Scaling in Plateau-to-Plateau Transition: A Direct Connection of Quantum Hall Systems with Anderson Localization Model

TL;DR

This study investigates the quantum Hall plateau transition at ultra-low temperatures, revealing perfect power-law scaling, a finite-size saturation effect, and critical exponents linking quantum Hall systems with Anderson localization.

Contribution

It provides the first direct measurement of critical exponents and demonstrates a finite-size effect causing scaling saturation in quantum Hall transitions.

Findings

Power-law scaling with rac=0.42 observed from 1.2K to 12mK

Scaling terminates sharply at T_srac{10mK}

Localization length exponent rac=2.38 and dynamic exponent z=1

Abstract

The quantum Hall plateau transition was studied at temperatures down to 1 mK in a random alloy disordered high mobility two-dimensional electron gas. A perfect power-law scaling with \kappa=0.42 was observed from 1.2K down to 12mK. This perfect scaling terminates sharply at a saturation temperature of T_s~10mK. The saturation is identified as a finite-size effect when the quantum phase coherence length (L_{\phi} ~ T^{-p/2}) reaches the sample size (W) of millimeter scale. From a size dependent study, T_s \propto W^{-1} was observed and p=2 was obtained. The exponent of the localization length, determined directly from the measured \kappa and p, is \nu=2.38, and the dynamic critical exponent z = 1.