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 $P<3\text{fW}$), we find that at low temperature $T$, the resistance at the Dirac point $R_0\left(H\right)$ undergoes a 1000-fold increase from $\sim 10\text{k}\Omega$ to $40\text{M}\Omega$ 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 $\Delta \sim 15\text{K}$ as $H\to H_c^{-}$, consistent with a field-induced insulating state.

• Received 4 February 2009

DOI:https://doi.org/10.1103/PhysRevB.79.115434