Séminaire du LPTMS: Cécile Repellin


14:00 - 15:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405

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

Cécile Repellin (MPI, Dresden, Allemagne)

The possibility of realizing anyons — quasiparticles with fractional  exchange statistics — is an exciting prospect in the field of  interacting topological phases. Non-abelian anyons, whose exchange is  characterized by a matrix rather than a simple phase, are of the most  exotic kind. They are highly sought after as they could be used as  qubits for quantum computation intrinsically immune to decoherence. While non-abelian anyons are expected to appear in the fractional  quantum Hall effect, engineering systems that purposefully favor their  emergence might be a better strategy to probe their properties. Progress  in creating quantum devices with Majorana bound states represents an  important achievement in this direction. Realizing the even more elusive  parafermions, which unlike Majoranas could support universal quantum  computation, would be an exciting next step.

Parafermion states have been envisioned to occur in heterostructures  using fractional quantum Hall (FQH) states and superconductors. Existing  theoretical studies of these systems have been entirely based on  effective theories of fractional quantum Hall edge states which cannot  offer any quantitative analysis of competing energy scales, correlation  lengths etc. To fill this gap, we propose and implement a numerical  setup for studying edge states of FQH droplets with a superconducting  instability. Using exact diagonalization, we report the first  observation in a fully microscopic model of gapped FQH edge modes with  topological degrees of freedom. The topological nature of these modes is  probed through fractional Josephson effect and flux insertion, and  evidence the cooper pairing of fractionalized quasiparticles.


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