The Nature of Quantum Hall States near the Charge Neutral Dirac Point in Graphene

We investigate the quantum Hall (QH) states near the charge neutral Dirac point of a high mobility graphene sample in high magnetic fields ($B$). We find that the QH states at filling factors $\nu=\pm2$ show thermally activated behavior with an energy gap as large as $\sim890$ K at $B=45$ T. This large energy gap between the $n=0$ Landau level (LL) and the $n=1$ LL, enables us to observe a well-defined QH effect in graphene over a wide temperature range and even up to room temperature. In addition, the data reveal an activation energy gap at filling factor $\nu=1$, which is considerably larger than the previous studied spin states at $\nu=\pm4$ and shows a square root dependence on $B$, suggesting a many-body origin of this state. Such an origin is further supported by tilted field measurements, in which the $\nu=\pm1$ gaps are found to depend only on the normal component of the field with respect to the graphene plane. We therefore propose that the $\nu=\pm1$ states arise from the lifting of the sublattice degeneracy of the $n=0$ LL.