Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

Klesse, Rochus; Metzler, Marcus

doi:10.1103/physrevlett.79.721

Cited by 52 publications

(92 citation statements)

References 24 publications

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“…For a two-dimensional system, however, it is well known that, from this quantity, it is difficult to provide a conclusive answer to questions related to the metal-insulator transition (MIT) [10]. On the other hand, level-statistics analysis [11] has been used in studying MIT. We follow the approach proposed by Klesse and Metzler [11].…”

Section: -1mentioning

confidence: 99%

“…On the other hand, level-statistics analysis [11] has been used in studying MIT. We follow the approach proposed by Klesse and Metzler [11]. A quantum state of the network model can be expressed by a vector F ͕͑f u i , f l i ͖͒, where f u i and f l i are the wave function amplitudes of the ith link of the upper band ͑u͒ and the lower band ͑l͒, respectively.…”

Section: -1mentioning

confidence: 99%

“…The great advantage of this approach is that all the eigenvalues of the evolution operator U͑E͒ can be used in the analysis. A characteristic quantity I 0 , defined by I 0 R s 2 P͑s͒ ds͞2, is used to examine the localization property, where P͑s͒ is the level-spacing distribution function of the quasienergies [11]. It is well known that I 0 1 for localized states [11].…”

Section: -1mentioning

confidence: 99%

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Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing

et al. 2001

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The electronic eigenstates of a quantum Hall (QH) system are chiral states. Strong inter-Landau-band mixings among these states can occur when the bandwidth is comparable to the spacing of two adjacent Landau bands. We show that mixing of localized states with opposite chirality can delocalize electronic states. Based on numerical results, we propose the existence of a metallic phase between two adjacent QH phases and between a QH phase and the insulating phase. This result is consistent with nonscaling behaviors observed in recent experiments on a quantum Hall liquid-to-insulator transition. DOI: 10.1103/PhysRevLett.87.216802 PACS numbers: 73.43. -f, 71.30. +h, 73.20.Jc Recently there has been a great renewal of interest on transitions from integer quantum Hall effect (IQHE) states to an insulator [1][2][3][4][5]. According to the scaling theory of localization [6], all electrons in a disordered two-dimensional system are localized in the absence of a magnetic field. In the presence of a strong magnetic field, a series of disorder-broadened Landau bands (LBs) will appear, and extended states reside at the centers of these bands while states at other energies are localized. The integrally quantized Hall (QH) plateaus are observed when the Fermi level lies in the localized states, with the value of the Hall conductance, s xy ne 2 ͞h, related to the number of filled LBs ͑n͒. As a function of the magnetic field, the Hall conductance jumps from one QH plateau to another when the Fermi energy crosses an extended-state level. Many previous studies [1][2][3][4][5] have been focused on how such a transition occurs.One overlooked issue regarding IQHE is the nature of a transition from one QH plateau to another. All existing theories assume it to be a continuous quantum phase transition. The fingerprint of a continuous phase transition is scaling laws around the transition point, and this assumption is mainly due to the early scaling experiments [7]. In the case of IQHE, a continuous quantum phase transition means algebraic divergence of the longitudinal Hallresistivity slope in temperature T at the transition point. However, recent experiments [5] showed that such slopes remain finite when they are extrapolated to T 0. This implies a nonscaling behavior around a transition point, contradicting the expectation of continuous quantum phase transitions suggested by the theories. It also means that one should reexamine the nature of plateau transitions.In this Letter we show that a narrow metallic phase may exist between two adjacent IQHE phases and between an IQHE phase and an insulating phase when the effect of interband mixing of opposite chirality is taken into account. Thus, it corresponds to two consecutive quantum phase transitions instead of one when the Hall conductance jumps from one plateau to another, consistent with the nonscaling behavior observed in experiments.According to the semiclassical theory [8], an electronic state in a strong magnetic field and in a smooth potential can be decomposed into a rapid c...

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Section: -1mentioning

confidence: 99%

Section: -1mentioning

confidence: 99%

Section: -1mentioning

confidence: 99%

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Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing

et al. 2001

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“…As a model of quantum percolation we employ the Chalker-Coddington (CC) model 26 which is one of the main "tools" for the quantitative study of the QH transition. [27][28][29][30][31][32][33][34][35][36][37][38] The CC model is a strong magnetic field (chiral) limit of a general network model, first introduced by Shapiro 39 and later utilized for the study of localization-delocalization transitions within different universality classes. [40][41][42][43][44][45] In addition to describing the QH transition, the CC model applies to a much broader class of critical phenomena since the correspondence between the CC model and thermodynamic, field-theory and Dirac-fermions models 46-54 was demonstrated.…”

Section: Introductionmentioning

confidence: 99%

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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“…A fundamental difference between level statistics property of extended states and localized states is that P (s) at s = 0 is zero for extended states and one for localized states. We shall follow the approach proposed by Klesse and Metzler 43 . A quantum state of a network model can be expressed by a vector whose components are electronic wave-function amplitudes on the links.…”

Section: The Application Of Level-statistics Technique On the Nementioning

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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Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

Cited by 52 publications

References 24 publications

Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing

Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing

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

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