Theory of Hall Effect in a Two-Dimensional Electron System

Ando, Tsuneya; Matsumoto, Yukio; Uemura, Yasutada

doi:10.1143/jpsj.39.279

Cited by 285 publications

(117 citation statements)

References 6 publications

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“…[55,56] Upon inverting the tensor including oscillatory σ xy and σ xx , "Type-3" oscillations were still obtained, as in Fig. 7(a).…”

Section: Discussion: Numerical Simulations Indicating the Possibilitymentioning

confidence: 88%

“…One might semi-empirically introduce oscillations into the diagonal conductivity, σ xx , as σ xx = σ 0 xx (1−Acos(2πE F /hω)). [54,55,56] Here, the minus sign ensures the proper phase, while σ…”

Section: Discussion: Numerical Simulations Indicating the Possibilitymentioning

confidence: 99%

“…[55] Although, the dominant scattering mechanism is long-ranged in GaAs/AlGaAs devices, we set σ xy = (σ 0 xx /ωτ − ne/B) − A(σ 0 xx /ωτ )cos(2πE F /hω). When τ = τ T , this approach again yielded Type-3 phase relations, as in the discussion above.…”

Section: Discussion: Numerical Simulations Indicating the Possibilitymentioning

confidence: 99%

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Phase study of oscillatory resistances in microwave-irradiated- and dark-GaAs/AlGaAs devices: Indications of an unfamiliar class of the integral quantum Hall effect

et al. 2009

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We report the experimental results from a dark study and a photo-excited study of the high mobility GaAs/AlGaAs system at large filling factors, ν. At large-ν, the dark study indicates several distinct phase relations ("Type-1", "Type-2", and "Type-3") between the oscillatory diagonal-and Hall-resistances, as the canonical Integral Quantum Hall Effect (IQHE) is manifested in the "Type-1" case of approximately orthogonal diagonal-and Hall resistance-oscillations. Surprisingly, the investigation indicates quantum Hall plateaus also in the "Type-3" case characterized by approximately "anti-phase" Hall-and diagonal-resistance oscillations, suggesting a new class of IQHE.Transport studies under microwave photo-excitation exhibit radiation-induced magneto-resistance oscillations in both the diagonal, Rxx, and off-diagonal, Rxy, resistances. Further, when the radiation-induced magneto-resistance oscillations extend into the quantum Hall regime, there occurs a radiation-induced non-monotonic variation in the amplitude of Shubnikov-de Haas (SdH) oscillations in Rxx vs. B, and a non-monotonic variation in the width of the quantum Hall plateaus in Rxy. The latter effect leads into the vanishing of IQHE at the minima of the radiation-induced Rxx oscillations with increased photo-excitation. We reason that the mechanism which is responsible for producing the non-monotonic variation in the amplitude of SdH oscillations in Rxx under photoexcitation is also responsible for eliminating, under photo-excitation, the novel "Type-3" IQHE in the high mobility specimen. INTRODUCTIONA 2-dimensional electron system (2DES) at high magnetic fields, B, and low temperatures, T , exhibits the integral quantum Hall effect (IQHE), which is characterized by plateaus in the Hall resistance R xy vs. B, at R xy = h/ie 2 , with i = 1,2,3,... and concurrent vanishing diagonal resistance R xx as T → 0 K, in the vicinity of integral filling factors of Landau levels, i.e., ν ≈ i. [1,2,3] With the increase of the electron mobility, µ, at a given electron density, n, and low T , IQHE plateaus typically become narrower as fractional quantum Hall effects (FQHE) appear in the vicinity of, where p/q denotes mostly odd-denominator rational fractions. [2,3] Experimental studies of the highest mobility specimens have typically focused upon FQHE and other novel phases. [2,3,4,5] Meanwhile, the possibility of new variations of IQHE that might appear with the canonical effect in the reduceddisorder specimen, especially at large-ν, has been largely unanticipated. In the first dark-study part of this paper, we show that three distinct phase relationships can occur between the oscillatory diagonal-and Hall-resistances in the high-mobility dark specimen at ν > 5, and that IQHE can be manifested in two of these variations. The results therefore suggest one new class of IQHE, as they provide insight into the origin of oscillatory variations in the Hall effect, and their evolution into Hall plateaus, in the low-B large-ν regime of the radiationinduced zero-resistance sta...

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“…[55,56] Upon inverting the tensor including oscillatory σ xy and σ xx , "Type-3" oscillations were still obtained, as in Fig. 7(a).…”

Section: Discussion: Numerical Simulations Indicating the Possibilitymentioning

confidence: 88%

Section: Discussion: Numerical Simulations Indicating the Possibilitymentioning

confidence: 99%

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Phase study of oscillatory resistances in microwave-irradiated- and dark-GaAs/AlGaAs devices: Indications of an unfamiliar class of the integral quantum Hall effect

et al. 2009

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“…19 Since the quantum-mechanical broadening of a Landau level is characterized by the single-particle scattering time, [20][21][22] or equivalently by the quantum mobility q , we also measured the transport and quantum mobility as a function of the electron concentration ͓Fig. 2͑c͔͒.…”

Section: Methodsmentioning

confidence: 99%

Reflection of finite-width edge channels

et al. 1996

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We have studied experimentally the edge channels in an externally controlled inhomogeneous twodimensional electron gas ͑2DEG͒ under quantum Hall conditions. The 2DEG is inhomogeneous in the sense that the electron concentration changes linearly across the width of the sample. In an impurity-free ͑or ideal͒ electron gas, these edge channels are wide compressible strips alternated with incompressible strips. However, when the presence of charged impurities ͑or disorder͒ is considered, localized compressible strips appear on both sides of the incompressible strips. We show that the width of the incompressible plus the localized compressible strips can be determined from resistance measurements. We further demonstrate that the macroscopically wide compressible strips in an inhomogeneous, disordered 2DEG act as if they are edge channels; they can be reflected at an interior potential and the values of the quantized resistances can be determined from the Landauer-Büttiker model. ͓S0163-1829͑96͒03028-7͔

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“…In a magnetic field transverse to the 2D electron array electron states are confined to the Landau levels (LL) with a width Á. The contribution [13][14][15] to Á from scattering is…”

Section: Theorymentioning

confidence: 99%

Magnetoresistivity of a Weakly-Screened, Low-Density, Two-Dimensional Electron Liquid

Karakurt

Dahm

2013

J. Phys. Soc. Jpn.

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We probe the strength of electron-electron interactions at intermediate magnetic fields in the classical regime using magnetoconductivity measurements of two-dimensional, non-degenerate electrons on liquid helium. We span both the independent-electron regime, where the data are qualitatively described by the self-consistent Born approximation (SCBA), and the strongly-interacting electron (Drude) regime. We observe a crossover from SCBA to Drude theory at finite magnetic fields as a function of electron density. The SCBA magnetoresistance is found to be density dependent. Our data confirm the theory for magnetoresistivity in a weakly screened, two-dimensional electron gas, and demonstrate that electron-electron interactions are important to very low densities.

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Theory of Hall Effect in a Two-Dimensional Electron System

Cited by 285 publications

References 6 publications

Phase study of oscillatory resistances in microwave-irradiated- and dark-GaAs/AlGaAs devices: Indications of an unfamiliar class of the integral quantum Hall effect

Phase study of oscillatory resistances in microwave-irradiated- and dark-GaAs/AlGaAs devices: Indications of an unfamiliar class of the integral quantum Hall effect

Reflection of finite-width edge channels

Magnetoresistivity of a Weakly-Screened, Low-Density, Two-Dimensional Electron Liquid

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