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Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a…
Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have…
Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a…
The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been…
The discovery of topological phases has recently led to a paradigm shift in condensed matter physics, and facilitated breakthroughs in engineered photonics and acoustic metamaterials. Topological insulators (TIs) enable the generation of…
The emerging field of topology has brought device effects to a new level. Higher-order topological insulators (HOTIs) go beyond traditional descriptions of bulk-edge correspondence, broadening the understanding of topologically insulating…
Recently, high-order topological insulators (HOTIs), accompanied by topologically nontrivial boundary states with codimension larger than one, have been extensively explored because of unconventional bulk-boundary correspondences. As a…
Higher-order topological insulators (HOTIs) are a novel type of topological phases which supports $d$-dimensional topological boundary states in $D$-dimensional systems with $D-d>1$. In this work, we theoretically predict that interlayer…
Higher-order topological insulators (HOTIs) have attracted increasing interest as a unique class of topological quantum materials. One distinct property of HOTIs is the crystalline symmetry-imposed topological state at the lower-dimensional…
We report the discovery of several classes of novel topological insulators (TIs) with hybrid-order boundary states generated from the first-order TIs with additional crystalline symmetries. Unlike the current studies on hybrid-order TIs…
Higher-order topological insulators (HOTIs) are unique topological materials supporting edge states with the dimensionality at least by two lower than the dimensionality of the underlying structure. HOTIs were observed on lattices with…
Second-order topological insulators (SOTIs) are the topological phases of matter in d dimensions that manifest (d-2)-dimensional localized modes at the intersection of the edges. We show that SOTIs can be designed via stacked Chern…
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…
The discovery and realization of topological insulators, a phase of matter which hosts metallic boundary states when the $d$-dimension insulating bulk is confined to ($d-1$)-dimensions, led to several potential applications. Recently, it…
Higher-order topological insulators (HOTIs) are described by symmetric exponentially decayed Wannier functions at some $necessary$ unoccupied Wyckoff positions and classified as obstructed atomic insulators (OAIs) in the topological quantum…
High-order topological insulators (TIs) are a family of recently-predicted topological phases of matter obeying an extended topological bulk-boundary correspondence principle. For example, a two-dimensional (2D) second-order TI does not…
The higher order topological insulator (HOTI) has enticed enormous research interests owing to its novelty in supporting gapless states along the hinges of the crystal. Despite several theoretical predictions, enough experimental…
Higher-order topological insulators (HOTIs) are a newly discovered class of topological insulators which exhibit unconventional bulk-boundary correspondence. Very recently, the concept of HOTIs has been extended to aperiodic…
A $d$-dimensional second-order topological insulator (SOTI) can host topologically protected $(d - 2)$-dimensional gapless boundary modes. Here we show that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to…
Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be…