<i>Introduction to the Theory of the Integer Quantum Hall Effect</i>

Janssen, Martin; Viehweger, O.; Fastenrath, U.; Hajdu, János; Girvin, S. M.

doi:10.1063/1.2808136

Cited by 103 publications

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“…The two-dimensional version of (1.1) is widely believed to serve as a minimal model for the integer quantum Hall effect [48], [21], [2] and has therefore been intensively investigated by physicists, see for instance [1], [26], [48], [21].…”

Section: Introductionmentioning

confidence: 99%

The fate of lifshits tails in magnetic fields

et al. 1995

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We investigate the integrated density of states of the Schrödinger operator in the Euclidean plane with a perpendicular constant magnetic field and a random potential. For a Poisson random potential with a non-negative algebraically decaying single-impurity potential we prove that the leading asymptotic behaviour for small energies is always given by the corresponding classical result in contrast to the case of vanishing magnetic field. We also show that the integrated density of states of the operator restricted to the eigenspace of any Landau level exhibits the same behaviour. For the lowest Landau level, this is in sharp contrast to the case of a Poisson random potential with a delta-function impurity potential.

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Section: Introductionmentioning

confidence: 99%

The fate of lifshits tails in magnetic fields

et al. 1995

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“…Theoretical work on the frequency dependence has used the concepts of percolation 15 and localization. 16,17 However, a comparison with the experiments is not straightforward.…”

Section: Diagonal Conductivitymentioning

confidence: 99%

The diagonal and off-diagonal AC conductivity of two-dimensional electron gases with contactless Corbino geometry in the quantum Hall regime

Petersen

Hansen

1996

Journal of Applied Physics

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We have investigated the AC conductivity elements in the quantum Hall regime of two-dimensional electron gases coupled capacitively to electrodes with Corbino geometry. The samples are GaAlAs/GaAs single heterostructures, and the measurements are made at low frequencies, up to 20 kHz. The diagonal conductivity is derived from magnetocapacitance measurements. It increases with increasing frequency according to a power law at integer filling factors. The exponent of the power law depends on both temperature and filling factor. Ratios between Hall conductivities at different filling factors are obtained by inductive measurements of the circulating current. They are found to agree with quantization in multipla of e2/h at the integer filling factors.

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“…A deeper analogy, which should also be noted, is provided by the phenomenon of localization in condensed matter physics. There is, in this case, a functional integral formalism, where smooth instantons may be found, giving expressions for the tails of the density of electron states [15]. The similarity with the turbulence problem is a strong one: while in the condensed matter system localized wavefunctions define some multifractal set, the same phenomenon takes place in turbulence, regarding the fluctuations of the velocity field.…”

Section: Instantons In the Msr Approachmentioning

confidence: 99%

Circulation statistics in three-dimensional turbulent flows

Moriconi

Takakura

1998

Phys. Rev. E

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We study the large λ limit of the loop-dependent characteristic functional Z(λ) =< exp(iλ c v · d x) >, related to the probability density function (PDF) of the circulation around a closed contour c. The analysis is carried out in the framework of the Martin-Siggia-Rose field theory formulation of the turbulence problem, by means of the saddle-point technique. Axisymmetric instantons, labelled by the component σzz of the strain field -a partially annealed variable in our formalism -are obtained for a circular loop in the xy plane, with radius defined in the inertial range. Fluctuations of the velocity field around the saddle-point solutions are relevant, leading to the lorentzian asymptotic behavior Z(λ) ∼ 1/λ 2 . The O(1/λ 4 ) subleading correction and the asymmetry between right and left PDF tails due to parity breaking mechanisms are also investigated.

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Introduction to the Theory of the Integer Quantum Hall Effect

Cited by 103 publications

References 0 publications

The fate of lifshits tails in magnetic fields

The fate of lifshits tails in magnetic fields

The diagonal and off-diagonal AC conductivity of two-dimensional electron gases with contactless Corbino geometry in the quantum Hall regime

Circulation statistics in three-dimensional turbulent flows

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