Lecture Metadata Lacks Primary Equations; Chern Insulator Physics Reconstructed from Haldane/Semenoff Models — E8 Intelligence Research

FINDING: Search returned only lecture/seminar metadata — no primary equations or data; the substantive physics must be reconstructed from the standard model of Chern insulators (Haldane 1988, Semenoff 1985), which the titles reference. MATH (the actual physics these lectures cover): Dirac Hamiltonian on honeycomb lattice with both mass terms: H(k) = ħv_F (τ_z σ_x k_x + σ_y k_y) + m_S σ_z + m_H τ_z σ_z - Semenoff mass m_S: breaks sublattice (A/B) inversion symmetry — same sign on both Dirac valleys K, K′. Gap Δ = 2|m_S|. Trivial insulator; preserves time-reversal T. - Haldane mass m_H: breaks time-reversal T, opposite sign on K vs K′ (τ_z). Gap Δ = 2|m_H|. Topological. Chern number from sign of masses: C = ½ [sgn(m_S + m_H) − sgn(m_S − m_H)] Phase transition occurs where a gap closes: m_S = ±m_H → C jumps by ±1. The transition is a Dirac-point gap closing, not a band inversion of extended states. Connection to Haldane model (next-nearest-neighbor flux φ): m_H = 3√3 t₂ sin φ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com