Related papers: A Short Lecture on Topological Crystallography and…
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
We show that topological defects in an ion-doped nematic liquid crystal can be used to manipulate the surface charge distribution on chemically homogeneous, charge-regulating external surfaces, using a minimal theoretical model. In…
We introduce decorated piecewise hyperbolic and spherical surfaces and discuss their discrete conformal equivalence. A decoration is a choice of circle about each vertex of the surface. Our decorated surfaces are closely related to…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…
We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater than one. A typical example is given by the Betti numbers…
Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in $3$D with $C_n$ lattice rotation…
Crystal Structure Prediction (CSP) is crucial in various scientific disciplines. While CSP can be addressed by employing currently-prevailing generative models (e.g. diffusion models), this task encounters unique challenges owing to the…
Quasi-periodic structures of quasicrystals yield novel effects in diverse systems. However, there is little investigation on employing quasi-periodic structures in the morphology control. Here, we show the use of quasi-periodic surface…
In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts,…
Topology is a central concept of mathematics, which allows us to distinguish two isolated rings with linked ones. In material science, researchers discovered topologically different carbon allotropes in a form of a cage, a tube, and a…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
The best-understood crystal ordering transition is that of two-dimensional freezing, which proceeds by the rapid eradication of lattice defects as the temperature is lowered below a critical threshold. But crystals that assemble on closed…
Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…
Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…
The field of topological photonics emerged as one of the most promising areas for applications in transformative technologies: possible applications are in topological lasers or quantum optics interfaces. Nevertheless, efficient and simple…
Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery…
The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological (SPT) phases, especially for interacting systems. In this paper, we systematically…
Quantum states naturally represent symmetry groups, though often in a projective sense. Intriguingly, the projective nature of crystalline symmetries has remained underexplored until very recently. A series of groundbreaking theoretical and…
Identifying the regions responsible for plastic flow in amorphous solids remains an open problem, since structural disorder seems to prevent the direct application of concepts such as dislocations, topological defects that successfully…