Graphene flakes deposited on SiO2 substrates were considered, in the early times of their discovery, as perfect two-dimensional mono-layers of carbon atoms arranged in a honeycomb lattice. However, it was soon realised that their interaction with the substrate leads to the formation of electron and hole puddles, turning graphene into an inhomogeneous medium . The fundamental electronic properties of graphene in the presence of charge puddles have been extensively studied both theoretically  and experimentally . However, little is known about their implications at very high magnetic field. For this purpose, pulsed-field magneto-transport experiments of up to 60T have been performed in disordered graphene samples having mobility in the range 2000 to 10 000 cm2/V.s.
Figure: Close to the charge neutrality point, the presence of charge puddles drive graphene into an inhomogeneous medium with fluctuating potential landscape. When a large magnetic field is applied, the Landau level structure evolve according to the local potential and allow the presence of mixed carriers (electrons and holes). As a consequence, the Hall effect vanishes at high field and low carrier density.
For high carrier density, the typical QHE for graphene is observed as a sequence of quantized plateaus of the Hall resistance and vanishing longitudinal resistance for filling factors ν=2, 6, 10 etc… On the other hand, as the system is driven close to the charge neutrality point, the Hall resistance is progressively attenuated suggesting the contribution of both electron/hole-type of carriers. This effect is directly attributed to the presence of local charge puddles which start to dominate the transport properties when the overall carrier density is low. In this regime, electron and hole-type carriers coexist and their ratio depends on the Fermi energy position within the LL band-structure, which is strongly magnetic field dependent. We show that the threshold magnetic field marking the onset of this effect is directly related to the mobility of the sample.
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This research was supported by EuroMagNET II under EU Contract No. 228043, by the French National Agency for Research (ANR) under Contract No. ANR-08-JCJC-0034-01. The authors would like to thank K.S. Novoselov and for providing some of the graphene samples used in this work.
This work was published in:
J.M. Poumirol et. al. Phys. Rev. B 82 (2010) 121401
J.M. Poumirol et. al. New J. Phys. 12 (2010) 083006
Members of the LNCMI implied in this work are:
J.M. Poumirol, W. Escoffier, B. Raquet, M. Goiran, A. Kumar