Parafermions in a multilegged geometry: Towards a scalable parafermionic network

TL;DR

This paper proposes a new multilegged star junction setup in quantum Hall states that can host and manipulate parafermionic zero modes, advancing towards scalable parafermionic quantum networks.

Contribution

It introduces a novel multilegged geometry for parafermionic zero modes, expanding potential architectures for topological quantum computation.

Findings

Parafermionic zero modes can exist in multilegged star junctions.

Detection and manipulation protocols using quantum antidots are demonstrated.

Star-shaped setups could serve as building blocks for 2D parafermionic networks.

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.