{\mathit{F}}$${\mathit{r}}_{\mathit{c}}$ (${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ is the Bohr magneton and ${\mathit{k}}_{\mathit{F}}$ 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 non- equidistant frequencies in the magneto-optical-absorption spectrum, due to transitions between electronic edge states localized near the antidot boundary, is predicted.