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

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 $\nu =1/3$ 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.

arXiv comment12 pages, 9 figures

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Cited by in corpus (11)

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• Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe${}_2$
• Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions
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• Model wavefunctions for interfaces between lattice Laughlin states
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• Topologically protected flatness in chiral moiré heterostructures
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• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures