FQH Liquids with Flux-Expulsion Islands allow Nonabelian Anyons

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 (FQH) systems, whose signatures have been experimentally observed by independent groups. Invoking 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 (surplus) 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.

arXiv comment7 pages, 2 figures; v2 (published version): wording adjusted to clarify, first, that (surplus) flux-expulsion is the required condition, while superconductivity is just the canonical candidate realization, and, second, that the result is lifting of the topological obstruction for nonabelian anyons and classification of their reps, not prediction of a specific braiding rep