Fractal topological band-gap structure induced by singularities in the one-dimensional Thue-Morse system

The physical origin of the fractal topological band-gap structure in the one-dimensional Thue-Morse system has been revealed, which is characterized by the evolutions of two types of topological singularities with zero-scattering properties and the paths of phase vortex points, which are the mirrored paths of the first-type singularities. The field distribution of the upper and lower gap-edge states will interchange when the traditional gaps are closed and reopened. The topologically protected edge-states are found at both traditional gaps and fractal gaps. Our work broadens the topological properties of quasicrystals or aperiodic systems and provides potential applications in new optoelectronic devices. (C) 2021 Chinese Laser Press