Quasiperiodic–Periodic Properties and Topological Transitions in Twisted Nested Moiré Patterns

ABSTRACT The moiré patterns generated by altering the structural parameters in two or more layers of periodic materials exhibit rich topological properties. However, the characteristics of twisted nested moiré patterns and their correlation with topological transitions remain unexplored. In this work, we propose a “twisted nested photonic crystal” (TNPC), a hierarchical superlattice structure previously unreported. TNPCs facilitate the design of nested superlattices with unique spatial geometries and a tunable Quasiperiodic‐periodic properties (evolution from quasiperiodicity to periodicity). We derive the underlying theory for the Hamiltonian of a twisted Su‐Schrieffer‐Heeger model. This work reveals the correlation between the functions, twisted nested moiré patterns, and topological transitions, obtaining higher‐order topological states with symmetry, and thereby provides unparalleled insight for the design and application of moiré photonics.