We have investigated experimentally an open semiconductor system in which electron confinement around an obstacle is obtained using a magnetic field. The magnetic field gives rise to Landau levels, and each associated edge state circulates around the obstacle, forming a set of quantized states. Tunable constrictions are fabricated by using a technique which enables us to control transport in and out of these states, producing Aharonov-Bohm oscillations as the magnetic field is swept. Surprisingly, a strong extra oscillation with the same h /e frequency develops, phase shifted by m. so that the frequency appears to have doubled. We explain these results in terms of charging of isolated circulating edge states.In a metal or semiconductor, the isolation of electrons in a potential well leads to charging efFects because electrons are indivisible. For example, at low applied bias, transport through a cavity via tunnel barriers on either side is blocked when extra energy is required to add an electron, a phenomenon known as Coulomb blockade (CB). For a semiconductor in a magnetic field, it is possible to confine the highest Landau levels (LL's) within the cavity while allowing the lowest ones to extend into the leads, by reducing the height of the tunnel barriers below the Fermi energy EF. The associated edge states can form closed paths and thus give rise to Aharonov-Bohm (AB) oscillations. ' Recently, combined AB and CB oscillations were found, indicating that the confined LL s can charge even when there are also extended states in the cavity.The confinement is usually produced by a physical barrier, such as the edge of a metal sample or the depletion region in a semiconductor structure. In contrast, we have made a completely open (two-dimensional) system, in which confinement around a microscopic obstacle is provided solely by a perpendicular magnetic field B. A11 LL's extend into the bulk, but some edge states (shown schematically as solid lines in the insets, Fig 1) for.m c1osed paths around the obstacle. If the path length is small and the temperature low, these paths are phase coherent. The accumulated phase depends on the circumference, wavelength, and the AB efFect which causes a change of 2n for each increase of h/e in the flux enclosed. Thus, a ladder of allowed single-particle (Sp) states forms. The states are also confined to an LL, which rises in energy as it approaches the edge, so states enclosing less area have higher energy and shorter wavelength. Changing B sweeps the states, each containing one electron, through EF, causing the net charge near the obstacle to osci11ate. In contrast, in electrostaticallyconfined systems the charge is independent of B. It might be expected that such excess charge would not occur, as electrons within the same, u n confine, LL would move to compensate. However, we observe a phenomenon which provides evidence for such charging, showing that edge states encircling the obstacle are unable to move sufFiciently to screen the charge because they consist of a series of quantiz...
We have used a torque magnetometer to measure de Haas - van Alphen oscillations in the magnetization of two-dimensional electrons in GaAs/AlGaAs heterostructures and multiple-quantum-well systems for temperatures ranging from 0.125 K to 4.2 K and in magnetic fields of up to 15 T. Our results indicate that for high magnetic fields the density of states can be described by a series of Lorentzian-broadened Landau levels with a broadening that is independent of the magnetic field, B, and Landau level index, n. However, at low magnetic fields the Lorentzian-broadened density of states becomes indistinguishable from a Gaussian one with a broadening that is proportional to . The high-field behaviour of the Landau level line-shape is shown to differ appreciably from the low-field case as reported by other workers using both magnetization and other experimental methods. The reliability of this and other experimental techniques is discussed.
We have studied Coulomb-blockade effects through a quantum dot formed by an impurity potential near a two-dimensional electron gas (2DEG) defined at a GaAs/Al"Ga& As heterojunction. We have compared the energy-level spacing within the quantum dot obtained by two methods: from the magnetic-field-induced gate-voltage shifts of the conductance peaks, and by applying a source-drain voltage across the dot. The use of the latter method in a magnetic field allows us to distinguish between charging and confinement effects, although the structure in the nonlinear excitation spectrum requires careful interpretation. As the number of electrons in the dot decreases, the barriers connecting the dot to the 2DEG thicken and the area of the dot decreases, giving rise to an increased charging energy that has been measured directly. After the final Coulomb-blockade conductance peak, we estimate that there are 20 electrons in the dot.
We have used MBE regrowth technology lo produce a non-planar 2DEG at a GaAslAlCaAs heterojunction grown over an etched facet. By applying a uniform magnetic field to this smcfure we obtain a spatially vqining field component normal to the 2DEG. When the magnetic field is applied in the plane of the subsme, the resistance measured from one side of the facet io the oiher is found to be quantized at approximately the quantum Hall plateaux.Rotating the plane of the sample with respect to the magnetic field allows us to investigate edge state propagation and reflection in the different regions of the sample. By making the appropriate four-rerminal resisfance measurement we can directly determine the filling factor on fhe facet. In particular we study lhe novel situation where the hansvene field component changes sign on the facet and the cyclohon orbifs rotate in the opposite sense to those on the planar region.
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