Quantized periodic orbits in large antidot arrays

Weiss, Dieter; Richter, Klaus; Menschig, A.; Bergmann, Ralf B.; Schweizer, H.; Klitzing, K. von; Weimann, G.

doi:10.1103/physrevlett.70.4118

Cited by 286 publications

(193 citation statements)

References 18 publications

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“…3(a) shows a device where both oscillations can be seen. It has been postulated that this periodicity is related to the radius R of a stable Aharonov-Bohm ring by the relationship 19,20 ∆B ⊥ ≈ h/πeR 2 . Fourier Transforming confirms the periodicity of these oscillations, and yields a radius R ≈ 500nm, well in line with the calculated average distance between background impurities with which conduction electrons could interact.…”

Section: Pacs Numbersmentioning

confidence: 99%

Low temperature transport in undoped mesoscopic structures

Sarkozy

Gupta

Siegert

et al. 2009

Applied Physics Letters

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Using high quality undoped GaAs/AlGaAs heterostructures with optically patterned insulation between two layers of gates, it is possible to investigate very low density mesoscopic regions where the number of impurities is well quantified. Signature appearances of the scattering length scale arise in confined two dimensional regions, where the zero-bias anomaly (ZBA) is also observed. These results explicitly outline the molecular beam epitaxy growth parameters necessary to obtain ultra low density large two dimensional regions as well as clean reproducible mesoscopic devices. PACS numbers:With potential applications to quantum computation as well as innate interest in fundamental physics such as localization and Quantum Hall effects, significant resources have been devoted to the study of electronelectron interactions 1,2 . Regardless of dimensionality, the relative importance of interactions increases with decreasing carrier concentration, providing substantial impetus for the study of low density systems. It is instructive to quantitatively analyze the requirements to ensure that phenomena observed are intrinsic to interactions in the two dimensional electron/hole gas (2DEG/2DHG), and not merely manifestations of impurity effects or disorder based localization. The cleanliness of the 2D gas at low densities is also crucial in studying pinch-off regions in one-dimensional (1D) channels and very low conductance characterization of zero-dimensional (0D) quantum dots, although this point is not often emphasized.

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Section: Pacs Numbersmentioning

confidence: 99%

Low temperature transport in undoped mesoscopic structures

Sarkozy

Gupta

Siegert

et al. 2009

Applied Physics Letters

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“…15,16 Experiments at a lower temperature T Ϸ 0.4 K reveal additional quantum oscillations superimposed on the classical peaks. 17 These quantum oscillations can be attributed to unstable periodic orbits of the electrons in the confinement potential by a semiclassical theory for the conductivity. 18,19 Generic systems have a phase space which is neither completely chaotic nor integrable but contains a mixture of regular islands and chaotic regions.…”

Section: Introductionmentioning

confidence: 99%

“…Examples are orbital magnetism in ballistic microstructures 14 and transport through antidot superlattices. [15][16][17][18][19] The latter consists of a two-dimensional electron gas at the interface of a GaAs/ Al x Ga 1−x As heterostructure into which a periodic array of holes is drilled. The effective potential is a periodic structure of high potential peaks, and if the potential is steep it may be considered as an experimental realization of the Sinai billiard.…”

Section: Introductionmentioning

confidence: 99%

Universal quantum signature of mixed dynamics in antidot lattices

2005

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We investigate phase coherent ballistic transport through antidot lattices in the generic case where the classical phase space has both regular and chaotic components. It is shown that the conductivity fluctuations have a non-Gaussian distribution, and that their moments have a power-law dependence on a semiclassical parameter, with fractional exponents. These exponents are obtained from bifurcating periodic orbits in the semiclassical approximation. They are universal in situations where sufficiently long orbits contribute.

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“…Over the last two decades much attention has been paid to the physics of periodic structures imposed onto the plane of the two-dimensional electron system (2DES), and particularly to the quantum interference phenomena yielded by applied magnetic fields and the way in which they modulate their energy structure and related transport properties [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Prompted by the advantages of the two-dimensional antidot lattices routinely fabricated nowadays, a new structure was proposed recently which seems to offer many attractive features in terms of flexibility, scalability, and operation in the pursuit of achieving solid-state quantum computation.…”

Section: Introductionmentioning

confidence: 99%

Magnetic modulation of the tunnelling between defect states in antidot superlattices

Movilla¹,

Planelles²

2012

J. Phys.: Condens. Matter

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Abstract. We show theoretically that the tunneling between properly designed defects in periodic antidot lattices can be strongly modulated by applied magnetic fields. Further, transport channels made up of linear arrangements of tunnel-coupled defects can accomodate Aharonov-Bohm cages, suggesting a magnetic control of the transport through the system. Evidence supporting an unusual robustness of the caging effect against electron-electron interactions is also provided.

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Quantized periodic orbits in large antidot arrays

Cited by 286 publications

References 18 publications

Low temperature transport in undoped mesoscopic structures

Low temperature transport in undoped mesoscopic structures

Universal quantum signature of mixed dynamics in antidot lattices

Magnetic modulation of the tunnelling between defect states in antidot superlattices

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