Theory of broken symmetry quantum Hall states in the $N=1$ Landau level of Graphene

Abstract

We study many-body ground states for the partial integer fillings of the $N=1$ Landau level in graphene, by constructing a model that accounts for the lattice scale corrections to the Coulomb interactions. Interestingly, in contrast to the $N=0$ Landau level, this model contains not only pure delta function interactions but also some of its derivatives. Due to this we find several important differences with respect to the $N=0$ Landau level. For example at quarter filling when only a single component is filled, there is a degeneracy lifting of the quantum hall ferromagnets and ground states with entangled spin and valley degrees of freedom can become favourable. Moreover at half-filling of the $N=1$ Landau level, we have found a new phase that is absent in the $N=0$ Landau level, that combines characteristics of the Kekulé state and an antiferromagnet. We also find that according to the parameters extracted in a recent experiment, at half-filling of the $N=1$ Landau level graphene is expected to be in a delicate competition between an AF and a CDW state, but we also discuss why the models for these recent experiments might be missing some important terms.

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Cited by in corpus (8)

• Global phase diagram of charge neutral graphene in the quantum Hall regime for generic interactions
• Spin-valley entangled quantum Hall states in graphene
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Magnon transmission across $\nu =1|-1|1$ mono-layer graphene junction as a probe of electronic structure
• Uniquely identifying quantum Hall phases in charge neutral graphene