Scaling of the quantum-Hall plateau-plateau transition in graphene

TL;DR

This study investigates the temperature scaling behavior of quantum Hall transitions in graphene, confirming universal critical exponents for higher Landau levels and revealing unique behavior in the zeroth level.

Contribution

It provides experimental evidence for universal scaling exponents in graphene's quantum Hall transitions and discusses the anomalous behavior of the zeroth Landau level.

Findings

Scaling exponents for higher Landau levels are approximately 0.37 and 0.41.

Universal critical scaling behavior is confirmed for N=1 and N=2 Landau levels.

The zeroth Landau level shows temperature-independent behavior, deviating from universal scaling.

Abstract

The temperature dependence of the magneto-conductivity in graphene shows that the widths of the longitudinal conductivity peaks, for the N=1 Landau level of electrons and holes, display a power-law behavior following $\Delta \nu \propto T^{\kappa}$ with a scaling exponent $\kappa = 0.37\pm0.05$. Similarly the maximum derivative of the quantum Hall plateau transitions $(d\sigma_{xy}/d\nu)^{max}$ scales as $T^{-\kappa}$ with a scaling exponent $\kappa = 0.41\pm0.04$ for both the first and second electron and hole Landau level. These results confirm the universality of a critical scaling exponent. In the zeroth Landau level, however, the width and derivative are essentially temperature independent, which we explain by a temperature independent intrinsic length that obscures the expected universal scaling behavior of the zeroth Landau level.