Percolation Approach to the Quantum Hall Effect

Abstract

The percolation description of electron states in a 2D electron gas in strong magnetic fields was developed in refs. [1–5]. Being essentially semi-classical, this picture alone is not sufficient to give a rigorous account of the most fundamental property of the integral QHE: the extraordinary precision of quantization of the Hall conductance. Nevertheless, the percolation description appears to be quite useful in that it allows to interpret in a simple manner a number of other experimental features of the QHE and relate them to a specific model of electronic states in the presence of disorder in the sample. In this work I shall review the basic picture, following refs. [3,4] as well as some unpublished work, mostly done in collaboration with R. F. Kazarinov.