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 R-0(H) undergoes a 1000-fold increase from similar to 10 k Omega to 40 M Omega 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 H-c. Results from five samples show that H-c depends systematically on the disorder, as measured by the offset gate voltage V-0. Samples with small V-0 display a smaller critical field H-c. Empirically, the steep increase in R-0 fits accurately a Kosterlitz-Thouless-type correlation length over three decades. The curves of R-0 vs T at fixed H approach the thermal-activation form with a gap Delta similar to 15 K as H -> H-c(-), consistent with a field-induced insulating state.