Schreiber FQH with Islands

An article that we have written at CQTS:

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• Hisham Sati$\phantom{-}$and$\phantom{-}$ Urs Schreiber:

  
  

  FQH Liquids with Flux-Expulsion Islands

  allow Nonabelian Anyons

  download: pdf, arXiv:2602.18748 cond-mat.mes-hall

  
  

  Europhysics Letters (2026)

  doi:10.1209/0295-5075/aea022

Abstract. The idea that topologically protected quantum states, such as anyons, may be attached to super/semiconductor heterostructures has received enormous attention, but experimental signatures in 1D systems remain elusive. Here we revisit theoretical underpinnings of anyons in 2D fractional quantum Hall systems (FQH), of which signatures have been experimentally observed by independent groups. We highlight novel theorems about the Hopfion or $\mathbb{C}P^1$-model understood as flux-quantization in 2-Cohomotopy, which retrodicts abelian FQH anyon properties in fine detail. Examining this theoretical model further, we find that islands of expelled flux enlarge the ground-state monodromy from an abelian group to a (framed spherical) braid group, nonabelian for two or more islands, so that nonabelian anyonic states become topologically admissible; superconducting islands are one candidate realization of such flux expulsion.

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This is a brief digest, in physics letter form, of some results from the article:

• Fractional Quantum Hall Anyons via the Algebraic Topology of exotic Flux Quanta

Related presentations:

• Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems

  talk at QMATH16, Munich (Sep 2025)