Related papers: Dimensional hierarchy of higher-order topology in …
The notion of higher-order topological insulators has endowed materials with topological states beyond the first order. Particularly, a three-dimensional (3D) higher-order topological insulator can host topologically protected 1D hinge…
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…
Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological…
The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at…
Topologically protected gapless edge/surface states are phases of quantum matter which behave as massless Dirac fermions, immunizing against disorders and continuous perturbations. Recently, a new class of topological insulators (TIs) with…
The recent discovery of higher-order topological insulators (TIs) has opened new possibilities in the search for novel topological materials and metamaterials. Second-order TIs have been implemented in two-dimensional (2D) systems…
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…
In the past years classical wave-systems have constituted an excellent platform for emulating complex quantum phenomena. This approach has been especially fruitful in demonstrating topological phenomena in photonics and acoustics: from…
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…
The emergent higher-order topological insulators significantly deepen our understanding of topological physics. Recently, the study has been extended to topological semimetals featuring gapless bulk band nodes. To date, higherorder nodal…
The recent discovery of higher-order topology has largely enriched the classification of topological materials. Theoretical and experimental studies have unveiled various higher-order topological insulators that exhibit topologically…
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…
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…
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…
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 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…
Topological insulators exhibit boundary states protected by bulk band topology, a principle first established in quantum systems and later extended to classical waves, including phononics. Conventionally, an $n$-dimensional bulk with…
In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases…
Higher-order topological insulators, which support lower-dimensional topological boundary states than the first-order topological insulators, have been intensely investigated in the integer dimensional systems. Here, we provide a new…
Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…