Related papers: Acoustic realization of quadrupole topological ins…

We describe two 3D-printing approaches for realizing tight-binding models in acoustic metamaterials using H-shaped resonators: a modular system with tunable interconnections and an integrated one-piece design for reducing dissipation. The…

Topological insulators are characterized by insulating bulk and conducting surface, the latter is a necessity consequence of the nontrivial topology of the wavefunctions forming the valence band. This chapter gives a historical overview of…

Quadrupole phase, as a novel high-order topological phase, exhibits nontrivial gapless states at the boundaries whose dimension is lower than bulk by two. However, this phase has not been observed experimentally in two-dimensional (2D)…

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…

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the…

Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk…

The Berry phase associated with energy bands in crystals can lead to quantized quantities, such as the quantization of electric dipole polarization in an insulator, known as a one-dimensional (1D) topological insulator (TI) phase. Recent…

Conventional topological insulators support boundary states that have one dimension lower than the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order…

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…

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory…

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…

Acoustic tweezers are gaining increasing attention due to their excellent biological compatibility. Recently, the concept of topology has been expanded from condensed matter physics into acoustics, giving rise to a robust wave manipulation…

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…

Ternary semiconducting or metallic half-Heusler compounds with an atomic composition 1:1:1 are widely studied for their flexible electronic properties and functionalities. Recently, a new material property of half-Heusler compounds was…

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…

Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects.…

Topological insulators are a new phase of matter with the distinctive characteristics of an insulating bulk and conducting edge states. Recent theories indicate there even exist topological edge states in the fractal-dimensional lattices,…

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to…

Topological phononic insulators are the counterpart of three-dimensional quantum spin Hall insulators in phononic systems and, as such, their topological surfaces are characterized by Dirac cone-shaped gapless edge states arising as a…

The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…