Non-Abelian Two-component Fractional Quantum Hall States

Abstract

A large class of fractional quantum Hall (FQH) states can be classified according to their pattern of zeros, which describes the order of zeros in ground state wave functions as various clusters of electrons are brought together. The pattern-of-zeros approach can be generalized to systematically classify multilayer/spin-unpolarized FQH states, which has led to the construction of a class of non-Abelian multicomponent FQH states. Here we discuss some of the simplest non-Abelian two-component states that we find and the possibility of their experimental realization in bilayer systems at $\nu =2/3$, 4/5, 4/7, 4/9, 1/4, etc.

4+epsilon pages

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Cited by in corpus (18)

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• Interlayer fractional quantum Hall effect in a coupled graphene double-layer
• Evidence for pairing states of composite fermions in double-layer graphene
• Floquet Mechanism for Non-Abelian Fractional Quantum Hall States
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• Light-induced fractional quantum Hall phases in graphene
• Abelian and non-Abelian statistics in the coherent state representation
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Engineering Quantum Hall Phases in Synthetic Bilayer Graphene System
• Identification of topological order in the fractional quantum Hall state at $\nu =1/4$
• Observation of 1/3 fractional quantum Hall physics in balanced large angle twisted bilayer graphene
• Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect
• Interlayer correlated fractional quantum Hall state in the ν = 4/5 bilayer system
• Variational wavefunctions for fractional topological insulators
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid
• Near-field heat transfer and drag resistance in bilayers of composite fermions
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$