The mesoscopic chiral metal-insulator transition

Kettemann, Stefan; Krämer, B.; Ohtsuki, Tomi

doi:10.1134/1.1813688

Cited by 5 publications

(13 citation statements)

References 52 publications

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“…It is remarkable that the conductance plateau transitions occur not at the peaks of the density of states, but are shifted up from the middle of the Landau bands. Furthermore, the CMIT observed for 0 η = [40,55] …”

Section: Unconventional Quantum Hall Transitions For Correlated Disordermentioning

confidence: 94%

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The quantum Hall effect in narrow quantum wires

Struck

Kawarabayashi

Zhuravlev

et al. 2008

Physica Status Solidi (b)

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The quantum phase diagram of disordered quantum wires in a strong magnetic field is reviewed. For uncorrelated disorder potential the 2‐terminal conductance, as calculated with the numerical transfer matrix method, shows zero temperature discontinuous transitions between exactly integer plateau values and zero. This is explained by the dimensional crossover of the bulk localisation length, which drives a transition from delocalised to localised edge states. In the thermodynamic limit, fixing the aspect ratio of the wire, there is a transition from the one dimensional chiral metal of extended edge states to localisation along the wire. In the vicinity of this chiral metal insulator transition (CMIT), states are identified which are superpositions of edge states with opposite chirality. The bulk contribution of such states is found to decrease with increasing wire width. Based on exact diagonalisation results for the eigenstates and their participation ratios, we conclude that these states are characteristic for the CMIT, and have the appearance of nonchiral edges states. Thereby these states are distinguishable from other states in the quantum Hall wire, namely, extended edge states, two‐dimensionally (2D) localized, quasi‐1D localized, and 2D critical states. In the presence of spatially correlated random potential we find with the numerical transfermatrix method that the potential correlation results in a shift of quantized conductance plateaus in long wires proportional to the strength of the random potential. This shift is found to be insensitive to the strength of magnetic fields and the same for all plateaus. A semiclassical explanation of this effect is proposed. We conclude with an outlook on modfications of the quantum phase diagram due to the spin degree of freedom of the electrons and their interactions. We discuss the stability of the phase diagram at finite temperature. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Section: Unconventional Quantum Hall Transitions For Correlated Disordermentioning

confidence: 94%

“…[40,55]. We use the tight-binding model described by the following Hamilto- y L L = Two leads are attached to both ends of the system and the fixed boundary condition is assumed in the transverse direction.…”

Section: The Conductance Of Quantum Hall Wires With Uncorrelated Disomentioning

confidence: 99%

The quantum Hall effect in narrow quantum wires

Struck

Kawarabayashi

Zhuravlev

et al. 2008

Physica Status Solidi (b)

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“…12,15 In a 2DES with broken time reversal symmetry, scaling theory 16,17,18,19 and numerical scaling studies 13,20 find that the bulk localization length ξ is independent of the wire width,…”

Section: The Quantum Phase Diagram Of the Cmitmentioning

confidence: 99%

“…1), with hard wall boundary conditions at y = ±L bulk /2 and finite length L = 2000a. 12 Here we have assumed a square lattice with lattice spacing a. The disorder potential is uniformly distributed in an interval [−W/2, W/2].…”

Section: The Quantum Phase Diagram Of the Cmitmentioning

confidence: 99%

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Nonchiral edge states at the chiral metal-insulator transition in disordered quantum Hall wires

et al. 2005

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The quantum phase diagram of disordered wires in a strong magnetic field is studied as function of wire width and energy. The 2-terminal conductance shows zero temperature discontinuous transitions between exactly integer plateau values and zero. In the vicinity of this transition, the chiral metal insulator transition (CMIT), states are identified which are superpositions of edge states with opposite chirality. The bulk contribution of such states is found to decrease with increasing wire width. Based on exact diagonalisation results for the eigenstates and their participation ratios, we conclude that these states are characteristic for the CMIT, have the appearance of nonchiral edges states, and are thereby distinguishable from other states in the quantum Hall wire, namely, extended edge states, two-dimensionally (2D) localized, quasi-1-D localized, and 2D critical states.

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