Quantized Hall conductance and edge states: Two-dimensional strips with a periodic potential

Abstract

We have investigated the energy levels of an electron in a periodic potential and a magnetic field, confined to a two-dimensional strip of infinite length but finite width, for two sets of boundary conditions. The bulk formula giving the quantized Hall conductance is explained in terms of a special gauge-invariance property of the edge states. This Communication clarifies the role of the geometry in the derivations of the quantized Hall effect.