Scaling of the Quantum Hall Plateau Transition

Abstract

We examine the transition between quantum Hall plateaus considering a number of different experiments. Measurements of the temperature and frequency dependence in the variable-range hopping regime allow to determine the localization length ξ, confirming the predicted scaling behavior ξ ∝ |B-Bc|-γ with a universal critical exponent γ=2.3±0.2. For devices of reduced size we observe conductance fluctuations at the plateau transition. Their temperature dependence turns out to differ from the temperature dependence of the width of the plateau transition. In a third experiment the dynamical scaling of the transition width is addressed by conductivity measurements at microwave frequencies. We combine these measurements with data from other experiments on dynamical scaling and observe a universal scaling function with an exponent k=0.5±0.1. The resulting dynamical exponent z=0.9±0.3 shows the relevance of electron-electron interactions.KeywordsQuantum Phase TransitionTransition WidthScaling BehaviorLocalization LengthDynamical ExponentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.