Observation of fractal higher-order topological states in acoustic metamaterials

Higher-order topological Anderson insulator on the Sierpiński lattice

“…We expect that the disorder-induced SOTI phase in the fractal system can be experimentally realized in some metamaterials in the future. The SOTI phases in fractal systems have been experimentally observed in both the acoustic [34,38] and the photonic [24] systems. On the other hand, the disorder effects have been introduced in both the acoustic [69,70] and the photonic [60][61][62]…”

“…For example, topological phases in fractals do not possess a well-defined bulk like their crystalline counterparts, but they are able to support topologically protected states on the boundary. [22] Topological phases have been widely investigated in different fractal systems, [23][24][25] such as the Chern insulator, [26][27][28][29][30][31] higher-order topological insulator, [32][33][34] non-Hermitian topological insulator, [35] and topological superconductor. [36,37] The second-order topological insulator (SOTI) in fractals exhibits unique inner corner modes.…”

“…[32] The Chern insulator in fractals is protected by the robust mobility gap instead of the direct bandgap in conven-tional topological insulators. [33] In the meantime, topological phases in fractals have been experimentally reported in various systems, such as the Chern insulator [33] and higherorder topological insulator [34,38] in acoustic systems and Floquet topological insulator [22,39] and higher-order topological insulator [24] in photonic systems.…”

Topological Flatband Loop States in Fractal‐Like Photonic Lattices

“…[18] In a similar vein, research efforts have been made to realize other forms of the CLSs by using the femtosecond laserwriting technique. [19] Quite recently, Floquet photonic topological insulators in fractal geometries [58] and acoustic fractal higherorder topological states [59,60] have also been realized successively. However, nontrivial flatband localized states, especially the NLSs that manifest the real-space topology, have not been investigated thus far in the fractal-like lattices, either in theory or experiment.…”

Sedimentary response and restoration of paleoshoreline of Taiyuan-Shanxi Formations in North China basin

“…One appealing feature associated with such phase is the existence of lowerdimensional topological boundary states, for example, the zero-dimension topological corner states. Topological corner states have recently attracted great interests in many platforms [21,22], such as photonics [23][24][25][26][27][28][29][30][31][32], phononics [33][34][35][36][37][38][39][40][41][42][43][44][45] and electric circuits [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. They have also motivated numerous important applications and studies, ranging from topological cavities and lasers [61,62] to nonlinear [63][64][65][66] and quantum optics [67,…”