Levitation of Current Carrying States in the Lattice Model for the Integer Quantum Hall Effect

Koschny, Thomas; Potempa, H.; Schweitzer, L.

doi:10.1103/physrevlett.86.3863

Cited by 28 publications

(22 citation statements)

References 30 publications

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“…55 Furthermore, the MRGM also seems suitable to perform ab-initio calculations of the integer Quantum Hall effect. 56 The challenge is in this case the inclusion of a disorder potential which is compatible with the separability conditions. P Q P Q…”

Section: Discussionmentioning

confidence: 99%

Ballistic quantum transport at high energies and high magnetic fields

et al. 2003

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We present an extension of the modular recursive Green's function method (MRGM) for ballistic quantum transport to include magnetic fields. Dividing the non-separable two-dimensional scattering problem into separable substructures allows us to calculate transport coefficients and scattering wavefunctions very efficiently. Previously unattainable energy and magnetic field regions can thereby be covered with high accuracy. The method is applied to magnetotransport through a circle and a stadium shaped quantum dot at strong magnetic fields and high energies. In the edge state regime we observe strong multi-frequency Aharonov-Bohm oscillations. By analyzing them in terms of a multi-channel interference model, we classify these fluctuations within the framework of Fano resonances and discuss their geometry independence. For high energies (mode numbers) we observe localization of the scattering wavefunction near classical trajectories.Comment: 20 pages, 10 figures, to appear in Phys.Rev.

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Section: Discussionmentioning

confidence: 99%

Ballistic quantum transport at high energies and high magnetic fields

et al. 2003

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“…The results of the numerical work for a disordered twodimensional lattice model can be summarized as follows: There is a genuine floating of the critical states to higher energies. 21,24,25,[28][29][30][31] This floating is, however, not easy to observe in systems with uncorrelated random disorder potentials due to a peculiar annihilation mechanism inherent in the lattice model. In this model the Chern states, which correspond to the critical electronic states in each Landau band that are responsible for the integer quantized Hall conductivity, get neutralized by the so called anti-Chern states originating from the center of the tight-binding band.…”

Section: Introductionmentioning

confidence: 99%

Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder

Koschny

Schweitzer

2003

Phys. Rev. B

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The fate of the current carrying states of a quantum Hall system is considered in the situation when the disorder strength is increased and the transition from the quantum Hall liquid to the Hall insulator takes place. We investigate a two-dimensional lattice model with spatially correlated disorder potentials and calculate the density of states and the localization length either by using a recursive Green function method or by direct diagonalization in connection with the procedure of level statistics. From the knowledge of the energy and disorder dependence of the localization length and the density of states (DOS) of the corresponding Landau bands, the movement of the current carrying states in the disorder-energy and disorder-filling-factor plane can be traced by tuning the disorder strength.We show results for all sub-bands, particularly the traces of the Chern and anti-Chern states as well as the peak positions of the DOS. For small disorder strength W we recover the well known weak levitation of the critical states, but we also reveal, for larger W , the strong levitation of these states across the Landau gaps without merging. We find the behavior to be similar for exponentially, Gaussian, and Lorentzian correlated disorder potentials. Our study resolves the discrepancies of previously published work in demonstrating the conflicting results to be only special cases of a general lattice model with spatially correlated disorder potentials.To test whether the mixing between consecutive Landau bands is the origin of the observed floating, we truncate the Hilbert space of our model Hamiltonian and calculate the behavior of the current carrying states under these restricted conditions.

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“…In a recent paper we have shown [20] that the lattice model can exhibit similar properties as the continuum model if long range correlated random disorder potentials are considered. Using exponentially correlated random potentials to model the intrinsic scattering potentials and other imperfections that may influence the movement of the charge carriers in real 2DEGs, we found that the floating up in energy can already be observed for correlation lengths larger than about half the lattice constant.…”

Section: Introductionmentioning

confidence: 99%

Influence of correlated disorder potentials on the levitation of current carrying states in the quantum Hall effect

Koschny

Schweitzer

2002

Physica E: Low-dimensional Systems and Nanostructures

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The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice system. We consider a Gaussian correlated random potential, study the behaviour of the current carrying states and trace their energetical position when the disorder strength is increased. Our results qualitatively resemble those obtained previously for exponentially correlated disorder potentials. We find both the downward movement of the anti-Chern states as well as the floating up of the Chern states across the Landau gap which is sometimes masked by the global broadening of the tight binding band.

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Levitation of Current Carrying States in the Lattice Model for the Integer Quantum Hall Effect

Cited by 28 publications

References 30 publications

Ballistic quantum transport at high energies and high magnetic fields

Ballistic quantum transport at high energies and high magnetic fields

Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder

Influence of correlated disorder potentials on the levitation of current carrying states in the quantum Hall effect

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