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In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological…
Topological edge states exist at the interfaces between two topologically-distinct materials. The presence and number of such modes are deterministically predicted from the bulk-band topologies, known as the bulk-edge correspondence. This…
Two-dimensional higher-order topological insulators can display a number of exotic phenomena such as half-integer charges localized at corners or disclination defects. In this paper, we analyze these phenomena, focusing on the paradigmatic…
The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intrinsic topological order, and is nearly entirely lacking for…
The study of the laws of nature has traditionally been pursued in the limit of isolated systems, where energy is conserved. This is not always a valid approximation, however, as the inclusion of features like gain and loss, or periodic…
We investigate the topological phases of two one-dimensional (1D) interacting superconducting wires and propose topological markers directly measurable from ground state correlation functions. These quantities remain powerful tools in the…
We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a…
Twisted bilayers offer a compelling and, at times, confounding platform for the engineering of new twistronic materials. Whereas standard studies almost exclusively focus on the explicit enigma that is presented by twist-angles, perhaps…
The discovery of topological phases of matter, initially driven by theoretical advances in quantum condensed matter physics, has been recently extended to classical wave systems, reaching out to a wealth of novel potential applications in…
Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…
Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For…
We perform a systematic study of the signatures of fragile topology in over 50 nonmagnetic two-dimensional materials with formula AB$_2$, belonging to space group $P$-$3m1$. Using group theory analysis in the framework of topological…
Topological insulators are bulk semiconductors that manifest in-gap massless Dirac surface states due to the topological bulk-boundary correspondence principle [1-3]. These surface states have been a subject of tremendous ongoing interest,…
Various unusual behaviors of artificial materials are governed by their topological properties, among which the edge state at the boundary of a photonic or phononic lattice has been captivated as a popular notion. However, this remarkable…
Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems…
Topological lattice defects, such as dislocations and grain boundaries (GBs), are ubiquitously present in the bulk of quantum materials and externally tunable in metamaterials. In terms of robust modes, localized near the defect cores, they…
Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases,…
In topological physics, one of the most intriguing phenomena is the presence of topological boundary states, accurately predicted by the well-established bulk-edge correspondence. For example, in three-dimensional Weyl semimetals, Fermi…
Vortex-carrying wave fields play a crucial role in photonics due to unusual propagation properties and interactions with matter, which enable numerous practical applications ranging from optical tweezers and imaging to information encoding…
Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is…