We report the direct measurement of the persistent current carried by a single electron by means of magnetization experiments on self-assembled InAs=GaAs quantum rings. We measured the first Aharonov-Bohm oscillation at a field of 14 T, in perfect agreement with our model based on the structural properties determined by cross-sectional scanning tunneling microscopy measurements. The observed oscillation magnitude of the magnetic moment per electron is remarkably large for the topology of our nanostructures, which are singly connected and exhibit a pronounced shape asymmetry. DOI: 10.1103/PhysRevLett.99.146808 PACS numbers: 73.21.La, 73.23.Ra, 78.67.Hc In quantum mechanics, particular attention is paid to phenomena occurring due to the phase coherence of charge carriers in doubly connected (ring) topologies. Electrons confined to a submicron ring manifest a topologically determined quantum-interference phenomenon, known as the Aharonov-Bohm (AB) effect [1], as a result of the oscillatory behavior of their energy levels as a function of an applied magnetic field. This behavior is usually associated with the occurrence of oscillatory persistent currents in the ring [2 -4]. Experimental evidence for AB oscillations has been detected in the mesoscopic regime in metallic [5,6] and semiconducting [7,8] rings, containing many electrons. We address the occurrence of the AB effect in defect-free self-assembled semiconductor nanostructures [9][10][11][12][13]. The ability to fill nanostructures with only a few (1-2) electrons offers the unique possibility to detect magnetic field induced oscillations in the persistent current carried by single electron states. We report the first direct measurement by means of ultrasensitive magnetization experiments of the oscillatory persistent current carried by a single electron in self-assembled InAs/GaAs ''volcanolike'' nanostructures. Remarkably, this single electron current occurs even in the absence of an opening [14] in our nanostructures, which is required for the AB effect in the standard treatment [1]. The magnetic field at which the first oscillation in the magnetic moment arises is much higher than expected from the diameter of the quantum rings as determined by atomic force microscopy [13]. However, the experiments are in good agreement with a model based on the structural parameters as determined with cross-sectional scanning tunneling microscopy (XSTM) measurements.The persistent current was determined via the magnetic moment of electrons in a highly homogeneous ensemble of InAs self-assembled nanostructures. The sample was grown by molecular beam epitaxy and contains 29 mutually decoupled periods [ Fig. 1(a)] [15]. Each period consists of a nanostructured InAs layer, between two 24 nm GaAs layers, and a 2 nm doped (7 10 16 cm ÿ3 Si) GaAs layer that provides electrons to the InAs nanostructures. We used a one-dimensional Poisson solver [16] to estimate the average number of electrons per nanostructure to be about 1.5. Considering the two possible spin orientations we ...

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We present torque-magnetometry measurements of a bilayer two-dimensional electron gas (2DEG) with an inter-well barrier thin enough to enable a strong coupling between the quantum wells. We observe magnetization steps related to symmetric–anti-symmetric (SAS) transitions. Increasing the in-plane magnetic field leads to a reduction of the SAS splitting. Surprisingly, the heights of the magnetization steps related to Landau-level transitions are reduced relative to those measured for single-layer 2DEGs, suggesting that an in-plane magnetization component plays a role. Finally, at total filling factor ν=4, we observe an unidentified magnetization peak superposed upon the Landau-level step.