Transport properties of two-dimensional disordered electron systems in strong magnetic fields

A numerical study of two-dimensional disordered electron systems in strong magnetic fields is performed. An extension to periodic boundary conditions is made, and the results for the ground and higher Landau sub-bands are obtained. The behaviours of the spatial extents of the eigenfunctions are investigated to study the Anderson localisation of the states near the edges of the Landau sub-bands, and the results are analysed in terms of the minimum metallic conductivity in this system. To further explore localisation from transport properties, the matrix elements of the current operator j have been calculated. It is shown that the matrix elements of j between localised states are smaller by one or two orders of magnitude than those between extended states. These results provide further evidence of the occurrence of the Anderson localisation in the present system from both the spatial behaviour of the wavefunctions and the transport properties.