The Influence of Percolation in the generalized Chalker-Coddington Model

TL;DR

This paper numerically explores how classical percolation affects the quantum Hall transition using a generalized network model, revealing a new length scale linked to percolation properties.

Contribution

It introduces a generalized Chalker-Coddington model controlling classical saddle points and identifies a new length scale related to percolation effects.

Findings

A new microscopic length scale scales with exponent ~1.36

The length scale relates to classical percolation length with exponent 4/3

Spectral statistics are affected similarly to potential correlation length increase

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 $\xi$ and its exponent $\nu_p=4/3$. 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.