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

Koschny, Thomas; Schweitzer, L.

doi:10.1016/s1386-9477(01)00426-x

Cited by 3 publications

(4 citation statements)

References 22 publications

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“…Using spatially correlated random disorder potentials instead, it could be shown that the effect of the anti-Chern states is reduced so that the expected levitation scenario and the floating of current carrying states across the Landau gap is seen also in the lattice model. 29,30 These results also imply that, contrary to other claims, 23,26 the direct transitions to the Hall insulator occurring within the lattice model with uncorrelated disorder potentials can of course not be held responsible for the direct transitions seemingly observed in experiments. 11 Here, finite size effects and limited resolution due to finite temperatures are the most probable causes 32 that account for the reported behavior.…”

Section: Introductioncontrasting

confidence: 54%

“…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%

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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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Section: Introductioncontrasting

confidence: 54%

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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“…As stated above, long-range spatial correlation can result in the delocalization for the 1D Anderson model. [17] It was shown that even the short-range correlated disorder models, such as the random-dimer model, [18,19] can exhibit an absence of localization. In this study, we show that the localization properties of the disordered systems can be well researched by using of the measure of concurrence.…”

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confidence: 99%

“…We normalize the power-law correlated site energies to the range [−W, W ] in the calculation. The Gaussian correlated disorder site energies are generated as follows: [18] (A) generating the uniform distributed random energies ε i at the interval of [−W, W ]; (B) the Gaussian correlated disordered random site energies are obtain by the following aver-…”

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confidence: 99%

Entanglement in One-Dimensional Anderson Model with Long-Range Correlated Disorder

Zi-zheng

2008

Chinese Phys. Lett.

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By using the measure of concurrence, the entanglement of the ground state in the one-dimensional Anderson model is studied with consideration of the long-range correlations. Three kinds of correlations are discussed. We compare the effects of the long-rang Gaussian and power-law correlations between the site energies on the concurrence, and demonstrate the existence of the band structure of the concurrence in the power-law case. The emergence of the sharp kink on the concurrence curve shown in the intraband or in the interband indicates the position at which the localization extent of the state may have the severe variation. We use the Rudin-Shapiro model to describe the site energy distribution of the nucleotides of the DNA chain: guanine (G), adenine (A), cytosine(C), thymine (T). This model is a tetradic quasiperiodic sequence and is shown to be long-range correlated. Our results show that correlations between the site energies increase the concurrences.

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Solitons in binary compounds with stacked two-dimensional honeycomb lattices

Muten,

Frankland,

McCann

2024

Phys. Rev. B

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We model the electronic properties of thin films of binary compounds with stacked layers where each layer is a two-dimensional honeycomb lattice with two atoms per unit cell. The two atoms per cell are assigned different on-site energies in order to consider six different stacking orders: ABC, ABA, AA, ABC′, ABA′, and AA′. Using a minimal tight-binding model with nearest-neighbor hopping, we consider whether a fault in the texture of on-site energies in the vertical, stacking direction supports localized states, and we find localized states within the bulk band gap for ABC, ABA, and AA′ stacking. Depending on the stacking type, parameter values, and whether the soliton is atomically sharp or a smooth texture, there are a range of different band structures including soliton bands that are either isolated or that hybridize with other states, such as surface states, and soliton bands that are either dispersive or flat, the latter yielding narrow features in the density of states. We discuss the relevance of our results to specific materials including graphene, hexagonal boron nitride, and other binary compounds. Published by the American Physical Society 2024

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

Cited by 3 publications

References 22 publications

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

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

Entanglement in One-Dimensional Anderson Model with Long-Range Correlated Disorder

Solitons in binary compounds with stacked two-dimensional honeycomb lattices

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