Michael R. Peterson, Chetan Nayak
We construct an effective Hamiltonian for electrons in the fractional quantum Hall regime for GaAs and graphene that takes into account Landau level mixing (for both GaAs and graphene) and sub-band mixing (for GaAs, due to the non-zero-width of the quantum well). This mixing has the important qualitative effect of breaking particle-hole symmetry as well as renormalizing the strength of the inter-particle interactions. Both effects could have important consequences for the prospect that the fractional quantum Hall effect at $\nu = 5/2$ is described by states that support non-Abelian excitations such as the Moore-Read Pfaffian or anti-Pfaffian states. For GaAs, Landau level and sub-band mixing break particle-hole symmetry in all Landau levels and sub-band mixing, due to finite-thickness, causes additional short-distance softening of the Coulomb interaction, further renormalizing the Hamiltonian. We find that in graphene, Landau-level mixing only breaks particle- hole symmetry outside of the lowest Landau level ($N\neq 0$). Landau level mixing is likely to be especially important in graphene since the Landau-level mixing parameter is independent of the external magnetic field and is of order one. Our realistic Hamiltonians will serve as starting points for future numerical studies.
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http://arxiv.org/abs/1303.1541
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