Tunneling and Universality in the Integer Quantum Hall Effect

TL;DR

This paper demonstrates that in the integer quantum Hall effect, tunneling alone results in a localization length exponent consistent with percolation theory, challenging previous semi-classical scaling assumptions.

Contribution

It provides an analytical and numerical analysis showing tunneling alone yields a percolation-like exponent, contrasting with earlier semi-classical predictions.

Findings

Omission of quantum interference yields nu=4/3

Tunneling alone does not produce nu=7/3

Results challenge semi-classical scaling assumptions

Abstract

We show analytically and numerically that omission of quantum interference from the Chalker-Coddington model of the integer quantum Hall effect gives a localization length exponent nu=4/3 as in ordinary two-dimensional percolation. Thus, contrary to semi-classical scaling arguments, tunneling alone does not lead to nu=7/3.