Resonance patterns of an antidot cluster: From classical to quantum ballistics

Abstract

We explain the experimentally observed Aharonov-Bohm ͑AB͒ resonance patterns of an antidot cluster by means of quantum and classical simulations and Feynman path integral theory. We demonstrate that the observed behavior of the AB period signals the crossover from a low B regime which can be understood in terms of electrons following classical orbits to an inherently quantum high B regime where this classical picture and semiclassical theories based on it do not apply. ͓S0163-1829͑97͒05036-4͔

Electron interactions in an antidot in the integer quantum Hall regime

“…In experiments, Aharonov-Bohm oscillations with an antidot were first observed by Smith and his coworkers [9]. Since then, the Aharonov-Bohm effect has been intensively investigated experimentally [1,2,17,18,19,20,21,22,23,24,25,26] in the integer quantum Hall regime and revealed some interesting features in the period, the line shape, and the temperature or bias dependence of the Aharonov-Bohm conductance oscillations that cannot be explained within the noninteracting model.…”

“…1). The localized orbits around a single antidot [1,2,17,18,19,20,21,22,23,24,25,26] and around an antidot molecule [27,28,29] have been studied in the integer quantum Hall regime by measuring Aharonov-Bohm oscillations of conductance, which occur when the localized orbits couple to extended edge channels along the boundary of the 2DEG. The antidot has also been investigated in the fractional quantum Hall regime experimentally [4,11,30,31,32,33,34,35] and theoretically [36,37,38,39,40,41] to understand quasiparticle tunneling, charge and statistics, composite fermions, chiral Luttinger liquids, and non-Abelian statistics of the fractional quantum Hall 5/2 state.…”

Magnetoconductance of a quantum wire with several antidots: A transfer-matrix study

“…Recently, we became aware of two recent works on the magnetotransport of the same antidot system 16,17 These studies use discrete lattice models to implement quantum simulations, and they are able to reproduce the main features related to the experiment. In particular, the effect of disorder has been investigated in Ref.…”

Classical orbit bifurcation and quantum interference in mesoscopic magnetoconductance

“…2), however, cannot be understood within this simple picture. They have been qualitatively reproduced in a quantum calculation by Kirczenov et al [21]. Our objective is to decide if these dislocations and the variation of the spacings between the maxima can be understood semiclassically (which was doubted in Refs.…”

“…These and two circular antidot gates are contacted individually. Details about the device are presented in [19][20][21] and the references cited therein. All measurements were taken at T ≈ 100 mK using standard low-excitation AC techniques.…”