Insulating to relativistic quantum Hall transition in disordered graphene

In two dimensional (2D) electron systems with an arbitrary weak elastic disorder, the scaling theory of localization predicts that at zero temperature all electron states are localized, resulting in an insulating system1,2. The transition from the high temperature regime characterized by a metallic behavior to the insulating one is still debated for 2DEGs3 and is even more controversial for graphene, where the relativistic nature of the excitations should hinder localization, at least for certain types of disorder4. Nevertheless, experiments show that in the presence of intervalley scattering, electrons in graphene are subject to localization, with a crossover from strong localization5 to weak localization6 behavior when the localization length ξ increases far beyond the phase coherence length Lϕ. The application of a perpendicular magnetic field can lead to the emergence of criticality in 2D disordered systems. At low field it increases the localization length by breaking the time reversal symmetry, it can therefore suppress localization. At high magnetic fields Landau levels are formed, with extended states near the band centers, which can account for electron transport in the quantum Hall (QH) regime. They also bring into play a new length scale, that is the magnetic length nm, here B is the magnetic field. Electron localization induced by disorder is also a key component of the QH effect, notably accounting for the finite width of the transverse magnetoresistance plateaus, and its role has been recently addressed in literature for graphene7,8. Here we discuss its relevance for the insulator-to-quantum Hall conductor (Ins-QH) transition at low field, where graphene proves itself as an ideal tool due to the robustness of Landau levels with respect to both disorder and temperature, arising from the large cyclotron gap . The high field case has also been discussed in litterature9. The peculiarity of our samples is evident if we compare the Drude mobility of the graphene, where a fully developed QH effect was found, on the order of few hundred cm2V−1s−1, to that of the disordered 2DEGs where the Ins-QH transition has been generally observed, typically on the order of several to several tens of thousands cm2V−1s−1 10,11,12,13,14,15.