Levitation and percolation in quantum Hall systems with correlated disorder

We investigate the integer quantum Hall system in a two dimensional lattice model with spatially correlated disorder by using the efficient method to calculate the Chern number proposed by Fukui $\mathit{\text{et}}\mathit{\text{al}}$. Distribution of charge density indicates that the extended states at the center of each Landau band have percolating current paths, which are topologically equivalent to the edge states that exist in a system with boundaries. As increasing the strength of disorder, floating feature is observed in an averaged Hall conductance as a function of filling factor. Its relation to the observed experiments is also discussed.