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Interplay between lattice-scale physics and the quantum Hall effect in graphene

Graphene's honeycomb lattice structure underlies much of the remarkable physics inherent in this material, most strikingly through the formation of two ``flavors'' of Dirac cones for each spin. In the quantum Hall regime, the resulting flavor degree of freedom leads to an interesting problem when a Landau level is partially occupied. Namely, while Zeeman splitting clearly favors polarizing spins along the field, precisely how the states for each flavor are occupied can become quite delicate. Here we focus on clean graphene sheets in the regime of quantum Hall ferromagnetism, and discuss how subtler lattice-scale physics, arising either from interactions or disorder, resolves this ambiguity to measurable consequence. Interestingly, such lattice-scale physics favors microscopic symmetry-breaking order coexisting with the usual liquid-like quantum Hall physics emerging on long length scales. The current experimental situation is briefly reviewed in light of our discussion.