Parafermions in a multilegged geometry: Towards a scalable parafermionic network

Abstract

Parafermionic zero modes are non-Abelian excitations which have been predicted to emerge at the boundary of topological phases of matter. Contrary to earlier proposals, here we show that such zero modes may also exist in multilegged star junctions of quantum Hall states. We demonstrate that the quantum states spanning the degenerate parafermionic Hilbert space may be detected and manipulated through protocols employing quantum antidots and fractional edge modes. Such star-shaped setups may be the building blocks of two-dimensional parafermionic networks.

7 pages, 4 figures. v2: Includes a new Supplemental Material + Minor changes to the article. v3: Published Version

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Measurement-Only Topological Quantum Computation
• 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
• Topological Kondo effect with Majorana fermions
• Fractional topological superconductors with fractionalized Majorana fermions
• A short introduction to Fibonacci anyon models
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Topological phase diagram of a three-terminal Josephson junction: From the conventional to the Majorana regime
• Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions
• Missing Shapiro steps and the $8\pi$-periodic Josephson effect in interacting helical electron systems
• Measurement-only topological quantum computation without forced measurements
• Clock model and parafermions in Rashba nanowires
• Insulating regime of an underdamped current-biased Josephson junction supporting ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ parafermions

Cited by in corpus (7)

• Majorana zero modes in Y-shape interacting Kitaev wires
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• Compatibility of Braiding and Fusion on Wire Networks
• Overlap of parafermionic zero modes at a finite distance
• Can Majorana zero modes in quantum Hall edges survive edge reconstruction?
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States
• Extending the planar theory of anyons to quantum wire networks