Transition from Abelian to non-Abelian quantum liquids in the second Landau level

Abstract

The search for non-Abelian quantum Hall states in the second Landau level is narrowed to the range of filling factors 7/3<ν_e<8/3. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at ν_e=5/2 (Moore--Read) and 12/5 (Read--Rezayi). Outside of it, the four-flux noninteracting composite fermion model is validated. The borderline ν_e=7/3 state is adiabatically connected to the Laughlin liquid, but its short-range correlations and charge excitations are different.

4 pages, 4 figures

References in corpus (16)

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• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Fractional Quantum Hall Effect in the Second Landau Level
• Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State
• Paired composite fermion wavefunctions
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
• Landau level mixing in the nu=5/2 fractional quantum Hall state
• Second Generation of Moore-Read Quasiholes in a Composite Fermion Liquid
• Effect of Landau Level Mixing on Braiding Statistics

Cited by in corpus (36)

• Nonconventional odd denominator fractional quantum Hall states in the second Landau level
• Landau Level Mixing and the Fractional Quantum Hall Effect
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Landau level mixing and the emergence of Pfaffian excitations for the 5/2 fractional quantum Hall effect
• Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
• Fractional charge and fractional statistics in the quantum Hall effects
• Hunting for Majoranas
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Role of exciton screening in the 7/3 fractional quantum Hall effect
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• Competing Topological Orders in the nu=12/5 Quantum Hall State
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• The enigmatic 12/5 fractional quantum Hall effect
• Tripartite Composite Fermion States
• A note contrasting two microscopic theories of the fractional quantum Hall effect
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Skyrmions in the Moore-Read state at nu=5/2
• The enigma of the $\nu =2+\frac{3}{8}$ fractional quantum Hall effect
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Anomalous Gap Reversal of the $3+1/3$ and $3+1/5$ Fractional Quantum Hall States
• Shape of the magnetoroton at $\nu =1/3$ and $\nu =7/3$ in real samples
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
• Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Particle-hole Asymmetry of Fractional Quantum Hall States in the Second Landau Level of a Two-dimensional Hole System
• Stability of the k=3 Read-Rezayi state in chiral two-dimensional systems with tunable interactions
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Search for electron liquids with non-Abelian quasiparticles
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures