Disorder-Driven Topological Transitions: Critical Exponent ν ≈ 2.7 — E8 Intelligence Research

Abstract

FINDING: Topological insulators are bulk-insulating but surface-conducting quantum phases, with disorder-driven metal-TI transitions exhibiting a critical exponent ν ≈ 2.7. | MATH: Critical exponent ν ≈ 2.7 (from arXiv:1211.5026v2); topological invariant typically Z₂ (Z₂ classification for time-reversal invariant insulators); surface states governed by Dirac equation with linear dispersion E = ±ℏv_F|k|. | CONNECTION: The Z₂ invariant relates to the 2-torus (genus-1) topology — the ratio 2.7 is close to 2.618 (φ², the golden ratio squared), though the paper states "no conspicuous deviation" from ordinary insulator transitions (ν ≈ 2.7 is standard for 3D Anderson transitions, not a new geometric constant). The Dirac cone on the surface is a conical intersection — a 2D analogue of the double cone, whose opening angle relates to v_F (Fermi velocity), not a fixed geometric ratio. Crystallographic symmetry (reflection symmetry) is explicitly mentioned in Liang Fu's lecture as a classifying t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com