Aharonov-Bohm electron interferometer in the integer quantum Hall regime

Abstract

We report experiments on a quantum electron interferometer fabricated from high mobility, low density AlGaAs/GaAs heterostructure material. In this device, a nearly circular electron island is defined by four front gates deposited in etched trenches. The island is separated from the 2D electron bulk by two nearly open constrictions. In the quantum Hall regime, two counterpropagating edge channels are coupled by tunneling in the constrictions, thus forming a closed electron interference path. For several fixed front gate voltages, we observe periodic Aharonov-Bohm interference oscillations in four-terminal resistance as a function of the enclosed flux. The oscillation period B ∆ gives the area of the interference path S via the quantization condition. We experimentally determine the dependence of S on the front gate voltage, and find that the Aharonov-Bohm quantization condition does not require significant corrections due to the confining potential. These results can be interpreted as a constant integrated compressibility of the island with respect to the front gates. We also analyze experimental results using two classical electrostatics models: one modeling the 2D electron density due to depletion from an etch trench, and another modeling the gate voltage dependence of the electron density profile in the island.

Anyons and Lowest Landau Level Anyons

“…Fractional charges have already been seen in shot noise FQHE experiments [56], but the nontrivial statistical nature of the charge carriers in FQHE edge currents has so far remained elusive in experiments which rely mainly on Aharonov-Bohm interferometry [28]. Note also a recent proposal for the possible experimental tracking of abelian and nonabelian anyonic statistics in Mach-Zehnder interferometers [57].…”

“…The quasiparticles can propagate quantum-coherently in chiral edge channels, and constructively or destructively interfere. Unlike electrons, the interference condition for Laughlin quasiparticles has a non-vanishing statistical contribution which might be observed experimentally [28].…”

Correlated time-dependent transport through a two-dimensional quantum structure

“…[5][6][7] Dynamical effects have been studied in open or closed quantum rings. Propagation of electron pulses in rings of finite width has been investigated by Chaves et al 8 and by Thorgilsson et al 9 within scattering theory, and nonadiabatic current generation in a closed finite quantum ring in an external magnetic field has been studied by integrating the Liouville-von Neumann equation for the density operator in time.…”

Time-dependent transport in Aharonov–Bohm interferometers

“…To describe electron transport in QH interferometers, the singleparticle edge-state approach [9] is common, but neglects the dependence of the area enclosed by the current-carrying channels on the magnetic field [10], as well as on the channel widths. However, as shown explicitly below, the actual paths can be obtained considering the full manybody electrostatics, which yields the spatial distribution of compressible and incompressible strips [11].The essential features of the observed AB oscillations in QH interferometers have been explained using edge-channel simulations and Coulomb interactions at the classical (Hartree) level [4,12,13]. However, a complete theoretical picture of the observed phenomenon is still missing [6,14].…”

“…The essential features of the observed AB oscillations in QH interferometers have been explained using edge-channel simulations and Coulomb interactions at the classical (Hartree) level [4,12,13]. However, a complete theoretical picture of the observed phenomenon is still missing [6,14].…”