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

Abstract

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 \( \lambda_n \) encode edge localization. For antichiral modes, the edge dispersion is \( E_\pm(k_x) = \pm v (k_x - \pi) \) (from the German-language source, with \( v \) the Fermi velocity), and the Chern number \( C \) is computed via the standard TKNN formula \( C = \frac{1}{2\pi i}\int_{BZ} \mathrm{Tr}[P \, dP \wedge dP] \), where \( P \) is the spectral projector. The Qi-Wu-Zhang model on a square lattice has Hamiltonian \( H(\mathbf{k}) = \sin k_x \sigma_x + \sin k_y \sigma_y + (m + \cos k_x + \cos k_y)\sigma_z \); the Haldane honeycomb model adds complex next-nearest-neighbor hopping \( t_2 e^{i\phi} \). The transfer matrix eige Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com