References & reading.
Foundational sources for the mathematical and physical ideas presented throughout the site. These are reading recommendations, not claims of direct quotation.
- M. Nakahara — Geometry, Topology and Physics
Mathematical foundations: manifolds, fiber bundles, gauge connections and characteristic classes.
- D. J. Thouless et al. (1982) — Quantized Hall Conductance in a Two-Dimensional Periodic Potential
TKNN relationship between Chern numbers and Hall response.
- M. V. Berry (1984) — Quantal Phase Factors Accompanying Adiabatic Changes
Foundational geometric phase derivation.
- D. Xiao, M.-C. Chang & Q. Niu (2010) — Berry Phase Effects on Electronic Properties
Review of Berry curvature and semiclassical transport.
- B. A. Bernevig & T. L. Hughes — Topological Insulators and Topological Superconductors
Band topology, edge modes, and symmetry-protected systems.
- M. Z. Hasan & C. L. Kane (2010) — Colloquium: Topological Insulators
Overview of time-reversal topological insulators.
- X.-G. Wen — Quantum Field Theory of Many-Body Systems
Topological order and fractionalization.
- A. Kitaev (2001) — Unpaired Majorana Fermions in Quantum Wires
Canonical Kitaev-chain model.
- A. Kitaev (2003) — Fault-tolerant Quantum Computation by Anyons
Anyonic/topological quantum computation.
- C. Nayak et al. (2008) — Non-Abelian Anyons and Topological Quantum Computation
Review of braiding and quantum computation.
- A. Kitaev (2003) — Fault-tolerant Quantum Computation by Anyons
Topological code context.
- J. K. Asbóth, L. Oroszlány & A. Pályi — A Short Course on Topological Insulators
Accessible SSH, Chern and edge-state derivations.
How to use the site
Each concept distinguishes the mathematical statement, physical mechanism, experimental manifestation and assumptions. Equations are rendered locally with bundled KaTeX. All pages work without an internet connection.