Quantum percolation and quantization of Hall resistance in two-dimensional electron gas

Abstract

A theory of the quantized Hall resistance ${R}_{\mathrm{xy}}$ in a two-dimensional electron gas is presented. The exactness of the quantization is explained as a purely topological effect. It is shown that lines of constant electrostatic potential represent an effective wave guide for electron waves. In the Corbino ring geometry the condition for quantization of ${R}_{\mathrm{xy}}$ is the existence of equipotentials encircling the central electrode. The quantum of ${R}_{\mathrm{xy}}=\frac{h}{{e}^{2}}$ is shown to be unaffected by a random scattering potential. Collapse of the Hall current on increasing disorder is interpreted as a percolation transition.