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

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 $Δν\propto T^κ$ with a scaling exponent $κ= 0.37\pm0.05$. Similarly the maximum derivative of the quantum Hall plateau transitions $(dσ_{xy}/dν)^{max}$ scales as $T^{-κ}$ with a scaling exponent $κ= 0.41\pm0.04$ 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.