Hopping conductivity in the quantum Hall effect -- revival of universal scaling

Abstract

We have measured the temperature dependence of the conductivity ${\sigma }_{xx}$ of a two-dimensional electron system deep into the localized regime of the quantum Hall plateau transition. Using variable-range hopping theory we are able to extract directly the localization length $\xi$ from this experiment. We use our results to study the scaling behavior of $\xi$ as a function of the filling factor distance $|\delta \nu |$ to the critical point of the transition. We find for all samples a power-law behavior $\xi \propto |\delta \nu {|}^{-\gamma }$ with a universal scaling exponent $\gamma =2.3$ as proposed theoretically.

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