Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells

Abstract

We study the nature of the ν=5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. We introduce a general method to analyze the Moore-Read Pfaffian state and its particle-hole conjugate, the anti-Pfaffian, under periodic boundary conditions in a "quartered" Brillouin zone scheme containing both even and odd numbers of electrons. We examine the rotational quantum numbers on the torus, and show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landau-level mixing the particle-hole symmetry is broken in such a way that the anti-Pfaffian is unambiguously favored, and becomes more robust in the vicinity of a transition to the compressible phase, in agreement with recent experiments.

4.5 pages, 3 figures

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• Graviton Chirality and Topological Order in the Half-filled Landau Level
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• The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels
• Observation of an anomalous density-dependent energy gap of the $\nu =5/2$ fractional quantum Hall state in the low density regime
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
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• Bootstrapping the Quantum Hall problem
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
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• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid
• Orbital Description of Landau Levels
• Fractional Quantum Hall Effects in HgTe Quantum Wells