Oscillations of 2D electron density in GaAs/Ga<sub>0.67</sub>Al<sub>0.33</sub>As heterostructures in the QHE regime

Raymond, André; Juillaguet, Sandrine; Elmezouar, I.; Zawadzki, W.; Sadowski, M. L.; Kamal-Saadi, M.; Etienne, B.

doi:10.1088/0268-1242/14/10/307

Cited by 11 publications

(14 citation statements)

References 44 publications

(48 reference statements)

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“…Observations of oscillations in the recombination energy of electrons with photoexcited holes in a δ modulation-doped heterojunction [95] support this idea. Also, cyclotron resonance data [96,79] strongly indicate oscillations in n s , and have been found to agree well with n s as calculated classically using the measured Hall effect in the same samples [79].…”

Section: Constraints On Number Densitysupporting

confidence: 71%

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Magnetometry of low-dimensional electron and hole systems

Usher¹,

Elliott²

2009

J. Phys.: Condens. Matter

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Abstract. The high magnetic field, low-temperature magnetic properties of lowdimensional electron and hole systems reveal a wealth of fundamental information. Quantum oscillations of the thermodynamic equilibrium magnetization yield the total density of states, a central quantity in understanding the quantum Hall effect in 2D systems. The magnetization arising from non-equilibrium circulating currents reveals details, not accessible with traditional measurements, of the vanishingly small longitudinal resistance in the quantum Hall regime. We review how the technique of magnetometry has been applied to these systems, the most important discoveries that have been made, and their theoretical significance.

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Section: Constraints On Number Densitysupporting

confidence: 71%

“…This possibility has been considered by several authors in the past [78,79,80]. If n s itself were allowed to oscillate with field, the high-field slope would become finite.…”

Section: Resultsmentioning

confidence: 99%

Magnetometry of low-dimensional electron and hole systems

Usher¹,

Elliott²

2009

J. Phys.: Condens. Matter

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“…The mechanism by which electrons could move into and out of the 2DES in our noncontacted samples is not known, although we note that the in-plane component of B might assist a tunnelling process between the 2DES and the doped ͑Al, Ga͒As, an effect invoked by Boebinger et al 30 to explain the enhanced coupling between parallel 2DESs in a double-quantum-well structure, caused by an in-plane magnetic field. Recent observations of oscillations in the recombination energy of electrons with photoexcited holes in a ␦-modulation-doped heterojunction 31 and analysis of cyclotron resonance data 32 have also been interpreted in terms of such a transfer of charge. Table I.…”

Section: Density Of Statesmentioning

confidence: 99%

Magnetization measurements of high-mobility two-dimensional electron gases

et al. 2003

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De Haas-van Alphen ͑dHvA͒ oscillations are observed for Landau levels ͑LLs͒ with filling factors between 4 and 52, at temperatures in the range 50 mK to 1 K, in experiments on high-mobility GaAs/͑Al, Ga͒As heterojunctions. The oscillations become sawtooth-shaped at low filling factors, and theoretical fits to the data, assuming the two-dimensional electron gas to be a non-interacting Fermi system, show the shape of LLs to be close to a ␦ function. The small residual width ͑ϳ0.4 meV or less͒ fits equally well to either a Gaussian or a Lorentzian density-of-states model. In almost all cases, a constant background density of states has to be included to obtain a satisfactory fit. Weak odd-filling-factor dHvA peaks are detected at high fields, from which a g-factor enhancement of 15 can be inferred. Comparison of the scattering time derived from the fits before and after illumination, with the momentum relaxation time derived from transport, reveals a counterintuitive behavior in the bulk-modulation-doped sample.

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“…Therefore, the search for the experimental evidence that would decide the right approach among those two different ones has been sought after for years. Now the latest experimental results seem to support solidly the electron reservoir hypothesis [6]. Encouraged by this recent experimental progress, in this paper we examine the effects of finite temperature on the Hall conductivity on the basis of the reservoir hypothesis.…”

mentioning

confidence: 85%

“…The experiment of von Klitzing et al was performed at temperature T=1.5K. The formula (6) shows the quantized plateaus begin to disappear at T=3K. At temperature above 10K, the formula gives the classical curve of the Hall conductivity [7].…”

mentioning

confidence: 99%

Integer Quantum Hall Effect at Finite Temperature

Toyoda¹,

Kaneko²,

Suwa³

et al. 2006

AIP Conference Proceedings

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On the basis of the field theoretical model of the integer quantum Hall effect developed by Toyoda, Gudmundsson and Takahashi [Physica 132A, 164 (1985)] we examine the temperature dependence of the Hall conductivity. The fundamental hypothesis in the theory is the existence of the electron reservoir, which has been experimentally confirmed recently. We discuss the continuous transition from the quantum regime to the classical regime as the temperature increases from 1K to 14K in the MOSFET experiment. The quantized plateaus disappear around T=3K.Since the discovery of the integer quantum Hall effect in 1980 [1], more than two decades have passed. The discovery made an enormous impact not only on the solid state physics but on an extremely wide range of physics, from applied physics to theoretical high energy physics. That a physical constant can be measured with such an amazing accuracy in a rather simple semiconductor experiment was genuinely an astonishing discovery. Naturally a considerable number of physicists have tried to find the fundamental theory to explain the mechanism of the integer quantum Hall effects. And yet, the microscopic mechanism of the effect has not been clarified. No consensus has been reached on the fundamental mechanism. If we carefully examine the proposed theoretical attempts, there seems to be two fundamentally different approaches in the theoretical attempts so far proposed. The crucial criterion that divides the two different approaches is the relation between the gate voltage and the electron number density in MOSFET experiment. In the theory based on the electron localization hypothesis [2], a simple linear relation between these two quantities is assumed. On the other hand, in the theory based on the electron reservoir hypothesis [3][4][5], the electron number density is given as the quantum statistical expectation value of the grand canonical ensemble, where the gate voltage appears as the shift of the chemical potential. These two different interpretations of the relation between the gate voltage and the electron density in the experiments lead to very different theoretical formulations. Therefore, the search for the experimental evidence that would decide the right approach among those two different ones has been sought after for years. Now the latest experimental results seem to support solidly the electron reservoir hypothesis [6]. Encouraged by this recent experimental progress, in this paper we examine the effects of finite temperature on the Hall conductivity on the basis of the reservoir hypothesis. Following Ref.[5], we consider a two-dimensional interacting electron gas under magnetic field and electric field. We also include the interaction between the electrons and impurity atoms. The current density operator of the electron system is

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Oscillations of 2D electron density in GaAs/Ga_0.67Al_0.33As heterostructures in the QHE regime

Cited by 11 publications

References 44 publications

Magnetometry of low-dimensional electron and hole systems

Magnetometry of low-dimensional electron and hole systems

Magnetization measurements of high-mobility two-dimensional electron gases

Integer Quantum Hall Effect at Finite Temperature

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Oscillations of 2D electron density in GaAs/Ga0.67Al0.33As heterostructures in the QHE regime

Cited by 11 publications

References 44 publications

Magnetometry of low-dimensional electron and hole systems

Magnetometry of low-dimensional electron and hole systems

Magnetization measurements of high-mobility two-dimensional electron gases

Integer Quantum Hall Effect at Finite Temperature

Contact Info

Product

Resources

About

Oscillations of 2D electron density in GaAs/Ga_0.67Al_0.33As heterostructures in the QHE regime