Hall Current Distributions in Quatum Hall Effect on Finite Cylinder Surface

Using the linear response theory, the Hall current distributions in the quantum Hall regime are calculated numerically for two dimensional systems of non- interacting electrons, confined to an area of a finite width. At the low filling factor region, the local current density is enhanced around the localized states. Such current density is much stronger than that in the impurity-free case, although the Hall conductivity, which is obtained by integrating the current density over the system, is much smaller than that in the impurity-free case. With the increase of the filling factor, the local enhancement spreads over the whole system. The current, however, flows uniformly almost in the same way as in the impurity-free case, when the Fermi level is in the bulk band gap, i.e., in the edge state region. It shows that the strong spatial fluctuations of the Hall current are locally compensated.