Disorder-Driven Metal-Topological Insulator Transition with Critical Exponent ν≈2.7 — E8 Intelligence Research

Abstract

FINDING: Topological insulators are bulk-insulating but surface/edge-conducting quantum phases, with disorder-driven metal-TI transitions showing critical exponent ν≈2.7. | MATH: Critical exponent ν≈2.7 (from arXiv:1211.5026v2); topological invariant (Z₂ index) classifying band structure; bulk-boundary correspondence linking edge states to bulk topology; no explicit golden-ratio or base-60 constants appear in the provided data. | CONNECTION: The Z₂ topological classification is rooted in time-reversal symmetry and lattice crystallography — the invariant is computed via parity eigenvalues at time-reversal-invariant momenta (TRIMs), which are determined by the crystal's Bravais lattice (e.g., cubic, hexagonal). This ties directly to crystallographic point groups and root systems (e.g., the 8 TRIMs of the simple cubic lattice correspond to the vertices of a cube, a root system of type B₃). No direct numerical ratio (0.382, 0.618, etc.) is evidenced in the search results. | DEPTH: 6 — The Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com