We present temperature-dependent magneto-transport experiments around the charge neutrality point in graphene and determine the amplitude of potential fluctuations $s$ responsible for the formation of electron-hole puddles. The experimental value $s
approx 20$ meV is considerably larger than in conventional semiconductors which implies a strong localization of charge carriers observable up to room temperature. Surprisingly, in the quantized regime, the Hall resistivity overshoots the highest plateau values at high temperatures. We demonstrate by model calculations that such a peculiar behavior is expected in any system with coexisting electrons and holes when the energy spectrum is quantized and the carriers are partially localized.
We have measured the quantum Hall activation gaps in bilayer graphene at filling factors $ u=pm4$ and $ u=pm8$ in high magnetic fields up to 30 T. We find that energy levels can be described by a 4-band relativistic hyperbolic dispersion. The Landau
level width is found to contain a field independent background due to an intrinsic level broadening and a component which increases linearly with magnetic field.
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 $Delta u propto T^{kappa}$ with
a scaling exponent $kappa = 0.37pm0.05$. Similarly the maximum derivative of the quantum Hall plateau transitions $(dsigma_{xy}/d u)^{max}$ scales as $T^{-kappa}$ with a scaling exponent $kappa = 0.41pm0.04$ 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.
We have performed a metrological characterization of the quantum Hall resistance in a 1 $mu$m wide graphene Hall-bar. The longitudinal resistivity in the center of the $ u=pm 2$ quantum Hall plateaus vanishes within the measurement noise of 20 m$Omeg
a$ upto 2 $mu$A. Our results show that the quantization of these plateaus is within the experimental uncertainty (15 ppm for 1.5$ mu$A current) equal to that in conventional semiconductors. The principal limitation of the present experiments are the relatively high contact resistances in the quantum Hall regime, leading to a significantly increased noise across the voltage contacts and a heating of the sample when a high current is applied.
