Domain-wall states in Chern insulator with in-plane ferromagnetism

Topological phase is global and beyond the Landau paradigm of phases described by local order parameters. In this work, we report the electronic and transport properties of in-gap domain-wall states between domains with the same topology but different local magnetic orders, which lie in plane. We consider a buckled honeycomb lattice model that can host Chern insulating phase from in-plane magnetization with azimuthal angle φ₀, which breaks the three-fold rotation symmetry of original lattice. The topological phase remains the same at different φ_p=φ₀+2π p/3 (p=0-2). Along the domain wall, we find one-dimensional in-gap states whose electronic dispersion depends on the magnetic structure and domain wall width despite the same Chern number at different domains. At a symmetric Y-shape junction formed by three regions of different φ_p, we find counter-intuitive chiral current partition law that is tunable by electrical means. In a network by combining Y-shape junction to form a honeycomb, we find that the in-gap states form nearly flat Bloch bands with different topological Chern numbers providing a intriguing platform to investigate many-body effects.