Percolation network in a smooth artificial potential

A percolation network of the edge states in an artificial potential of a gate-controlled antidot lattice has been studied in a high magnetic field. The longitudinal resistance of the antidot lattice shows a boxlike behavior in certain ranges of the magnetic field, because of the reflection of the topmost edge state by the saddle potential between two antidots. The riser between zero and quantized resistance shows a temperature dependence due to the broadening of the percolation transition by inelastic scattering. The shift of the transition point in magnetic field with the temperature is found to originate from the mixing between Landau levels due to the inelastic scattering. It allows us to separate the exponent of the scattering mechanism and the critical exponent in the localization-delocalization transition.