Anderson localization and quantum Hall effect: Numerical observation of two-parameter scaling

Miklós Antal Werner, Arne Brataas, Felix Von Oppen, Gergely Zaránd

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

A two-dimensional disordered system of noninteracting fermions in a homogeneous magnetic field is investigated numerically. By using a modified Landau gauge, we explore the renormalization group flow of the longitudinal and Hall conductances and find that the flow is consistent with the predictions of Pruisken and Khmelnitskii. The extracted critical exponents agree with the results obtained by using transfer matrix methods. The necessity of a second scaling parameter is also demonstrated in the level curvature distribution. Near the critical point the distribution slightly differs from the prediction of random matrix theory, in agreement with previous works. Close to the quantum Hall fixed points the distribution is lognormal since here states are strongly localized.

Original languageEnglish
Article number125418
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume91
Issue number12
DOIs
Publication statusPublished - Mar 12 2015

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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