Theory of the fractional quantum Hall effect: The two-phase model

Abstract

A phenomenological theory of the quantum Hall effect in a large homogeneous 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 quasielectron and the quasihole phase originating from two neighboring points of incompressibility. The two phases have different values of the local Hall conductivity which are quantized at low temperatures due to localization of quasiparticles by disorder. The effective diagonal resistivity of this system is found to be small everywhere except in a narrow interval of filling factors near the percolation threshold where the crossover between plateaus in the Hall resistivity takes place. Using an exact symmetry transformation, we show that both components of the resistivity tensor are related by a universal dependence which represents a semicircle. At low temperatures, the maximum value of the diagonal resistivity is finite and is determined by the heights of adjacent plateaus only.