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Abstract

The nature of states in the quantum Hall regime of graphene in higher Landau levels remains poorly under-stood partly because of the lack of a model that captures its valley-dependent symmetry breaking interactions. In this paper we develop systematically such a model, which interestingly, and in contrast to the N = 0 Landau level, features not only pure 8 function interactions, but also some of its derivatives. We show that this model can lead to qualitatively new ground states relative to the N = 0 Landau level, such as ground states with entangled spin and valley degrees of freedom that compete with simpler broken symmetry states. Moreover, at half-filling we have found a new phase that is absent in the N = 0 Landau level which combines characteristics of a valence-bond solid and an antiferromagnet. We discuss the estimation of parameters of this model based on recent compressibility experiments.