Related papers: Umbilic Lines in Orientational Order
Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely…
Three types of geometric structure---grid triangulations, rectangular subdivisions, and orthogonal polyhedra---can each be described combinatorially by a regular labeling: an assignment of colors and orientations to the edges of an…
We show that band topology can dramatically change the photophysics of two-dimensional (2D) semiconductors. For systems in which states near the band extrema are of multiple orbitals character and the spinors describing the orbital…
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional…
A ribbon is a double structure on P^1. The geometry of a ribbon is closely related to that of a smooth curve. In this note we consider linear series on ribbons. Our main result is an explicit determinantal description for the locus…
The relation between crystal symmetries, electron correlations, and electronic structure steers the formation of a large array of unconventional phases of matter, including magneto-electric loop currents and chiral magnetism. Detection of…
Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these…
Molecular chirality leads to a wonderful variety of equilibrium structures, from the simple cholesteric phase to the twist-grain-boundary phases, and it is responsible for interesting and technologically important materials like…
Magnetic hopfions are non-collinear spin textures that are characterized by an integer topological invariant, called Hopf index. The three-dimensional magnetic solitons can be thought of as a tube with a twisted magnetization that has been…
We present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes. This theory is based on a continuum elastic free energy that permits variations in the direction of molecular…
Chirality is an intriguing property of certain molecules, materials or artificial nanostructures, which allows them to interact with the spin angular momentum of the impinging light field. Due to their chiral geometry, they can distinguish…
A significant effort in condensed matter physics is dedicated to the search for exotic arrangements of electric dipoles in crystals. Non-collinear dipolar arrangements mimicking magnetic spin textures, such as polar vortices and skyrmions,…
We report that in cylindrical nanorods skyrmion chains, i.e., three-dimensional spin textures, emerge dynamically, as revealed by micromagnetic simulations. The skyrmion-chain state occurs when the diameter of the rod is larger than the…
In this article we combinatorially describe the triangles that are present in two types of line arrangements, those which have global cyclicity and those which are infinity type line arrangements. A combinatorial nomenclature has been…
Topological semimetals is a new class of condensed matter systems with nontrivial electronic structure topology. Their unusual observable properties may often be understood in terms of quantum anomalies. In particular, Weyl and Dirac…
We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties are investigated. We are mainly concentrated on integral…
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order…
A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries.…
We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytopes theory, we introduce the concept of chirality, a…
In most topological insulators, the valence and conduction band appear in reverse or inverted order compared to an equivalent insulator with isolated atoms. Here, we explore a different route towards topologically nontrivial states that may…