# Topological Phases & Anyons: State of the Field (October 2026)

Research dossier · v1 · updated 2026-10-30 · 4,056 words · 64 sources · 27 claims · verification: verified

This dossier covers topological insulators and semimetals, zero-field fractional Chern insulators in moire and graphene systems, anyon statistics, and the contested Majorana-readout evidence. The main takeaway is that topological band phases are firmly established, zero-field fractional Chern insulators are now reported in at least two material families, and, in the sources reviewed, no solid-state non-Abelian anyon has yet been unambiguously identified.

## Contents

- Executive summary
- Background and core concepts
- Timeline of key milestones
- State of the art
  - Quantum anomalous Hall states and magnetic topological insulators
  - Fractional and anomalous Chern insulators
  - Anyon statistics and interferometry
  - Non-Abelian platforms and Majorana modes
  - Topological semimetals and crystalline phases
  - Classical-wave and cold-atom realizations
  - Quantitative benchmarks
- Open problems and active debates
- Major programs and players
- Outlook: what to watch (near term)
- Key papers
- Glossary

## Sample findings

- Two-dimensional quantum spin Hall insulators and three-dimensional topological insulators have a bulk energy gap with symmetry-protected gapless boundary states.
- Chang et al. reported a zero-field anomalous Hall resistance equal to the quantized value h/e^2 in Cr-doped (Bi,Sb)2Te3 thin films.

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