Scaling Behavior and Variable Hopping Conductivity in the Quantum Hall Plateau Transition

TL;DR

This study investigates the temperature-dependent resistivity during the quantum Hall plateau transition, comparing experimental data with theoretical scaling functions, revealing region-specific validity of different models.

Contribution

It provides a detailed experimental analysis of the scaling behavior of resistivity and compares two theoretical models, highlighting their applicability in different regimes.

Findings

Different scaling functions are valid in distinct regions.

Experimental data supports the variable range hopping theory in certain regimes.

Results clarify the applicability of scaling theories in quantum Hall transitions.

Abstract

We have measured the temperature dependence of the longitudinal resistivity $% \rho_{xx}$ of a two-dimensional electron system in the regime of the quantum Hall plateau transition. We extracted the quantitative form of scaling function for $\rho_{xx}$ and compared it with the results of ordinary scaling theory and variable range hopping based theory. We find that the two alternative theoretically proposed scaling functions are valid in different regions.