Unveiling quantum Hall transport by Efros-Shklovskii to Mott variable-range hopping transition in graphene

Abstract

The quantum Hall effect is universal and expected to occur in all two-dimensional electron systems in perpendicular high-magnetic field. We revisit quantum localization thanks to the high-energy scale of the quantum Hall effect in graphene, where the electron dynamics obey the Dirac equation. We solve a long debated question on the nature of electron transport in the transition region between Hall resistance plateaus. Is it of metallic or of variable-range hopping type as proposed, respectively, by Pruisken and Polyakov-Shklovskii? To the best of our knowledge, no experiment was able to discriminate between these models. Here, measurements of the conductance peak width scaling exponents with both temperature and current and determination of the localization length validates the variable-range hopping scenario. This shows that the usual assumption of a metallic behavior of the two-dimensional electron gas (2DEG) between Hall resistance plateaus is unnecessary for macroscopic samples.