The quantised Hall effect in strong magnetic fields

Abstract

The Hall conductance is expressed in terms of classical drift trajectories in the high-H limit. The connection of sigma xy with the properties of edge states is established, which explains the quantisation of sigma xy. The quantisation is shown to be exact in the infinite system at zero temperature. The finite frequency effects are also discussed and the AC response is related to the geometrical characteristics of the equipotential lines of the external potential.