Nonabelian Anyons attached to Superconducting Islands in FQH Liquids

TL;DR

This paper explores the theoretical possibility of nonabelian anyons emerging in fractional quantum Hall systems with superconducting islands, providing a robust prediction based on advanced topological theorems.

Contribution

It introduces novel topological theorems to predict nonabelian anyonic states in FQH systems with superconducting islands, advancing understanding of topologically protected quantum states.

Findings

Theoretical prediction of nonabelian anyons in FQH systems with superconducting islands.

Application of Hopfion and $ ext{C}P^1$-model theorems to flux quantization.

Robust topological framework supporting potential experimental realization.

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, we demonstrate a robust prediction for possibly nonabelian anyonic states induced by superconducting islands.