Electron interactions in an antidot in the integer quantum Hall regime

Abstract

A quantum antidot, a submicron depletion region in a two-dimensional electron system, has been actively studied in the past two decades, providing a powerful tool for understanding quantum Hall systems. In a perpendicular magnetic field, electrons form bound states around the antidot. Aharonov-Bohm resonances through such bound states have been experimentally studied, showing interesting phenomena such as Coulomb charging, h/2e oscillations, spectator modes, signatures of electron interactions in the line shape, Kondo effect, etc. None of them can be explained by a simple noninteracting electron approach. Theoretical models for the above observations have been developed recently, such as a capacitive-interaction model for explaining the h/2e oscillations and the Kondo effect, numerical prediction of a hole maximum-density-droplet antidot ground state, and spin density-functional theory for investigating the compressibility of antidot edges. In this review, we summarize such experimental and theoretical works on electron interactions in antidots.

Scanning gate spectroscopy of transport across a quantum Hall nano-island

“…The QHI is thus in the quantum limit of CB defined by k B T E e 2 /C ∼ 1.6 meV obtained from figure 3(b) [39], which justifies the 1/T temperature dependence found previously in [35]. Assuming that the Coulomb excited states emerge as a consequence of circular confinement, we can determine the average of the derivative of the confining potential dU/dr using the relation [14,15,17] E =hv/r = |dU/dr |h/(e r B),…”

“…In particular, McClure et al [7] used interference checkerboard patterns generated in a Fabry-Pérot geometry to determine the edge state velocity in the quantum Hall regime. In the other extreme, σ 2e 2 / h, quantum Hall islands (QHIs) created by patterned quantum dots [13] or antidots [14][15][16][17][18] led to the observation of a fractional electric charge [18][19][20] and to the characterization of localized states' confining potential [15][16][17].…”

Capacitive interaction model for Aharonov-Bohm effects of a quantum Hall antidot

“…The expression of δQ α has the compensation of gate charge Q G α , in addition to the charge accumulation due to δB in eÑ α ; see Eq. (2). From Eq.…”

Imaging backscattering through impurity-induced antidots in quantum Hall constrictions

“…6,9-11 Indeed, both mechanisms can be expected to play a role in artificial AD devices, as highlighted by a number of investigations in past years reviewed in Ref. 12 and by recent experiments specifically designed to address this issue. 13,14 In our experiment, the SGM tip modulates the transport through random localized states, inducing a suitable coupling between them and the extended edge modes.…”