System-Size Dependence of Quantum Hall Transitions

Abstract

The quantum Hall plateau-to-insulator (plateau) transition is studied in small GaAs two-dimensional electron gas systems, where the system size L is comparable to or smaller than the correlation length L cor of potential fluctuation. At low temperatures, the transition depends on the system size but the dependence is not explained in terms of Anderson localization. At elevated temperatures, the transition width exhibits a power-law dependence but the exponent κ takes nonuniversal values. It is suggested that the transition crosses over from the well-known, Anderson localization dominated regime to the semiclassical percolation-dominated regime when the system size is reduced below L cor .