Two-dimensional electron transport in the presence of magnetic flux vortices

We have considered the conductivity properties of a two dimensional electron gas (2DEG) in two different kinds of inhomogeneous magnetic fields, i.e. a disordered distribution of magnetic flux vortices, and a periodic array of magnetic flux vortices. The work falls in two parts. In the first part we show how the phase shifts for an electron scattering on an isolated vortex, can be calculated analytically, and related to the transport properties through a force balance equation. In the second part we present numerical results for the Hall conductivity of the 2DEG in a periodic array of flux vortices. We find characteristic peaks in the Hall conductance, when plotted against the filling fraction. It is argued that the peaks can be interpreted in terms of ``topological charge'' piling up across local and global gaps in the energy spectrum.