Experiments on Delocalization and University in the Integral Quantum Hall Effect

Wei, Huang; Tsui, D. C.; Paalanen, M. A.; Pruisken, A. M. M.

doi:10.1103/physrevlett.61.1294

Cited by 501 publications

(463 citation statements)

References 17 publications

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“…Thouless showed that localized states have zero Chern numbers 12 , which is easy to understand, because localized states are rather insensitive to changes in the boundary conditions used to calculate the Chern number 9 . This is verified by numerical calculations 10,11 , which find that non-zero Chern numbers appear near the centre of the Landau level, with a distribution in perfect agreement with the scaling theory of the integer quantum Hall effect [13][14][15] (IQHE).…”

supporting

confidence: 54%

Spectral weight transfer in the integer quantum Hall effect and its consequences

Zhou

Berciu

2007

Nature Phys

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The energy spectrum of a two-dimensional electron gas placed in a transversal magnetic field B consists of quantized Landau levels. In the absence of disorder, the degeneracy of each Landau level is N = B A/φ 0 , where A is the area of the sample and φ 0 = h/e is the magnetic flux quantum. With disorder, localized states appear at the top and bottom of the broadened Landau level, whereas states in the centre of the Landau level (the critical region) remain delocalized. This single-electron theory adequately explains most aspects of the integer quantum Hall effect 1 . One unnoticed issue is the location of the new states that appear in the Landau level with increasing B. Here, we show that they appear predominantly inside the critical region. This situation leads to a 'spectral ordering' of the localized states, which explains the stripes observed in measurements of the local inverse compressibility 2,3 , of two-terminal conductance 4 and of Hall and longitudinal resistances 5 without the need to invoke interactions as done in previous work 6-8 .The spectrum and eigenstates of a disorder-broadened Landau level can be studied with the well-established approach of diagonalizing the single-electron hamiltonianwhere V (r) is the disorder. We choose A(r) = (0, Bx) and apply periodic boundary conditions (PBCs) to a system of area A = L × L. Owing to the PBCs, the degeneracy of each Landau level, N = BL 2 /φ 0 , is an integer. Usually, in theoretical studies the magnetic field is kept fixed and the electron density n e or, equivalently, the filling factor ν = n e A/N, is swept by adjusting the Fermi energy E F .As the experiments mentioned above investigate the behaviour of various quantities in the (n e , B) plane, we need to understand how the spectrum changes when B is also tuned. Given the constraint that an integer number of fluxes must penetrate the sample, B can only change in discrete steps of φ 0 /L 2 . Therefore, we ask the following question: how do single-electron wavefunctions evolve when one more magnetic flux is inserted?Let |i, N , 1 ≤ i ≤ N be the eigenstates of a spin-polarized Landau level corresponding to a given disorder V (r) and a magnetic field B = N φ 0 /L 2 . The states are ordered by their energies E 1 < E 2 < ··· < E N (accidental degeneracies can be lifted with minute changes in V (r)).To see how the wavefunctions evolve when B increases, we calculate their disorder-averaged overlaps:where 1 ≤ i ≤ N and 1 ≤ j ≤ N + 1 label two eigenstates of the hamiltonian (1) with the same disorder potential but different magnetic fields. The overline indicates a disorder average. In the results presented here we typically average over 1,000 disorder realizations, and show results only for the spin-polarized lowest Landau level. Similar results are expected in higher Landau levels. The disorder potential V (r) is modelled as a sum of many shortrange, randomly placed gaussian scatterers. We show four sets of data, for L = 250, 400, 500, 750 nm, N = 50, 128, 200, 550 and therefore B = 1.654 T for the first t...

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supporting

confidence: 54%

Spectral weight transfer in the integer quantum Hall effect and its consequences

Zhou

Berciu

2007

Nature Phys

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“…Besides these universal scaling laws, there are other interesting universal aspects of the LDT, such as the existence of a single critical point (as opposed to a line of critical points) for the unitary symmetry class, universal values of the critical transport coefficients and universal renormalization flow-diagrams of the transport coefficients with the temperature or with the system-size. Such universal characteristics at the plateau-plateau (PPT) and plateau-insulator (PIT) transitions in the Integer Quantum Hall Effect (IQHE) have preoccupied the experimental [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and theoretical 22,[26][27][28][29][30][31][32][33][34][35] condensed matter communities for decades, resulting in some of the best experimental data and computer simulations available for a quantum transition. With the discovery of Topological Insulators (TI), [36][37][38][39][40][41][42][43] the principles of universality will receive renewed scrutiny.…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality at the Chern-to-normal insulator transition

Xue

Prodan

2013

Phys. Rev. B

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Using the non-commutative Kubo formula for aperiodic solids and a recently developed numerical implementation, we study the conductivity σ and resistivity ρ tensors as functions of Fermi level E F and temperature T, for models of strongly disordered Chern insulators. The formalism enabled us to converge the transport coefficients at temperatures low enough to enter the quantum critical regime at the Chern-to-trivial insulator transition. We find that the ρ xx -curves at different temperatures intersect each other at one single critical point, and that they obey a single-parameter scaling law with an exponent close to the universally accepted value for the unitary symmetry class. However, when compared with the established experimental facts on the plateau-insulator transition in the Integer Quantum Hall Effect, we find a universal critical conductance σ c xx twice as large, an ellipse rather than a semi-circle law, and absence of the Quantized Hall Insulator phase.

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“…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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Experiments on Delocalization and University in the Integral Quantum Hall Effect

Cited by 501 publications

References 17 publications

Spectral weight transfer in the integer quantum Hall effect and its consequences

Spectral weight transfer in the integer quantum Hall effect and its consequences

Quantum criticality at the Chern-to-normal insulator transition

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

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