Abstract
We investigate the quantum Hall effect in a single Landau level in the presence of a square superlattice of δ-function potentials. The interplay between the superlattice spacing a_s and the magnetic length ℓ_B in clean system leads to three interesting characteristic regimes corresponding to a_s ℓ_B, a_s ≫ ℓ_B and the intermediate one where a_s ∼ ℓ_B . In the intermediate regime, the continuous magnetic translation symmetry breaks down to discrete lattice symmetry. In contrast, we show that in the other two regimes, the same is hardly broken in the topological band despite the presence of the superlattice. In the presence of weak disorder (white-noise) one typically expects a tiny fraction of extended states due to topological protection of the Landau level. Interestingly, we obtain a large fraction of extended states throughout the intermediate regime which maximizes at the special point a_s = √2π ℓ_B. We argue the superlattice induced percolation phenomenon requires both the breaking of the time reversal symmetry and the continuous magnetic translational symmetry. It could have a direct implication on the integer plateau transitions in both continuous quantum Hall systems and the lattice based anomalous quantum Hall effect.