Localization length exponent, critical conductance distribution and multifractality in hierarchical network models for the quantum hall effect

We study hierarchical network models which have recently been introduced to approximate the Chalker‐Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 5 (1997) 1422; Arovas et al., PRB 56 (1997) 4751). The hierarchical structure is due to a recursive method start...

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Bibliographic Details
Published inAnnalen der Physik Vol. 7; no. 3; pp. 159 - 173
Main Authors Weymer, Andreas, Janssen, Martin
Format Journal Article
LanguageEnglish
Published Leipzig WILEY-VCH Verlag 01.03.1998
WILEY‐VCH Verlag
Subjects
Mesoscopic systems
Multifractality
Quantum Hall effect
Renormalization group
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Summary:We study hierarchical network models which have recently been introduced to approximate the Chalker‐Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 5 (1997) 1422; Arovas et al., PRB 56 (1997) 4751). The hierarchical structure is due to a recursive method starting from a finite elementary cell. The localization‐delocalization transition occurring in these models is displayed in the flow of the conductance distribution under increasing system size. We numerically determine this flow, calculate the critical conductance distribution, the critical exponent of the localization length, and the multifractal exponents of critical eigenstates.
Bibliography:istex:2D2211682B04A50C17D2CA090A7ACC69E09A5DD1
Deutsche Forschungsgemeinschaft
ArticleID:ANDP2090070303
ark:/67375/WNG-1RD5B4C6-S
ISSN:0003-3804
1521-3889
DOI:10.1002/andp.2090070303