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.

arXiv comment7 pages, 4 figures. v2: Includes a new Supplemental Material + Minor changes to the article. v3: Published Version

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• Dynamics of parafermionic states in transport measurements
• Compatibility of Braiding and Fusion on Wire Networks
• Overlap of parafermionic zero modes at a finite distance
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• Extending the planar theory of anyons to quantum wire networks