Finite-Size Scaling in the Dissipative Transport Regime Between Quantum Hall Plateaus

Abstract

The magnetoresistance of a two-dimensional electron gas shows a novel scaling behaviour in the dissipative transport regime between adjacent integer quantum Hall plateaus when studied in samples of different size. At low temperatures (≥ 25mK) the phase coherence length L in may exceed the size W of small samples (W ≥ 8µm). Under these conditions the width ΔB of the magnetic field region where dissipative transport is observed becomes independent of temperature. Then ΔB only depends on the size of the sample and increases with decreasing size. Thus the critical exponent v of the localization length ξ ∝ (ΔB)−v can be determined directly. The resulting exponent v = 2.3±0.1 does not depend on the specific sample and, furthermore, is independent of the (spin-resolved) Landau level. This experimental result agrees with the predictions of several theoretical approaches to the metal-insulator transition in the quantum Hall regime. The effect described occurs both in Hall bars and in Corbino geometries, with essentially identical results. On the other hand, in a Landau level where spin-splitting is not resolved, a considerably larger value of v = 6.5 ± 0.6 is observed for the localization length exponent.