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

MPG-Autoren
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Repellin,  Cecile
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

Externe Ressourcen
Volltexte (frei zugänglich)

1707.08579
(Preprint), 16KB

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Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
Zitation

Repellin, C., Cook, A. M., Neupert, T., & Regnault, N. (2018). Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures. npj Quantum Materials, 3: 14. doi:10.1038/s41535-018-0085-4.


Zitierlink: http://hdl.handle.net/21.11116/0000-0001-5104-F
Zusammenfassung
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 nu = 1/3 states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional 6 pi 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.