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

FINDING: Topological insulators are bulk-insulating, edge-conducting quantum phases; disorder-driven metal-TI transition exhibits critical exponent ν≈2.7, consistent with conventional metal-insulator universality. MATH: - **Z₂ topological invariant** (Fu-Kane-Mele): ν₀ ∈ {0,1} distinguishes trivial vs. topological insulator, computed via Pfaffian of the Bloch Hamiltonian's time-reversal polarization: \[ (-1)^{ν₀} = \prod_{TRIM} \frac{\text{Pf}[w(\Gamma_i)]}{\sqrt{\det[w(\Gamma_i)]}} \] where Γᵢ are time-reversal invariant momenta (TRIM). - **Bulk-boundary correspondence**: edge states count = |ν₀| mod 2 (for 2D), or surface Dirac cones for 3D. - **Critical exponent** from arXiv:1211.5026: ν = 2.7 ± 0.1 (localization length scaling), matching metal-ordinary insulator transitions (ν ≈ 2.7) — no new universality class. - **Higher-order TIs** (Bradlyn talk): corner/hinge modes governed by nested Wilson loops, quantized by **Z₂ × Z₂** or **Z₄** invariants — e.g., 3D se

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com