${\mathbb{Z}}_3$ parafermionic zero modes without Andreev backscattering from the $2/3$ fractional quantum Hall state

Abstract

Parafermionic zero modes are a novel set of excitations displaying non-Abelian statistics somewhat richer than that of Majorana modes. These modes are predicted to occur when nearby fractional quantum Hall edge states are gapped by an interposed superconductor. Despite substantial experimental progress, we argue that the necessary crossed Andreev reflection in this arrangement is a challenging milestone to reach. We propose a superconducting quantum dot array structure on a fractional quantum Hall edge that can lead to parafermionic zero modes from coherent superconducting forward scattering on a quantum Hall edge. Such coherent forward scattering has already been demonstrated in recent experiments. We show that for a spin-singlet superconductor interacting with loops of spin unpolarized $2/3$ fractional quantum edge, even an array size of order ten should allow one to systematically tune into a parafermionic degeneracy.

4 pages, 3 figures, 5 pages of supplementary material

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Observation of Majorana fermions with spin selective Andreev reflection in the vortex of topological superconductor
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Ballistic Majorana nanowire devices
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Inducing Superconducting Correlation in Quantum Hall Edge States
• Generalized Eilenberger theory for Majorana zero-mode-carrying disordered $p$-wave superconductors

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• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• Chiral supercurrent through a quantum Hall weak link
• Bosonization for fermions and parafermions
• Chiral Quasiparticle Tunneling Between Quantum Hall Edges in Proximity with a Superconductor
• Edge ${\mathbb{Z}}_3$ parafermions in fermionic lattices
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators
• Can Majorana zero modes in quantum Hall edges survive edge reconstruction?
• Emergent Haldane phase in an alternating bond ${\mathbb{Z}}_3$ parafermion chain
• Phase diagram of an extended parafermion chain