Experimental studies of the localization transition in the quantum Hall regime.

Abstract

We study experimentally the localization-to-delocalization transition in the transport regime between adjacent integer-quantum-Hall plateaus. We use small Hall bar geometries at millikelvin temperatures so that the phase-breaking length exceeds the sample size. Under these conditions the width \ensuremath{\Delta}B of the transition region scales with the size W of the sample according to W\ensuremath{\propto}(\ensuremath{\Delta}B${)}^{\mathrm{\ensuremath{-}}\ensuremath{\nu}}$. We obtain a universal scaling exponent \ensuremath{\nu}=2.3\ifmmode\pm\else\textpm\fi{}0.1. This result agrees with the predictions of several theoretical approaches to the metal-insulator transition in the integer-quantum-Hall regime. The numerical result agrees with the findings of the trajectory network model (\ensuremath{\nu}=2.5\ifmmode\pm\else\textpm\fi{}0.5), the percolation picture including quantum tunneling (\ensuremath{\nu}=7/3), and recent numerical studies (e.g., \ensuremath{\nu}=2.34\ifmmode\pm\else\textpm\fi{}0.04). The temperature exponent of the inelastic-scattering rate can be measured in the same experiment. We obtain results in the range from p=2.7\ifmmode\pm\else\textpm\fi{}0.3 to p=3.4\ifmmode\pm\else\textpm\fi{}0.4, which are considerably larger than commonly assumed values. Small reproducible magnetoresistance fluctuations are observed, which do not substantially influence the scaling behavior. By studying the effect of current heating, it is shown that noise heating does not play a role in the measurements. We discuss the present results in comparison with previous experimental and theoretical investigations.