Antichiral Edge Modes Break Bulk-Edge Correspondence in Topological Semimetals — E8 Intelligence Research

FINDING: Antichiral edge modes in topological semimetals violate the usual bulk-edge correspondence — two copropagating edge channels with opposite velocities emerge from a Chern-number-carrying bulk, characterized via transfer matrix eigenvalues. | MATH: The key structure is the transfer matrix \( T(k_x) \) across the finite-width strip; its eigenvalues \( λ_n \) encode edge localization. For antichiral modes, the edge dispersion is \( E_±(k_x) = ± v (k_x - π) \) (from the German-language source, with \( v \) the Fermi velocity), and the Chern number \( C \) is computed via the standard TKNN formula \( C = 1/2π i∫BZ Tr[P \, dP dP] \), where \( P \) is the spectral projector. The Qi-Wu-Zhang model on a square lattice has Hamiltonian \( H(k) = sin k_x σ_x + sin k_y σ_y + (m + cos k_x + cos k_y)σ_z \); the Haldane honeycomb model adds complex next-nearest-neighbor hopping \( t_2 eiφ \). The transfer matrix eige Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com