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The Influence of Percolation in the generalized Chalker-Coddington Model

Marcus Metzler
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Abstract

We numerically investigate the influence of classical percolation on the quantum Hall localization-delocalization transition. This is accomplished within the framework of the generalized Chalker--Coddington network model which allows us to control the number of {\em classical} saddle points by setting the width $W$ of the saddle point distribution. It is found that increasing this width causes a new microscopic length scale to appear which depends on $W$ and scales with the exponent $X\approx 1.36$ which indicates a close connection to the classical percolation length $ξ$ and its exponent $ν_p=4/3$. Furthermore, the influence of an increase in $W$ on the spectral statistics of the quasienergies of the network model is investigated. An effect similar to the increase of the potential correlation length in the Landau model is seen.

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Marcus Metzler. 1998-09-22. The Influence of Percolation in the generalized Chalker-Coddington Model. https://doi.org/10.1143/jpsj.68.144

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