Topological phase transition from periodic edge states in moiré superlattices

Topological mosaic pattern can be formed in two-dimensional moiré superlattices, where periodic edge states are located at the boundary between topologically trivial/nontrivial domains. We construct a minimized continuum model to describe these edge states and find that these edge states can be captured by $p_xpm ip_y$ orbitals on the honeycomb lattice, in which an effective atomic spin-orbit coupling (SOC) emerges. As a result, twisting angle will alter the effective SOC strength and drives an overall topological phase transition. Our work reveals a moiré-induced effective SOC mechanism and provides a phase diagram to manipulate the local and global topological properties in moiré systems.