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 $\sim$10 k$\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 5 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 acccurately a Kosterlitz-Thouless-type correlation length over 3 decades. The curves of $R_0$ vs. $T$ at fixed $H$ approach the thermal-activation form with a gap $\Delta\sim$15 K as $H\to H_c^{-}$, consistent with a field-induced insulating state.