The Influence of Percolation in the generalized Chalker-Coddington Model
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≈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.