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Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures


Repellin, Cécile; Cook, Ashley M; Neupert, Titus; Regnault, Nicolas (2018). Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures. npj Quantum Materials, 3(1):14.

Abstract

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin ν = 1/3 states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional 6π Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The versatility and efficiency of our setup make it a well suited method to tackle wider questions of edge phases and phase transitions in fractional quantum Hall systems.

Abstract

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin ν = 1/3 states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional 6π Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The versatility and efficiency of our setup make it a well suited method to tackle wider questions of edge phases and phase transitions in fractional quantum Hall systems.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Language:English
Date:1 December 2018
Deposited On:30 Nov 2018 14:29
Last Modified:30 Jan 2020 13:00
Publisher:Nature Publishing Group
ISSN:2397-4648
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1038/s41535-018-0085-4

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