Superconducting analogue of the parafermion fractional quantum Hall states

Abstract

Read and Rezayi $Z_k$ parafermion wavefunctions describe $\nu =2+\frac{k}{kM+2}$ fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gates can be designed. However, there is no experimental evidence for these non-Abelian anyons to date. In this paper, we study the $\nu =2/k$ FQH-superconductor heterostructure and find the superconducting analogue of the $Z_k$ parafermion FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional (1D) chains each with a pair of counter-propagating modes. We show that by inducing intra-chain pairing and charge preserving backscattering with identical couplings, the 1D chains flow into gapless $Z_k$ parafermions when $k<4$. By studying the effect of inter-chain coupling, we show that every parafermion mode becomes massive except for the two outermost ones. Thus, we achieve a fractional topological superconductor whose chiral edge state is described by a $Z_k$ parafermion conformal field theory. For instance, we find that a $\nu =2/3$ FQH in proximity to a superconductor produces a $Z_3$ parafermion superconducting state. This state is topologically indistinguishable from the non-Abelian part of the $\nu =12/5$ Read-Rezay state. Both of these systems can host Fibonacci anyons capable of performing universal quantum computation through braiding operations.

11 pages, 3 figures

References in corpus (21)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Fractional topological superconductors with fractionalized Majorana fermions
• Classification of Topological Defects in Abelian Topological States
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Topological Quantum Compiling
• Measurement-Only Topological Quantum Computation via Tunable Interactions
• Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Braiding of non-Abelian anyons using pairwise interactions
• Fractional quantum Hall effect at zero magnetic field

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