Related papers: Higher-order topological band structures
Topological materials are typically characterized by gapless boundary states originated from nontrivial bulk band topology, known as topological bulk-boundary correspondence. Recently, this fundamental concept has been generalized in…
Bound states in the continuum (BICs) are polarization singularities in momentum space whose topological charges (TCs) govern advanced light-matter interactions. While lattice symmetry protects the existence of robust BICs at the…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals,…
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…
Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond…
Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…
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…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
The discovery of topological insulators and semimetals has opened up a new perspective to understand materials. Owing to the special band structure and enlarged Berry curvature, the linear responses are strongly enhanced in topological…
Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although…
Topological crystalline insulators are a class of materials with a bulk energy gap and edge or surface modes, which are protected by crystalline symmetry, at their boundaries. They have been realized in electronic systems: in particular, in…
We study the vibrational spectrum of a constrained classical ring. Due to the presence of 2-order exceptional points, a topologically trivial band at the infinity can make the vibrational band topologically nontrivial. The symmetry, which…
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…
Band structure for a crystal generally consists of connected components in energy-momentum space, known as band complexes. Here, we explore a fundamental aspect regarding the maximal number of bands that can be accommodated in a single band…
Chiral symmetry plays an indispensable role in topological classifications as well as in the understanding of the origin of bulk or boundary flat bands. The conventional definition of chiral symmetry refers to the existence of a constant…
We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d…
The existence of topological interface states is investigated at the boundary between a binary photonic crystal and a quaternary photonic crystal, with each possessing inversion symmetric unit cells. Conditions are established that describe…
The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order…