Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases

Abstract

We examine the possibility of creating the Moore-Read Pfaffian in the lowest Landau level when the multicomponent Halperin 331 state (believed to describe quantum Hall bilayers and wide quantum wells at the filling factor $\nu =1/2$) is destroyed by the increase of tunneling. Using exact diagonalization of the bilayer Hamiltonian with short-range and long-range (Coulomb) interactions in spherical and periodic rectangular geometries, we establish that tunneling is a perturbation that drives the 331 state into a compressible composite Fermi liquid, with the possibility for an intermediate critical state that possesses some properties of the Moore-Read Pfaffian. These results are interpreted in the two-component BCS model for Cauchy pairing with a tunneling constraint. We comment on the conditions to be imposed on a system with fluctuating density in order to achieve the stable Pfaffian phase.

10 pages, 7 figures

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• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
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• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Non-Abelian phases in two-component $\nu =2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons
• Matrix Product State description of the Halperin States
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Disorder-generated non-Abelions
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Phase diagram of $\nu =\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Two-component parton fractional quantum Hall state in graphene
• Non-Abelian $\nu =1/2$ quantum Hall state in ${\Gamma }_8$ Valence Band Hole Liquid
• Fractional Quantum Hall Effect in n=0 Landau Band of Graphene with Chern Number Matrix
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Variational wavefunctions for fractional topological insulators
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Torus geometry eigenfunctions of an interacting multi-Landau level Hamiltonian
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids