Localization and conductance fluctuations in the integer quantum Hall effect: Real-space renormalization-group approach

Galstyan, A.; Raǐkh, M. É.

doi:10.1103/physrevb.56.1422

Cited by 54 publications

(84 citation statements)

References 38 publications

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“…The actual initial distributions, P 0 (t), were chosen in such a way that corresponding conductance distributions, P 0 (G), were either uniform or parabolic, or identical to the FP distribution found semianalytically in Ref. 55. All these distributions are symmetric with respect to G = 0.5.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…55 Also, note that, in Refs. 70 and 72 the critical exponent ν was calculated using a procedure different from that described in Sec.…”

Section: Comparison With Previous Simulationsmentioning

confidence: 99%

“…We now apply a real-space RG approach 55,56 to the CC network. 57,58 The RG approach is based on the assumption that a certain part of the network containing several SP's, the RG unit, represents the entire network.…”

Section: Test Of the Rg Approach To The CC Modelmentioning

confidence: 99%

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Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder

et al. 2001

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We theoretically study the effect of long-ranged inhomogeneities on the critical properties of the integer quantum Hall transition. For this purpose we employ the real-space renormalization-group (RG) approach to the network model of the transition. We start by testing the accuracy of the RG approach in the absence of inhomogeneities, and infer the correlation length exponent ν = 2.39 from a broad conductance distribution. We then incorporate macroscopic inhomogeneities into the RG procedure. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law, r −α . Similar to the classical percolation, we observe an enhancement of ν with decreasing α. Although the attainable system sizes are large, they do not allow one to unambiguously identify a cusp in the ν(α) dependence at αc = 2/ν, as might be expected from the extended Harris criterion. We argue that the fundamental obstacle for the numerical detection of a cusp in the quantum percolation is the implicit randomness in the Aharonov-Bohm phases of the wave functions. This randomness emulates the presence of a short-range disorder alongside the smooth potential.

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Section: Numerical Resultsmentioning

confidence: 99%

“…55 Also, note that, in Refs. 70 and 72 the critical exponent ν was calculated using a procedure different from that described in Sec.…”

Section: Comparison With Previous Simulationsmentioning

confidence: 99%

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Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder

et al. 2001

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“…An example in the case of V 0 < 0 is shown in Fig.1(a). In the absence of interband mixing, numerical calculations have suggested that there is still only one extended state in each LB while the value of the critical exponent ν is modified to be around 7/3 10 .…”

Section: The Semiclassical Model Including Inter-landau-band Mixingmentioning

confidence: 99%

“…The integrally quantized Hall plateaus (IQHP) are observed when the Fermi level lies in localized states, with the value of the Hall conductance, σ xy = ne 2 /h, related to the number of occupied extended states(n). Many previous studies 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23 have been focused on so-called plateau transitions. The issue there is how the Hall conductance jumps from one quantized value to another when the Fermi level crosses an extended state.…”

Section: Introductionmentioning

confidence: 99%

Possible existence of a band of extended states induced by inter-Landau-band mixing in a quantum Hall system

Xiong

Wang

Niu

et al. 2006

J. Phys.: Condens. Matter

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The mixing of states with opposite chirality in quantum Hall system is shown to have delocalization effect. It is possible that extended states may form bands because of this mixing, as is shown through a numerical calculation on a two-channel network model. Based on this result, a new phase diagram with a narrow metallic phase separating two adjacent QH phases and/or separating a QH phase from the insulating phase is proposed. The data from recent non-scaling experiments is reanalyzed and shown that they seem to be consistent with the new phase diagram. However, due to finite-size effects, further study on large system size is still needed to conclude whether there are extended state bands in thermodynamic limit.

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S-matrix network models for coherent waves in random media: construction and renormalization

1998

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Networks of random quantum scatterers @S-matricesA form paradigmatic models for the propagation of coherent w aves in random media. S-matrix network models cover universal localization-delocalization properties and have some advantages over more traditional Hamiltonian models. In particularD a straightforward implementation of real space renormalization techniques is possible. Starting from a nite elementary cell of the S-matrix networkD hierarchical network models can be constructed by recursion. The localization-delocalization properties are contained in the ow of the forward scattering strength @9conductance9A under increasing system size. With the aid of 9small scale9 n umerics qualitative aspects of the localization-delocalization properties of S-matrix network models can be worked out.

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Localization and conductance fluctuations in the integer quantum Hall effect: Real-space renormalization-group approach

Abstract: We consider the network model of the integer quantum Hall effect transi-

Cited by 54 publications

References 38 publications

Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder

Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder

Possible existence of a band of extended states induced by inter-Landau-band mixing in a quantum Hall system

S-matrix network models for coherent waves in random media: construction and renormalization

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