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Higher-order topological states (HOTS) have been extensively investigated in classical wave systems. They do not exist in the band gaps of infinite materials, while exhibit as the in-gap localized modes once the infinite materials are…
Higher-order topological insulators have triggered great interests because of exhibitions of non-trivial bulk topology on lower-dimensional boundaries like corners and hinges. While such interesting phases have been investigated in a…
We consider weak topological insulators with a twofold rotation symmetry around the dark direction, and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by…
Topological lasers are a new class of lasers that seek to exploit the special properties of topological states of light. A typical limiting factor in their performance is the existence of non-topological states with quality factors…
Higher order topological insulators are a new class of topological insulators in dimensions $\rm d>1$. These higher-order topological insulators possess $\rm (d - 1)$-dimensional boundaries that, unlike those of conventional topological…
Quasi-1D materials Bi$_{4}$X$_{4}$ (X=Br,I) are prototype weak topological insulators (TI) in the $\beta$ phase. For the $\alpha$ phases, recent high-throughput database screening suggests that Bi$_{4}$Br$_{4}$ is a rare higher-order TI…
We investigate a topological switch between second-order topological insulators (SOTIs) and topological crystalline insulators (TCIs). Both the SOTI and the TCI are protected by the mirror and inversion symmetries, for which we define the…
Correlated physics in nearly flat topological bands is a central theme in the study of moir\'e materials. While ground states at integer fillings are typically identified as quantum Hall ferromagnets within a Hartree-Fock framework, we…
Topological Anderson insulators (TAIs) provide a mechanism for topological phase transitions in disordered systems and have implications for quantum material design. In this work, we investigate the emergence of multiple TAIs in a…
Topological band insulators and (semi-) metals can arise out of atomic insulators when the hopping strength between electrons increases. Such topological phases are separated from the atomic insulator by a bulk gap closing. In this work, we…
We explore topological properties of a modulated Haldane model (MHM) in which the strength of the nearest-neighbor and next-nearest-neighbor terms is made unequal and the three-fold rotational symmetry $\mathcal{C}_3$ is broken by…
The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic…
High-order topological insulators (TIs) develop the conventional bulk-boundary correspondence theory and rise the interest in searching innovative topological materials. To realize a high-order TI with a wide passband of 1D and 2D…
Higher-order topological~(HOT) states,~hosting topologically protected modes on lower-dimensional boundaries,~such as hinges and corners, have recently extended the realm of the static topological phases.~Here we demonstrate the possibility…
Topological phases of matter have been extensively studied for their intriguing bulk and edge properties. Recently, higher-order topological insulators with boundary states that are two or more dimensions lower than the bulk states, have…
Topological band theory has achieved great success in the high-throughput search for topological band structures both in paramagnetic and magnetic crystal materials. However, a significant proportion of materials are topologically trivial…
Monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase have been recently classified as higher-order topological insulators (HOTI), protected by $C_3$ rotation symmetry. In addition, theoretical calculations show…
Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently…
The existence of fractionally quantized topological corner states serves as a key indicator for two-dimensional second-order topological insulators (SOTIs), yet has not been experimentally observed in realistic materials. Here, based on…
Topological phononic states, facilitating acoustic unique transports immunizing to defects and disorders, have significantly revolutionized our scientific cognition of acoustic wave systems. Up to now, the theoretical and experimental…