Topological Phases Under Entropic Suppression: Coherence, Transitions, and Material Design

This work extends the universal 1/E^2 suppression framework to topological matter, demonstrating how entropy-driven coherence decay governs topological invariants, phase transitions, and edge-state stability. We derive modified Chern numbers, predict suppression-induced topological transitions in quantum Hall systems, and establish design principles for entropy-stabilized topological materials. The theory is validated against quantum spin Hall experiments, anyonic interferometry, and high-pressure topological insulator studies. The Chern number becomes energy-dependent under suppression: C(E) = (1/2π) ∫ BZ Ω(k) [1 + (E/E0)^2]^-1 d²k (1) where Ω(k) is the Berry curvature. At E >> E0, C(E) → 0, destroying topological order. In 1D systems, the suppression-modified Zak phase: ϕZ = π/a − π/a ⟨uk|i∂k|uk⟩ [1 + (E/E0)^2]^-1 dk (2) explains the 7.3× reduction in edge-state conductance observed in Bi2Se3 nanowires at E = 0.5E0.