Abstract
We study the interplay of particle-hole symmetry and fermion-vortex duality in multicomponent half-filled Landau levels, such as quantum Hall gallium arsenide bilayers and graphene. For the bilayer, we show that particle-hole-symmetric interlayer Cooper pairing of composite fermions leads to precisely the same phase as the electron exciton condensate realized in experiments. This equivalence is easily understood by applying the recent Dirac fermion formulation of to two components. It can also be described by Halperin-Lee-Read composite fermions undergoing interlayer pairing. A renormalization group analysis showing strong instability to interlayer pairing at large separation demonstrates that two initially decoupled composite Fermi liquids can be smoothly tuned into the conventional bilayer exciton condensate without encountering a phase transition. We also discuss multicomponent systems relevant to graphene, derive related phases including a gauge theory with spin-half visons, and argue for symmetry-enforced gaplessness under full flavor symmetry when the number of components is even.
- Received 12 December 2016
DOI:https://doi.org/10.1103/PhysRevB.95.085135
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