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

Abstract

FINDING: Topological insulators are gapped bulk materials with gapless, symmetry-protected surface states; disorder-driven metal-TI transition exhibits critical exponent ν ≈ 2.7. MATH: - Bulk gap Δ > 0; surface states protected by time-reversal symmetry (TRS) with Z₂ topological invariant (ν₀ ∈ {0,1} in 2D/3D). - Critical exponent ν ≈ 2.7 (from arXiv:1211.5026v2) — consistent with 3D Anderson transition universality class (ν ≈ 1.57–2.7 depending on symmetry), no new universality. - Z₂ invariant: (−1)^ν₀ = ∏ᵢ δᵢ, where δᵢ are parity eigenvalues at time-reversal invariant momenta (TRIM). - Berry phase/curvature: γ = ∮ A(k)·dk (mod 2π) — quantized to 0 or π for TRS. CONNECTION: - Z₂ classification is a **binary symmetry** — not directly golden-ratio related. - However, the **lattice symmetries** (e.g., inversion, mirror) that protect the topological phase often involve **crystallographic point groups** (e.g., C₄, C₆, T_d) — root systems of A, B, C, D types appear in band s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com