de Haas-van Alphen and Aharonov-Bohm-type Persistent Current Oscillations in Singly Connected Quantum Dots

We discuss the effect of edge states on the de Haas-van Alphen oscillations in a small singly connected sample made of a 2D electron gas in the quantum-Hall-effect regime. We find that because of the "ring topology" of these states the magnetization oscillates with a period $\frac{\mathrm{hc}}{e}$ in the total flux through the system. This oscillation survives a substantial amount of disorder. Its detectability is discussed and a related oscillation in the longitudinal and transverse resistances suggested.

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