Quantum Percolation in the Quantum Hall Regime

Sohrmann, Christoph; Oswald, Josef; ömer, R.A.R

doi:10.1007/978-3-540-85428-9_6

Cited by 5 publications

(4 citation statements)

References 75 publications

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“…As a first step toward understanding the origin of these hotspots and how they relate to the underlying electron trajectories, we employ numerical simulations based on the percolation of single-particle states near the center of disorder-broadened Landau bands. While our noninteracting model cannot account for the charge rearrangements in compressible dots, for the resulting Coulomb blockade effects, and in general, for the evolution of the potential due to screening as the filling factor is varied, it has been pointed out by some authors − that the predicted critical behavior at the transition between plateaus may exhibit no differences with respect to that obtained with self-consistent Hartree–Fock calculations. In particular, the localization behavior of the wave functions has been found to be similar to that characteristic of a single-particle model.…”

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confidence: 89%

Unraveling Quantum Hall Breakdown in Bilayer Graphene with Scanning Gate Microscopy

et al. 2012

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Investigating the structure of quantized plateaus in the Hall conductance of graphene is a powerful way of probing its crystalline and electronic structure and will also help to establish whether graphene can be used as a robust standard of resistance for quantum metrology. We use low-temperature scanning gate microscopy to image the interplateau breakdown of the quantum Hall effect in an exfoliated bilayer graphene flake. Scanning gate images captured during breakdown exhibit intricate patterns where the conductance is strongly affected by the presence of the scanning probe tip. The maximum density and intensity of the tip-induced conductance perturbations occur at half-integer filling factors, midway between consecutive quantum Hall plateau, while the intensity of individual sites shows a strong dependence on tip-voltage. Our results are well-described by a model based on quantum percolation which relates the points of high responsivity to tip-induced scattering in a network of saddle points separating localized states.

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confidence: 89%

Unraveling Quantum Hall Breakdown in Bilayer Graphene with Scanning Gate Microscopy

et al. 2012

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“…In order to revisit the many-body screening effects of a two-dimensional electron system (2DES) in the IQHE, we utilize a) a modeling of the many-particle ground state, for which we use a fully self-consistent Hartree-Fock implementation discussed in refs. [17][18][19]; b) we also need a model for electron transport close to equilibrium while driving the electron system out of equilibrium. In order to avoid any violation of the physics of coherent many-particle quantum transport, the model also must not make explicit use of single-carrier flow.…”

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confidence: 99%

Exchange-mediated dynamic screening in the integer quantum Hall effect regime

Oswald

Römer

2017

EPL

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Quantum Hall effects PACS 73.43.Nq -Quantum phase transitions PACS 73.23.-b -Electronic transport in mesoscopic systemsAbstract -We study many-body interaction effects in the spatially-resolved filling factor (ν) distribution for higher Landau levels (LLs) via self-consistent Hartree-Fock simulations in the integer quantum Hall (IQH) regime. Our results indicate a strong, interaction-induced tendency to avoid the simultaneous existence of partially filled spin-up and spin-down LLs. Rather, we find that such partially filled LLs consist of coexisting regions of full and empty LLs. At the boundaries between the regions of full and empty LLs, we observe edge stripes of nearly constant ν close to half filling. This suggests that the exchange interaction induces a behavior similar to a 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 static Thomas-Fermi screening [1]. Our results are consistent with a local, lateral ν dependence of the exchange-enhanced spin splitting. Hence, on quantum-coherent length scales as probed here, the electron system of the IQH effect behaves similar to a non-interacting single particle system -not because of the absence, but rather due to the dominance of many-body effects.

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“…Ref. [9]). Furthermore, for realistic magnetic fields of several Tesla and sample parameters as used in real experiments, the quantization due to the magnetic confinement dominates strongly over the contribution of the electrical field.…”

Section: The Edge Channel Picturementioning

confidence: 99%

“…This Eq. (9) has been extracted from a paper of Beenakker et al [34] who deals with edge channel transport in the fractional quantum Hall regime. Equation(9) can be seen as an appropriate approach to give a correct interpolation between conductance steps.…”

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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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Quantum Percolation in the Quantum Hall Regime

Cited by 5 publications

References 75 publications

Unraveling Quantum Hall Breakdown in Bilayer Graphene with Scanning Gate Microscopy

Unraveling Quantum Hall Breakdown in Bilayer Graphene with Scanning Gate Microscopy

Exchange-mediated dynamic screening 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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