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Random network models with variable disorder of geometry

A. Klümper, W. Nuding, and A. Sedrakyan
Phys. Rev. B 100, 140201(R) – Published 2 October 2019
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Abstract

Recently it was shown [I. A. Gruzberg, A. Klümper, W. Nuding and A. Sedrakyan, Phys. Rev. B 95, 125414 (2017)] that taking into account random positions of scattering nodes in the network model with U(1) phase disorder yields a localization length exponent 2.37±0.011 for plateau transitions in the integer quantum Hall effect. This is in striking agreement with the experimental value of 2.38±0.06. Randomness of the network was modeled by replacing standard scattering nodes of a regular network by pure tunneling (respectively, reflection) with probability p where the particular value p=1/3 was chosen. Here we investigate the role played by the strength of the geometric disorder, i.e., the value of p. We consider random networks with arbitrary probability 0<p<1/2 for extreme cases and show the presence of a line of critical points with varying localization length indices having a minimum located at p=1/3.

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  • Received 6 July 2019
  • Revised 19 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.140201

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Klümper and W. Nuding

  • Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany

A. Sedrakyan

  • Yerevan Physics Institute, Br. Alikhanian 2, Yerevan 36, Armenia and International Institute of Physics, Natal, Brazil

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Issue

Vol. 100, Iss. 14 — 1 October 2019

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