Hall potential distribution in quantum Hall experiments

Ebert, G.; Klitzing, K. von; Weimann, G.

doi:10.1088/0022-3719/18/10/003

Cited by 109 publications

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“…These local properties remain controversial, with some theories suggesting that the current flow and associated voltage drops are concentrated at the edges of the sample [2][3][4][5], while others predict a distribution extending throughout the bulk of the sample [6][7][8]. Attempts have been made to address these questions with local imaging techniques [9][10][11][12][13], transport measurements of the breakdown of the QH effect [14], inductive measurements [15], capacitance measurements [16], and internal voltage probes [17]. The results, while informative, have lacked sufficient spatial and/or energy resolution to determine unambiguously how the current is partitioned between edge and bulk channels and the shape of the associated voltage profile across the QHC.…”

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Scanned potential microscopy of edge and bulk currents in the quantum Hall regime

et al. 1999

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Using an atomic force microscope as a local voltmeter, we measure the Hall voltage profile in a 2D electron gas in the quantum Hall (QH) regime. We observe a linear profile in the bulk of the sample in the transition regions between QH plateaus and a distinctly nonlinear profile on the plateaus. In addition, localized voltage drops are observed at the sample edges in the transition regions. We interpret these results in terms of theories of edge and bulk currents in the QH regime.PACS numbers: 73.40. Hm, 61.16.Ch, Since the discovery of the quantum Hall (QH) effect [1], the electrical characteristics of quantum Hall conductors (QHCs) have been intensely studied. The universal nature of the quantization in QHCs leads to a resistance that is independent of the microscopic properties of the sample. As a consequence, local properties of a QHC such as the current and voltage distributions within the sample are inaccessible with standard transport measurements. These local properties remain controversial, with some theories suggesting that the current flow and associated voltage drops are concentrated at the edges of the sample [2-5], while others predict a distribution extending throughout the bulk of the sample [6][7][8] The results, while informative, have lacked sufficient spatial and/or energy resolution to determine unambiguously how the current is partitioned between edge and bulk channels and the shape of the associated voltage profile across the QHC.To address these issues, we have used a scanned potential microscope to study the potential distribution in a QHC with submillivolt voltage and submicron spatial resolution. We find that at low magnetic fields the Hall voltage drop is linear, indicating uniform current flow throughout the sample. At high magnetic fields, large voltage drops are seen at the sample edges in the transition regions between QH plateaus, indicating that the current is concentrated near the edges. On the QH plateaus, the current is distributed throughout the bulk in a complex, non-uniform way. These results are in good agreement with existing results for edge and bulk transport in the QH regime.The samples consist of 10-20 µm wide Hall bars defined by wet etching of a GaAs/AlGaAs heterostructure with a 2D electron gas lying 77 nm beneath the surface. Results will be presented on two samples with mobilities of 8 and 70 m 2 /V-s and densities of 2.8 x 10 15 and 2.6 x 10 15 m -2 . All measurements were performed at temperatures between 0.7 and 1.0 K. The samples were also characterized by standard transport measurements.We measure the local voltage with a lowtemperature atomic force microscope (AFM) operating in non-contact mode [18]. As shown schematically in Fig. 1, an AC potential V 0 is applied to the contacts of the sample, producing inside the sample the AC potential V(x,y) whose spatial distribution is to be measured. The local sample potential V(x,y) interacts electrostatically with the sharp, metallized AFM tip, deflecting the AFM cantilever with a force that can be simply modelled...

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Scanned potential microscopy of edge and bulk currents in the quantum Hall regime

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“…Namely, the charge density in the state (8.13) has the following form: 14) where θ 0 is the argument of the position, ξ G , of the modulation gate. This function correctly captures the effects of a modulation gate: the local depletion of the 2DEG at the point ξ G = r U e iθ0 and the homogeneous expansion of the QH liquid due to its incompressibility.…”

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“…It is interesting, that in spite of such precise quantization and universal behavior, distribution of currents in a sample at Hall plateaus is highly inhomogeneous and changes between the plateaus and even at the same plateau [14].…”

Section: General Introductionmentioning

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“…The first measurements of the longitudinal and Hall resistance of the high quality 2DEG in strong magnetic field have given exciting results. Namely, around the values of the magnetic field which correspond to the integer values of Landau levels filling factor (1.26) longitudinal resistance becomes suppressed by a factor as high as 10 13 , while at the same time the Hall resistance becomes equal to 14) where n is the integer closest to the value of the filling factor [1]. The precision of quantization of the Hall resistance at these so called Hall plateaus is extremely high, and can be as high as δR H /R H 10 −10 in the modern samples.…”

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“…The picture described above, is, of course, an idealization. According to the experiment [14], there always exist some delocalized states in bulk, which also carry some current density. But it is important, that scattering between the states in the bulk does not spoil the quantization of the Hall conductance.…”

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Liquid Site Model and Self‐Consistent Potentials in the Theory of Quantum Hall Effect

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By %IKP and 1t. KEIPNRTo explain the quantum Hall effect (QHE) as a macroscopic quantum phenomenon with interference character the liquid site model is discussed in more detail. The calculated thermodynamic potential containing the magnetic field energy shows minima near the filling factors v = p / ( 2 n + 1) ( p = 1,2, ...; n = 0, 1,2, ...). Electron correlation in strong magnetic fields leads t o a local Hall potential satisfying the two-dimensional Laplace equation. The liquid site model permits t o discuss the necessity for a n optimum degree of disorder as well as the high precision attainable in &HE measurements.Um den Quantenhalleffekt (QHE) als makroskopisches Quantenphiinomen mit Interferenzcharakter zu erklaren, wird das "liquid site"-Model1 ausfiihrlicher diskutiert. Das berechnete thermodynamische Potential, das die magnetische Feldenergie enthalt, zeigt Minima in der Niihe des Fullfaktors v = p/(2n + 1) ( p = 1,2, ... ; n = 0, 1, 2, ...). Elektronenkorrelation in starken Magnetfeldern fiihrt zu einem lokalen Hallpotential, das der zweidimensionalen Laplacegleichung genugt. Das "liquid site"-Modell erlaubt, sowohl die Notwendigkeit fur einen optimalen Grad der Fehlordnung als auch die hohe Priizision, die in QHE-Messungen erreichbar ist, zu diskutieren.

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Hall potential distribution in quantum Hall experiments

Cited by 109 publications

References 5 publications

Scanned potential microscopy of edge and bulk currents in the quantum Hall regime

Scanned potential microscopy of edge and bulk currents in the quantum Hall regime

Mesoscopic Quantum Hall Effect

Liquid Site Model and Self‐Consistent Potentials in the Theory of Quantum Hall Effect

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