Related papers: Topological D-Class Physics with Passive Acoustic …
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…
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…
Topological insulators (TIs) with robust boundary states against perturbations and disorders provide a unique approach for manipulating waves, whereas curved space can effectively control the wave propagation on curved surfaces by the…
While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this paper, we develop a characterization and classification of…
Topological insulators are a new class of materials, that exhibit robust gapless surface states protected by time-reversal symmetry. The interplay between such symmetry-protected topological surface states and symmetry-broken states (e.g.…
It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on…
Topological disclinations, crystallographic defects that break rotation lattice symmetry, have attracted great interest and exhibited wide applications in cavities, waveguides, and lasers. However, topological disclinations have thus far…
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 phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
We discuss the thermal (or gravitational) responses in topological superconductors and in topological phases in general. Such thermal responses (as well as electromagnetic responses for conserved charge) provide a definition of topological…
Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk…
We study solutions of $2 \times 2$ systems $(h D_t + \mathcal{D}) \Psi_t = 0$ on $\mathbb{R}^2$ in the semiclassical regime $h \rightarrow 0$. Our Dirac operator $\mathcal{D}$ is a standard model for interfaces between topological…
The existence of an excitation gap in the bulk spectrum is one of the most prominent fingerprints of topological phases of matter. In this paper, we propose a family of two dimensional Hamiltonians that yield an unusual class $D$…
Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…
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…
The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point…
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…
Topological superconductors possess a nodeless superconducting gap in the bulk and gapless zero energy modes, known as "Majorana zero modes", at the boundary of a finite system. In this work, we introduce a new class of topological…
In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of 1D systems. We focus on the TR-invariant Majorana chain (BDI symmetry class). While the band…
Recent advances in topological artificial systems open the door to realizing topological states in dimensions higher than the usual three-dimensional space. Here, we present a "tensor product" theory, which offers a method to construct…