Topological phase transition from periodic edge states in moir\'e superlattices

Topological mosaic pattern (TMP) can be formed in two-dimensional (2D) moir\'e superlattices, a set of periodic and spatially separated domains with distinct topologies give rise to periodic edge states on the domain walls. In this study, we demonstrate that these periodic edge states play a crucial role in determining global topological properties. By developing a continuum model for periodic edge states with C6z and C3z rotational symmetry, we predict that a global topological phase transition at the charge neutrality point (CNP) can be driven by the size of domain walls and moir\'e periodicity. The Wannier representation analysis reveals that these periodic edge states are fundamentally chiral px +- ipy orbitals. The interplay between on-site chiral orbital rotation and neighboring hopping among chiral orbitals leads to band inversion and a topological phase transition. Our work establishes a general model for tuning local and global topological phases, paving the way for future research on strongly correlated topological flat minibands within topological mosaic patterns