A New Approach to the Quantum Hall Effect

Woltjer, R.; Eppenga, R.; Mooren, J.; Timmering, C.E.; André, J.P.

doi:10.1209/0295-5075/2/2/013

Cited by 45 publications

(15 citation statements)

References 13 publications

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“…Such a classical local magnetotransport model has previously been used to explain, for inhomogeneous samples, a finite width of quantum Hall plateaus without the assumption of localized states, and to simulate the magnetic-field dependence of Hall-type voltages in Hall bars with internal contacts. 19,20 More recently such a local model has also proven useful for the understanding of the current and electric field distribution in antidot systems close to the breakdown of the QHE.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent local equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields

2003

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Recent spatially resolved measurements of the electrostatic-potential variation across a Hall bar in strong magnetic fields, which revealed a clear correlation between current-carrying strips and incompressible strips expected near the edges of the Hall bar, cannot be understood on the basis of existing equilibrium theories. To explain these experiments, we generalize the Thomas-FermiPoisson approach for the self-consistent calculation of electrostatic potential and electron density in total thermal equilibrium to a local equilibrium theory that allows to treat finite gradients of the electrochemical potential as driving forces of currents in the presence of dissipation. A conventional conductivity model with small values of the longitudinal conductivity for integer values of the (local) Landau-level filling factor shows that, in apparent agreement with experiment, the current density is localized near incompressible strips, whose location and width in turn depend on the applied current.

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Section: Introductionmentioning

confidence: 99%

Self-consistent local equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields

2003

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“…is the conductivity tensor of a homogeneous 2DES of electron density el . n A similar local Ohmic magnetotransport model has previously been used to explain, for inhomogeneous samples, a finite width of quantum Hall plateaus without the assumption of localized states, and to simulate the magnetic-field dependence of Hall-type voltages in Hall bars with internal contacts [33,34]. More recently such a local model has also proven useful for the understanding of the current and electric field distribution in antidot systems close to the breakdown of the QHE [35][36][37].…”

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confidence: 99%

The effect of screening on current distribution and conductance quantisation in narrow quantum Hall systems

Gerhardts

2008

Physica Status Solidi (b)

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We summarize and critically discuss the screening theory of the integer quantized Hall effect (IQHE), which was recently developed in order to understand scanning‐force‐microscope experiments on the current distribution in narrow Hall bars. The theory is based on the combination of a self‐consistent, non‐linear screening theory with a linear, local transport theory. In addition to the explanation of the mentioned experiments, it allows a simple understanding of the IQHE, including the enormous reproducibility of the measured quantized resistance values. Both achievements result from two key mechanisms: The first, which follows from the screening theory, is the existence of incompressible strips, with integer values of the local Landau level filling factor and quantized values of longitudinal and Hall resistivity, in certain magnetic field intervals. The second, a result of the local transport theory, is the confinement of an imposed dissipative current to these strips. This confinement leads to the quantization of the global resistances, without any localization assumptions. We also discuss limitations and possible extensions as well as further applications of this theory. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…Recently, we have shown 2 that current can flow chiefly along the edges of 2DEG channels in the integral quantized Hall regime, probably because of the large density gradients occurring there. Woltjer et al 3 have proposed an explanation for the integral quantized Hall effect in which electron density fluctuations, not localization, account for the presence of Hall plateaus. Syphers and Stiles 4 undertook an investigation of the potential distribution in contiguous regions of differing electron density, but failed to address the question of conduction across the density discontinuity.…”

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Evidence of Inter-Landau-Level Tunneling in the Integral Quantum Hall Effect

1988

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We have investigated conduction across electron density discontinuities induced by a front gate on GaAs/AUGai-jcAs single-interface heterostructures in the integral quantized Hall regime. When the gate is biased so that the Fermi level must cross between adjacent Landau levels at the gate edge, the boundary between higher-and lower-density regions behaves like a backward diode, suggesting the presence in these devices of inter-Landau-level tunneling.PACS numbers: 72.20. My, 73.40.Gk, 73.40.Kp, 85.30.Mn While electronic transport in the integral quantized Hall regime has by now been thoroughly studied, * most work has been confined to systems in which the carrier density is uniform. Nevertheless, density inhomogeneities in the two-dimensional electron gas (2DEG) can have important consequences. Recently, we have shown 2 that current can flow chiefly along the edges of 2DEG channels in the integral quantized Hall regime, probably because of the large density gradients occurring there. Woltjer et al. 3 have proposed an explanation for the integral quantized Hall effect in which electron density fluctuations, not localization, account for the presence of Hall plateaus. Syphers and Stiles 4 undertook an investigation of the potential distribution in contiguous regions of differing electron density, but failed to address the question of conduction across the density discontinuity.We have investigated the current-voltage (I-V) characteristics of abrupt density discontinuities in the integral quantized Hall regime. We have found that when the Fermi level (E?) must cross between adjacent Landau levels at the discontinuity, the I-V characteristic of the discontinuity is similar to that of a backward diode: When the device is forward biased (electrons flow from the high-density to the low-density region), conduction is small until a temperature-dependent threshold voltage is reached, when the current rapidly increases. When the device is reverse biased, the magnitude of / gradually increases with V, and is temperature independent. The similarity of our devices to backward diodes suggests that the conduction mechanisms are the same in both, implying the existence of inter-Landau-level tunnel currents across the discontinuity.Our experiments were performed on a GaAs/ Al x Gaix As single interface heterostructure with a 2DEG density of 5.

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A New Approach to the Quantum Hall Effect

Abstract: A new model is proposed to explain some important experimental results on the * * * We want t o thank J. M. LAGEMAAT, J. A. PALS and M. F. H. SCHUURMANS for stimulating discussions.

Cited by 45 publications

References 13 publications

Self-consistent local equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields

Self-consistent local equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields

The effect of screening on current distribution and conductance quantisation in narrow quantum Hall systems

Evidence of Inter-Landau-Level Tunneling in the Integral Quantum Hall Effect

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