Related papers: Local markers for crystalline topology

The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…

Photonic topological states have revolutionized our understanding on the propagation and scattering of light. Recent discovery of higher-order photonic topological insulators opens an emergent horizon for zero-dimensional topological corner…

Topological photonics has recently emerged as a very general framework for the design of unidirectional edge waveguides immune to back-scattering and deformations, as well as other platforms that feature extreme nonreciprocal wave…

In 2+1D, topological electromagnetic phases are defined as atomic-scale media which host photonic monopoles in the bulk band structure and respect bosonic symmetries. Additionally, they support topologically protected spin-1 edge states,…

Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as…

Higher-order topology is prized for its ability to realize lower-dimensional boundary states which are stable beyond fine-tuning. However, disorder presents a failure mechanism that can destroy topological in-gap states. Here, we…

Topological states enable robust transport within disorder-rich media through integer invariants inextricably tied to the transmission of light, sound, or electrons. However, the challenge remains to exploit topological protection in a…

Topological photonics harnesses the physics of topological insulators to control the behavior of light. Photonic modes robust against material imperfections are an example of such control. In this work, we propose a soft-matter platform…

Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to…

This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…

We show how machine learning techniques can be applied for the classification of topological phases in leaky photonic lattices using limited measurement data. We propose an approach based solely on bulk intensity measurements, thus exempt…

Topological surface states, a new kind of electronic state of matter, have recently been observed on the cleaved surfaces of crystals of a handful of small band gap semiconductors. The underlying chemical factors that enable these states…

In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…

The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of…

Higher-order topological phases (HOTPs) feature protected gapless modes on boundaries of higher codimension, such as the corners or hinges of a crystal. They are understood as being protected by lattice symmetries: If the latter are broken,…

Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary…

Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an…

The proposition that band geometry alone can protect optical states against disorder has proven not merely theoretically elegant but experimentally incontrovertible. A key attribute of photonic topological systems is their capacity to…

Topological photonic crystals (TPhCs) provide robust manipulation of light with built-in immunity to fabrication tolerances and disorder. Recently, it was shown that TPhCs based on weak topology with a dislocation inherit this robustness…