Enclosed flux dependence of the eigenvalue spectrum: localisation and quantised Hall conductivity in a two-dimensional electron gas

The authors consider a two-dimensional electron gas in a strong magnetic field and confined by an infinite potential to a strip of finite width. The dependence of the eigenvalue spectrum on the choice of origin for a Landau-gauge vector potential has been examined numerically for the case in which a weak random potential is also present. For an electric potential difference across the system which is large compared with the Landau level width they find that the behaviour is similar to the semiclassical situation in which states may be associated with equal-potential contours and is in agreement with earlier work. However for an electric potential difference which is small compared with the Landau level width they find more complicated behaviour in disagreement with the recent study of Aoki (1982,1983).