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 $\Delta \nu \propto T^{\kappa }$ with a scaling exponent $\kappa =0.37\pm 0.05$. Similarly the maximum derivative of the quantum Hall plateau transitions $(d{\sigma }_{xy}/d\nu {)}^{max}$ scales as $T^{-\kappa }$ with a scaling exponent $\kappa =0.41\pm 0.04$ 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.

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