SEMICLASSICAL QUANTUM PERCOLATION IN THE QUANTUM HALL SYSTEM

We study localization of electrons moving in two dimensions in a smoothly varying potential and a strong perpendicular magnetic field. Classically, the localization-delocalization transition in this system is a percolation transition. However, tunneling changes the universality class of this transition. Using the semiclassical approximation that dominates close to criticality, we determine all the quantum corrected percolation exponents. In particular, we verify the value 7/3 for the delocalization exponent. We also argue that interference effects play a less important role in this problem than tunneling. © 1995 The American Physical Society.