Localization Length Exponent, Critical Conductance Distribution and Multifractality in Hierarchical Network Models for the Quantum Hall Effect

Details Localization Length Exponent, Critical Conductance Distribution and Multifractality in Hierarchical Network Models for the Quantum Hall Effect Localization Length Exponent, Critical Conductance Distribution and Multifractality in Hierarchical Network Models for the Quantum Hall Effect

1998-05-06

arxiv.org/abs/cond-mat/9805063v1

Annalen der Physik, 7 (1998) 159

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages REVTeX, 9 postscript figures and 1 postscript table

Scientific paper

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 56 1422 (1997); Arovas et al., PRB 56, 4751 (1997)). 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.

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