A Numerical Study of Non-local Magneto Transport Effects in Quantum Hall Device Structures

Oswald, Josef; Uiberacker, C.; Stecher, Christian

doi:10.1088/1742-6596/334/1/012020

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…This version of a QH network has been demonstrated to be quite successful for a variety of transport simulations of realistic sample structures and experimental setups. 28,33,34 The backscattering function can be rewritten using the filling factor formulation…”

Section: B the Non-equilibrium Network Model (Nnm)mentioning

confidence: 99%

Manifestation of many-body interactions in the integer quantum Hall effect regime

Oswald

Römer

2017

Phys. Rev. B

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We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall (IQH) regime in terms of many-body physics at higher Landau levels (LL). The results exhibit a strong tendency to avoid the simultaneous existence of partly filled spin-up and spin-down LLs. Partly filled LLs appear as a mixture of coexisting regions of full and empty LLs. We obtain edge stripes with approximately constant filling factor ν close to half-odd filling at the boundaries between the regions of full and empty LLs, which we explain in terms of the g-factor enhancement as a function of a locally varying ν across the compressible stripes.The many-particle interactions follow a behaviour as it would result from applying Hund's rule for the occupation of the spin split LLs. The screening of the disorder and edge potential appears significantly reduced as compared to screening based on a Thomas-Fermi approximation. For addressing carrier transport, we use a non-equilibrium network model (NNM) that handles the lateral distribution of the experimentally injected non-equilibrium chemical potentials µ. PACS numbers: 73.43.-f, 73.43.Nq, 73.23.-b arXiv:1707.01364v1 [cond-mat.mes-hall] 5 Jul 2017 which allows seamless integration to the self-consistent Hartree-Fock approach of section II A (here ν denotes SUPPORTING INFORMATION

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Section: B the Non-equilibrium Network Model (Nnm)mentioning

confidence: 99%

Manifestation of many-body interactions in the integer quantum Hall effect regime

Oswald

Römer

2017

Phys. Rev. B

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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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A Numerical Study of Non-local Magneto Transport Effects in Quantum Hall Device Structures

Cited by 2 publications

References 9 publications

Manifestation of many-body interactions in the integer quantum Hall effect regime

Manifestation of many-body interactions in the integer quantum Hall effect regime

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

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