Disorder-Driven Metal-Topological Insulator Transition Exhibits Universal Critical Exponent ν≈2.7 — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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 = ∏TRIM Pf[w(Γi)]/√(det[w(Γi)]) 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
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BibTeX
@misc{caldin2026disorderdriven,
title = {{Disorder-Driven Metal-Topological Insulator Transition Exhibits Universal Critical Exponent ν≈2.7 — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23525889},
url = {https://zenodo.org/records/23525889},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Disorder-Driven Metal-Topological Insulator Transition Exhibits Universal Critical Exponent ν≈2.7 — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23525889
UR - https://zenodo.org/records/23525889
AB - 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 = ∏_TRIM Pf[w(Γ_i)]/√(det[w(Γ_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
ER -