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

Abstract

We have measured the temperature dependence of the conductivity $σ_{xx}$ 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 $ξ$ from this experiment. We use our results to study the scaling behavior of $ξ$ as a function of the filling factor distance $|δν|$ to the critical point of the transition. We find for all samples a power-law behavior $ξ\propto|δν|^{-γ}$ with a universal scaling exponent $γ= 2.3$ as proposed theoretically.