On the theory of the integral quantized Hall effect

1991

Il Nuovo Cimento D

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Summary. --The ground-state energy of two-dimensional interacting electrons in a strong magnetic field in the angular-momentum representation is studied using a modified Lanczos diagonalization method. In the presence of a positive background density the ground-state energy increases with the total angular momentum, while a cusp-type behaviour appears. The problem of the electron-impurities interaction is formulated as well. The results are discussed in connection with the observed fractional quantum Hall states.PACS 73.40Kp-III-V semiconductor-to-semiconductor contacts, p-n junctions, and heterojunctions. PACS 73.20.Dx -Electron states in low-dimensional structures (including quantum wells, superlattices, layer structures, and intercalation compounds). PACS 73.50.Jt -Galvanomagnetic and other magnetotransport effects (including thermomagnetic effects).

“…Also the Schrauben functions we have previously used in connection with the IQHE [27] are such type of eigenstates.…”

Section: Iz-z't ] 41o J"mentioning

confidence: 99%

Ground-state energy of two-dimensional interacting electrons in strong magnetic fields

1991

Il Nuovo Cimento D

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“…Using the basis (27), the matrix elements of the potential V (x, y) can be derived for each crystal momentum q = (q x , q y ):…”

Section: Electron Energy Spectrum Under Weak Periodic Modulation Pote...mentioning

confidence: 99%

“…Schrauben functions describe free electrons in a uniform magnetic field in the symmetric gauge and have been used in the past for magnetoconductance calculations. [26,27] The paper has the following structure: In Section 2 the model is formulated and the projection operator of the M.T.G corresponding to the problem is introduced. In Section 3 we construct a basis of appropriately symmetric Bloch-like wavefunctions as linear combination of Schrauben functions.…”

Section: Introductionmentioning

confidence: 99%

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

Divari

2006

Int. J. Mod. Phys. B

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In this paper we present calculations on the electronic band structure of a two-dimensional lateral superlattice subject to a perpendicular magnetic field by employing a projection operator technique based on the ray-group of magnetotranslation operators. We construct a new basis of appropriately symmetrized Bloch-like wavefunctions as linear combination of well-localized magnetic-Wannier functions. The magnetic field was consistently included in the Wannier functions defined in terms of free-electron eigenfunctions in the presence of external magnetic field in the symmetric gauge. Using the above basis, we calculate the magnetic energy spectrum of electrons in a lateral superlattice with bi-directional weak electrostatic modulation. Both a square lattice and a triangular one are considered as special cases. Our approach based on group theory handles the cases of integer and rational magnetic fluxes in a uniform way and the provided basis could be convenient for further both analytic and numerical calculations.

“…Current theoretical understanding of the quantum Hall effect (QHE) [1,2] Recently, the author et. a/ [7] presented a model calculation of the Hall conductivity as a function of level broadening assuming a simple form for the density of states. Our purpose in this paper is the investigation of the influence of Landau level broadening on the structure of the Hall conductance as well as the application of a fitting process of our model to the available experimental data.…”

mentioning

confidence: 99%

Effect of the Landau level broadening on the quantum Hall conductance

1991

Il Nuovo Cimento D

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Summary. --In a previous paper, Kliros et al. presented a model calculation of the Hall conductivity as a function of the Landau level broadening F for finite temperatures. In this paper, the effect of Landau-level broadening on the structure of the Hall conductivity is investigated. The experimental data regarding the Si-MOSFET and GaAs-heterostructure experiments are reproduced including a functional dependence of F on the magnetic field. The influence of the effective g-factor is considered as well.PACS 72.20.My -Galvanomagnetic and other magnetotransport effects. PACS 73.20.Dx -Electron states in low-dimensional structures (including quantum wells, superlattices, layer structures, and intercalation compounds).In a two-dimensional electron system, a magnetic field perpendicular to the plane of electrical confinement leads to full quantization of the electron motion. The energy spectrum consists of Landau levels (LL) separated by the cyclotron energy ho~r In an unperturbed system, the LL are discrete and highly degenerate, with (2~ 10)-1 (10 is the magnetic length) possible states.In a real system the LL are broadened due to scattering by phonons, impurities and other possible mechanisms. In the case of high magnetic fields, where hue >>F, real gaps appear between LL. Current theoretical understanding of the quantum Hall effect (QHE) [1,2] Recently, the author et. a/ [7] presented a model calculation of the Hall conductivity as a function of level broadening assuming a simple form for the density of states. Our purpose in this paper is the investigation of the influence of Landau level broadening on the structure of the Hall conductance as well as the application of a fitting process of our model to the available experimental data. 99