A novel transport model for the metal-to-insulator transition in quasi-three-dimensional wide quantum wells

Homer, A.; Ganitzer, P.; Span, G.; Oswald, Josef

doi:10.1006/spmi.1998.0636

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…The wide parabolic quantum wells at large filling factors had been created by the Narrow Gap Semiconductor PbTe and instead of quantum Hall plateaus magneto-resistance fluctuations have been found at temperatures below 100 mK and at small current of the order of a few nA. The temperature and current dependence of these fluctuations that also appeared in a so-called non-local contact configuration even at macroscopic sample size [30] indicated the involvement of quantum channels [31]. In this context, the relations between the potentials of channels that meet at non-equilibrium situation seem to be valid also for that regime far from the standard quantum Hall regime in the clean two-dimensional case.…”

Section: Discussionmentioning

confidence: 98%

Linking Non-equilibrium Transport with the Many Particle Fermi Sea in the Quantum Hall Regime

Oswald¹

2016

Research Advances in Quantum Dynamics

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Tνe communξcatξon of tνe electron system wξtν tνe outsξde world at low excξtatξon transport experξments νappens by excνangξng electrons at tνe Fermξ level. We argue tνat tνe locatξons wνere tνξs ξs possξble ξn tνe quantum Hall effect regξme are tνe so-called edge cνannels. We explaξn tνat tνese cνannels can be understood as a more general representatξon of tνe many-partξcle quantum Hall QH system close to equξlξbrξum tνat allows descrξbξng transport due to non-equξlξbrξum on a very fundamental level. "ased on fundamental prξncξples of quantum pνysξcs, a transfer matrξx formulatξon for tνe local non-equξlξbrξum electrocνemξcal potentξal ξn a network of ξnterconnected dξrected quantum cνannels can be used to solve tνe lateral dξstrξbutξon of tνe non-equξlξbrξum excξtatξon potentξals. Instead of usξng tνe Landauer formula or otνer tools lξke tνe Kubo formula for addressξng conductance's just a transfer matrξx formulatξon for tνe transfer of electrocνemξcal potentξals ξs used to fξnd tνe self-consξstent lateral dξstrξbutξon of tνe non-equξlξbrξum electrocνemξcal potentξals. Currents and potentξals tνat are measured at contacts are only calculated as a post-processξng step rξgνt at tνe contacts, and tνey allow calculatξng all tνe resξstances and conductance's lξke known from QH experξ-ments. Tνe ξnterplay between transport and tνe many-partξcle system ξs of general ξnterest wνen dealξng wξtν accessξng ξnformatξon about quantum systems. Our approacν allows modelξng electron systems ξn tνe QH regξme for realξstξc sample geometrξes, ξncludξng ξnνomogeneξtξes, lξke present ξn real samples or tνat are forced by gate electrodes as well as tνe random dξsorder potentξal. We combξne our network model for transport wξtν tνe Hartree Fock metνod tνat allows tνe ξnclusξon of realξstξc screenξng effects as well as tνe magnetξc fξeld-dependent enνanced g-factor.Keywords: network model, quantum Hall effect, magneto-transport, conductance quantξzatξon, non-equξlξbrξum transport, excνange ξnteractξon, Hartree-Fock approxξ-matξon, many partξcle quantum system © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. . IntroductionEven more tνan years after dξscoverξng tνe ξnteger quantum Hall effect [ ], ξt ξs stξll a lξvely dξscussed topξc at many conferences. In tνe quantum Hall QH regξme, tνe many-partξcle quantum nature of tνe electron system can be studξed from mesoscopξc to nearly macroscopξc lengtν scales. Tνe cνallenge ξn modelξng electron transport ξn tνξs regξme ξs tνat tνe manypartξcle quantum states of tνe electron system exξst as statξonary states at tνermal equξlξbrξ-um, wνξle transport ξs drξven by ξntroducξng devξatξons from tνe equξlξbrξum. Even for tνe QH experξments tνat νappen close to tνermal equξlξbrξum, a dξrect modelξng of current flow does not fξt tνe world of statξona...

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Section: Discussionmentioning

confidence: 98%

Linking Non-equilibrium Transport with the Many Particle Fermi Sea in the Quantum Hall Regime

Oswald¹

2016

Research Advances in Quantum Dynamics

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Circuit type simulations of magneto-transport in the quantum Hall effect regime

Oswald¹,

Oswald²

2006

J. Phys.: Condens. Matter

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Localization in the bulk is one of the most important ingredients for the theory of the quantum Hall effect and much attention has been paid to this topic for more than two decades. However, less effort has been made to model the current transport itself. Network models are frequently used in this context and an answer should be given as to whether these are also suitable for modelling the lateral distribution of experimentally excited currents and voltages in the quantum Hall effect (QHE) regime. The term ‘network model’ is of more general meaning and therefore the term ‘circuit type simulations’ should be used instead for expressing this kind of modelling. 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 two-dimensional electron systems in the high magnetic field regime. This approach allows us to build up a network model, which describes correctly the effect of non-equilibrium currents injected via metallic contacts as in real experiments. In this context we suggest a network model, which serves as a circuit type representation of magneto-transport. It is demonstrated that it is in full agreement with a treatment of bulk current transport as a quantum tunnelling process between magnetic bound states, which exist in the high magnetic field regime. Additionally, we find a striking correspondence between our network representation and the bulk current picture in terms of mixed phases mapped on a chequerboard: at half filled Landau level (LL) coupled droplets of a quantum Hall (QH) liquid phase and coupled droplets of an insulator phase exist at the same time, with each of them occupying half of the bulk area. Removing a single electron from such a QH liquid droplet at half filling completes the QH plateau transition to the next higher QH plateau, while adding a single electron to such a droplet at half filling completes the QH plateau 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. We furthermore demonstrate that our model can also be used as a theoretical concept for discretization of a long range random potential on a regular grid. We also find a correspondence between our model and the so called localization picture of the QH plateau transitions. Alternative approaches like the Chalker–Coddington (CC) network as the coherent counterpart and a resistor network as the classical counterpart are discussed in comparison with our network approach. On the one hand the CC model was originally developed to treat the localization problem; on the other hand it also assigns currents to channels, and in this context the CC model will be discussed in the context of circuit type simulations as well. Finally, we compare our simulation results to results obtained on the basis of an adapted lattice model by Ando (1...

show abstract

A novel transport model for the metal-to-insulator transition in quasi-three-dimensional wide quantum wells

Cited by 2 publications

References 6 publications

Linking Non-equilibrium Transport with the Many Particle Fermi Sea in the Quantum Hall Regime

Linking Non-equilibrium Transport with the Many Particle Fermi Sea in the Quantum Hall Regime

Circuit type simulations of magneto-transport in the quantum Hall effect regime

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