Exact density of states of a two-dimensional electron gas in a strong magnetic field and a long-range correlated random potential

Spies, Lothar; Apel, W.; Krämer, B.

doi:10.1103/physrevb.55.4057

Cited by 18 publications

(25 citation statements)

References 30 publications

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“…The DOS resulting from disorder having a finite correlation length was calculated in Ref. [38]: Both approaches predict a monotonic dependence of the background DOS on disorder and include the case of vanishing background for sufficiently low disorder and low inhomogeneity, respectively. In Ref.…”

Section: Feature Articlementioning

confidence: 99%

Magnetometry on quantum Hall systems: Thermodynamic energy gaps and the density of states distribution

Wilde

Springborn

Roesler

et al. 2008

Physica Status Solidi (b)

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We review experiments on the de Haas–van Alphen (dHvA) effect, i.e., the quantum oscillatory behavior of the magnetization M, in modulation‐doped AlGaAs/GaAs heterostructures at low temperature T. In particular we focus on the thermodynamic energy gaps and the density of states (DOS) of two‐dimensional electron systems (2DES's) in the integer quantum Hall regime. M as a thermodynamic quantity yields direct access to both quantities. Energy gaps due to Landau quantization at even integer filling factors ν are extracted from different samples that cover a wide range of electronic parameters. They are varied by heterostructure growth parameters. For the quantitative analysis we simulate the magnetization starting from a single‐particle model DOS. We find that a DOS consisting of, both, levels with a Gaussian broadening and a background that increases linearly with ν is essential to model magnetization data for the different heterostructures over a wide range of ns and T. In particular we discuss the correlation of the Landau level broadening with the specific sample parameters. Oscillations in M at odd filling factors resulting from the spin splitting of Landau levels are investigated as a function of magnetic field and electron density ns. We recalculate the exchange‐energy contribution to the spin splitting and find a disagreement with Hartree–Fock calculations. However, our results are consistent with previously published magnetocapacitance measurements. In the sample exhibiting the lowest level broadening we observe discontinuous jumps of M at even ν. This specific feature of the 2DES magnetization was predicted more than 70 years ago by Peierls but never reported for dHvA effect studies before. Both, the significant improvements of the measurement technique and the optimization of heterostructure growth during recent years have allowed us to observe such discontinuities in M. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Section: Feature Articlementioning

confidence: 99%

Magnetometry on quantum Hall systems: Thermodynamic energy gaps and the density of states distribution

Wilde

Springborn

Roesler

et al. 2008

Physica Status Solidi (b)

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“…Despite there exist several experimental features apparently related to electron interaction [51,52,53,54,55,56,57,58,59], it seems that the integer quantization of the Hall conductance can be understood within the localization model without taking into account the correlations between the electrons [5]. On the other hand, for explaining the fractionally quantized Hall effect, interaction and correlation effects are generally accepted to constitute the necessary ingredients for generating the excitation gaps between the many-electron ground states associated with rational filling factors.…”

Section: The Localization Modelmentioning

confidence: 99%

Random network models and quantum phase transitions in two dimensions

2005

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“…In the 1990s, calculations of the DOS included acoustic phonon scattering [20][21][22] and electron electron scattering. 23 Finally, a finite background density between LL peaks was predicted in the case of long range scatterers, [24][25][26] which could explain experimental results. [27][28][29][30] Although the DOS has been widely studied, calculations were performed by taking into account only a few terms in the perturbative series ͑SCBA approximations͒, and always yielded a symmetric and harmonic DOS.…”

Section: Introductionmentioning

confidence: 75%

Anharmonicity and asymmetry of Landau levels for a disordered two-dimensional electron gas

et al. 2006

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We calculate the density of states of a two-dimensional electron gas located at the interface of a strongly disordered GaAlAs/ GaAs heterojunction. The disorder potential is created by two delta doped layers. The first layer includes the parent donors which provides the well with electrons and creates a smooth disorder potential. The second layer is doped with either acceptor or donor impurities, and is located inside the well, thus creating a strongly disordered potential. We calculate the density of states in the presence of a magnetic field of arbitrary strength by taking into account all perturbative terms in the fifth Klauder's approximation. We find an anharmonic spectrum, strongly asymmetric, for the Landau level density of states. At low field, the attractive potential creates the well-known band tails or impurity bands. At higher field, we show that impurity bands are also created by repulsive potentials. We discuss the consequences of the anharmonicity and asymmetry on physical properties in the quantum Hall effect regime.

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Exact density of states of a two-dimensional electron gas in a strong magnetic field and a long-range correlated random potential

Cited by 18 publications

References 30 publications

Magnetometry on quantum Hall systems: Thermodynamic energy gaps and the density of states distribution

Magnetometry on quantum Hall systems: Thermodynamic energy gaps and the density of states distribution

Random network models and quantum phase transitions in two dimensions

Anharmonicity and asymmetry of Landau levels for a disordered two-dimensional electron gas

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