A new network model for the integer quantum Hall effect

Oswald, Josef; Homer, A.

doi:10.1016/s1386-9477(01)00165-5

Cited by 12 publications

(12 citation statements)

References 19 publications

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“…By using a representative 2-dimensional Cosine potential modulation, a result by Büttiker [114] for the saddle point problem at high magnetic fields was transformed into the back scattering function P (∆ν), which is used for the nodes of the network according to Ref. [85]. One main extension as compared to Ref.…”

Section: Discussionmentioning

confidence: 99%

“…On this basis it is possible to model the shape the sample by shaping the lateral carrier distribution. By doing so, it has been shown for the first time, that the influence of sample geometry (such as contact arms) and carrier density inhomogeneities (like introduced by gate electrodes) can be successfully addressed on the basis of a network model in full agreement with experimental results [85,90]. While the main task of [85] was to present the technical aspects and examples for applications of the network model, the main purpose of this paper is to provide the theoretical and physical back ground.…”

Section: Introductionmentioning

confidence: 99%

“…By doing so, it has been shown for the first time, that the influence of sample geometry (such as contact arms) and carrier density inhomogeneities (like introduced by gate electrodes) can be successfully addressed on the basis of a network model in full agreement with experimental results [85,90]. While the main task of [85] was to present the technical aspects and examples for applications of the network model, the main purpose of this paper is to provide the theoretical and physical back ground. Since the network model is based on the idea of tunneling between magnetic bound states at saddles of the interior potential landscape, a systematic study of this tunneling process will be presented.…”

Section: Introductionmentioning

confidence: 99%

“…In Fig.1 a single node of the network is shown, which transmits potentials from the incoming to the outgoing channels. The transmitted potentials of the outgoing channels as a function of P is calculated as follows [85]:…”

Section: Introductionmentioning

confidence: 99%

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Gate Controlled Separation of Edge and Bulk Current Transport in the Quantum Hall Effect Regime

Oswald

Uiberacker

2010

J Low Temp Phys

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In preceding papers a Landauer-Büttiker type representation of bulk current transport has been successfully used for the numerical simulation of the magneto transport of 2-dimensional electron systems in the high magnetic field regime. In this paper it is demonstrated, that this representation is in full agreement with a treatment of the bulk current transport as a tunneling process between magnetic bound states. Additionally we find a correspondence between our network representation and the bulk current picture in terms of mixed phases mapped on a checkerboard: At half filled Landau level (LL) coupled droplets of a quantum Hall (QH) liquid phase and coupled droplets of an insulator phase phase exist at the same time, with each of them occupying half of the sample area. Removing a single electron from to such a QH liquid droplet at half filling completes the QH transition to the next higher QH plateau. Adding a single electron to such a droplet at half filling completes the QH transition to the previous lower QH plateau. As a consequence, the sharpness of the QH plateau transitions on the magnetic field axis depends on the typical size of the droplets, which can be understood as a measure of the disorder in the sample.Concerning modeling of quantum transport, one of the very first attempts can be attributed to R.Landauer [111,112]. A major step forward was achieved by M. Büttiker by introducing the so-called Landauer-Büttiker (LB) formalism and the EC-picture of the QHE[1]. For modeling quantum transport and localzation in the bulk, mainly network models on the basis of the Chalker Coddington (CC) network [113] are used. However, a model, which generates data in terms of voltages and resistances, which would allow a direct comparison which experimental data for realistically shaped samples had not been developed so far. In order to do so, an approach to combine EC transport and bulk transport has been made some time ago [68,71]. Subsequently that model has been expanded to a network [85], which is also the subject of this paper. Although the basic idea of our network is common with the basic idea of the CC network, our handling of the nodes is substantially different: In contrast to a CC network our network does not use a transfer matrix for amplitudes and phases. We use transmission by tunneling, but incorporating the effect of tunneling according to the LB formalism. The nodes are described by a back scattering function P , which is the ration of reflection and transmission coefficient R/T .

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gate Controlled Separation of Edge and Bulk Current Transport in the Quantum Hall Effect Regime

Oswald

Uiberacker

2010

J Low Temp Phys

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“…The local carriers density enters the nodes via the function P, which depends locally on Ep -ELL, with Ep the Fermi energy and ELL the Landau level (LL) center. Therefore P is in general different for different nodes and each involved Landau band is represented by a complete network 3 . In this way contact leads, gate electrodes and the effect of inhomogeneities can be a) Fig.…”

Section: Modeling Of Magneto-transportmentioning

confidence: 99%

Circuit Type Simulations of Magneto-Transport in the Quantum Hall Effect Regime

Oswald

2007

Int. J. Mod. Phys. B

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A Landauer-Biittiker type representation of bulk current transport is used for the numerical simulation of the magneto-transport of 2-dimensional electron systems. It allows us to build up a network model, which describes the effect of non-equilibrium currents injected via metallic contacts like in real experiments. Our model suggests a peak-like contribution of de-localized states to the bulk conductance, which appears embedded in the density of states (DOS) of the Landau levels (LLs). In contrast, the localization picture of the quantum Hall effect suggests almost sharp boundaries between localized and de-localized states and does not explicitly map out their contribution to the bulk conductance. Most recent experiments by B.A. Piot et al. suggest a similar peak-like contribution of de-localized states near the center of the LLs. Our simulation results for the same parameter values as determined by Piot et al reproduce their experimental data very well.

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