{"slug":"topological-matter","topic":"topological-matter","title":"Topological Phases & Anyons: State of the Field (October 2026)","summary":"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.","version":1,"published_at":"2026-10-30","updated_at":"2026-10-30","stats":{"words":4056,"citations":64,"claims":27,"timeline":20,"benchmarks":6,"open_problems":5,"key_papers":15,"glossary":15},"verification":{"status":"verified","method":"automated figure and citation-relevance triage against cited abstracts, targeted AI review with web checks of flagged statements, and a close-out pass hedging or removing unconfirmed statements; automated citation resolution","claims_checked":10,"issues_fixed":1,"verified_at":"2026-10-30"},"ai_assisted":true,"price":{"usd":"0.20","protocol":"x402","network":"eip155:84532","asset":"USDC"},"url":"https://space-kitty.com/dossiers/topological-matter","preview_url":"https://space-kitty.com/api/v1/dossiers/topological-matter/preview","purchase_url":"https://space-kitty.com/api/v1/dossiers/topological-matter","toc":[{"level":2,"text":"Executive summary","anchor":"executive-summary"},{"level":2,"text":"Background and core concepts","anchor":"background-and-core-concepts"},{"level":2,"text":"Timeline of key milestones","anchor":"timeline-of-key-milestones"},{"level":2,"text":"State of the art","anchor":"state-of-the-art"},{"level":3,"text":"Quantum anomalous Hall states and magnetic topological insulators","anchor":"quantum-anomalous-hall-states-and-magnetic-topological-insulators"},{"level":3,"text":"Fractional and anomalous Chern insulators","anchor":"fractional-and-anomalous-chern-insulators"},{"level":3,"text":"Anyon statistics and interferometry","anchor":"anyon-statistics-and-interferometry"},{"level":3,"text":"Non-Abelian platforms and Majorana modes","anchor":"non-abelian-platforms-and-majorana-modes"},{"level":3,"text":"Topological semimetals and crystalline phases","anchor":"topological-semimetals-and-crystalline-phases"},{"level":3,"text":"Classical-wave and cold-atom realizations","anchor":"classical-wave-and-cold-atom-realizations"},{"level":3,"text":"Quantitative benchmarks","anchor":"quantitative-benchmarks"},{"level":2,"text":"Open problems and active debates","anchor":"open-problems-and-active-debates"},{"level":2,"text":"Major programs and players","anchor":"major-programs-and-players"},{"level":2,"text":"Outlook: what to watch (near term)","anchor":"outlook-what-to-watch-near-term"},{"level":2,"text":"Key papers","anchor":"key-papers"},{"level":2,"text":"Glossary","anchor":"glossary"}],"sample_claims":["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."],"includes":["markdown","claims","timeline","benchmarks","open_problems","key_papers","glossary","bibliography"],"citation_count":64,"how_to_buy":"GET https://space-kitty.com/api/v1/dossiers/topological-matter with an x402 client ($0.20, USDC on Base Sepolia (testnet))."}