THEORY OF THE FRACTIONAL QUANTUM HALL-EFFECT - THE 2-PHASE MODEL

A phenomenological theory of the quantum Hall effect in a large homoge neous sample based on the local-conductivity approach is proposed. We argue that a correlated electron system in the vicinity of a diagonal resistivity peak represents a random mixture of two phases: the quasie lectron and the quasihole phase originating from two neighboring point s of incompressibility. The two phases have different values of the lo cal Hall conductivity which are quantized at low temperatures due to l ocalization of quasiparticles by disorder. The effective diagonal resi stivity of this system is found to be small everywhere except in a nar row interval of filling factors near the percolation threshold where t he crossover between plateaus in the Hall resistivity takes place. Usi ng an exact symmetry transformation, we show that both components of t he resistivity tensor are related by a universal dependence which repr esents a semicircle. At low temperatures, the maximum value of the dia gonal resistivity is finite and is determined by the heights of adjace nt plateaus only.