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 k to 40 M 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 H₂. Results from five samples show that H₂ depends systematically on the disorder, as measured by the offset gate voltage V₀. Samples with small V₀ display a smaller critical field H₂. 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 15 K as HH₂^-, consistent with a field-induced insulating state.