Quantum Hall Ferromagnetism in Graphene

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. When Zeeman and spin-orbit interactions are neglected, its Landau levels are fourfold degenerate, explaining the $4e^2/h$ separation between quantized Hall conductivity values seen in recent experiments. In this Letter we derive a criterion for the occurrence of interaction-driven quantum Hall effects near intermediate integer values of $e^2/h$ due to charge gaps in broken symmetry states.

Figure 1

Phase diagram for $SU(4)$ quantum Hall ferromagnetism in the $n=0$ and $n=1$ Landau levels of graphene. In our model the ordered region is bounded by a maximum value of ${\nu }_s$, the ratio of the density of Coulomb scatterers to the density of a full Landau level. ${\nu }_s$ is inversely proportional to the product of the sample mobility and the external field strength and order near integer filling factors requires the minimum values for this product indicated on the right-hand vertical axis.