Robustness of topological corner modes in photonic crystals

Wannier Function Methods for Topological Modes in 1D Photonic Crystals

“…Since the two modes are related by inversion symmetry, however, this cannot be -instead each defect mode consists of a superposition of states originating in the lower and upper frequency band. This represents a photonic realization of the "fill-ing anomaly" from condensed matter physics [18,21,[33][34][35]68]. In a system with N unit cells and no defects, if we "fill" m bands, then we would have m × N photons in the system.…”

“…From a more theoretical perspective, photonic systems provide the ideal platform to explore the physics of band theory: the lack of interactions between photons in linear dielectrics, combined with the ability to address individual states with precise momentum and frequency resolution allows for the study of topological phenomena in photonic crystals that may be difficult to observe in electronic systems. Two timely example are the realization of quantum anomalous Hall "insulators" [14] through modulated coupling of Weyl points in three dimensions [15][16][17], and the observation of higher-order topological corner modes and filling anomalies in two-dimensional photonic crystals [18][19][20][21][22].…”

Second‐Order Photonic Topological Corner States in Square Lattices with Low Symmetry

“…[16][17][18] Such a behavior is the key advantage over the conventional photonic structures and make them useful for the practical applications. As novel topological phases, higher-order topological insulating (HOTI) phases have recently been discovered in various quantum and classical systems, including crystalline [19] and amorphous materials, [20,21] photonic [15,16,[22][23][24][25][26][27][28][29][30][31] and phononic The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/andp.202100075 DOI: 10.1002/andp.202100075 crystals, [32][33][34][35] and electric circuits. [36,37] As one of the most well-known and simplest second-order topological insulator (SOTI), one might take the SOTI in the systems described by 2D SSH model (see, e.g., ref.…”

Chiral-Symmetric Higher-Order Topological Phases of Matter

“…Higher-order topological phases have been found in Bismuth [56] and Bi 4 Br 4 [57]. More recently, the mechanisms for the protection and confinement of modes of higher-order topology have found fertile ground in photonics, acoustics, and topoelectric circuits [58][59][60][61][62][63][64][65][66][67][68], where they can be used to create robust cavities [69,70] and lasers [71,72]. In fact, since chiral-symmetric HOTPs with large MWNs require increasingly stronger longerrange hoppings, these phases may be hard to attain in solid-state systems, where the electron's hoppings attenuate with separation.…”