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A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero-dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear…
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…
Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological invariants associated with the quantization…
Higher-order topological phase as a generalization of Berry phase attracts an enormous amount of research. The current theoretical models supporting higher-order topological phases, however, cannot give the connection between lower and…
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…
Topological electric quadrupole is a recently proposed concept that extends the theory of electric polarization of crystals to higher orders. Such a quadrupole phase supports topological states localized on both edges and corners. In this…
Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here,…
We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological…
Recent progress in spintronics within the paradigm of altermagnets (AMs) opens new avenues for next-generation electronic device design. Here, we establish a spin-corner locking mechanism that generates second-order topological states in…
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…
We numerically and experimentally study corner states in a continuous elastic plate with em-bedded bolts in a hexagonal pattern. While preserving C6 crystalline symmetry, the system can transition from a topologically trivial to a…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…
One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial…
A wide variety of higher-order symmetry protected topological phase(HOSPT) with gapless corners or hinges had been proposed as a descendant of topological crystalline insulator protected by spatial symmetry. In this work, we address a new…
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…
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…
Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well…
We propose theoretically a reconfigurable two-dimensional (2D) hexagonal sonic crystal with higher-order topology protected by the six-fold, $C_6$, rotation symmetry. The acoustic band gap and band topology can be controlled by rotating the…
Recently, higher-order topological phases that do not obey the usual bulk-edge correspondence principle have been introduced in electronic insulators and brought into classical systems, featuring with in-gap corner/hinge states. So far,…