Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field

We have investigated the behavior of the resistance of graphene at the $n=0$ Landau level in an intense magnetic field H. Employing a low-dissipation technique (with power P<3 fW), we find that at low temperature T, the resistance at the Dirac point R₀(H) undergoes a 1000-fold increase from ~10 kΩ to 40 MΩ within a narrow interval of field. The abruptness of the increase suggests that a transition to an insulating ordered state occurs at the critical field Hc. Results from five samples show that Hc depends systematically on the disorder, as measured by the offset gate voltage V₀. Samples with small V₀ display a smaller critical field Hc. Empirically, the steep increase in R₀ fits accurately a Kosterlitz-Thouless-type correlation length over three decades. The curves of R₀ vs T at fixed H approach the thermal-activation form with a gap Δ~15 K as H→Hc^-, consistent with a field-induced insulating state.