Related papers: Toroidal Crystals
Toroidal nematics are nematic liquid crystals confined within a circular torus and subject to planar degenerate anchoring on the boundary of the torus. They may be droplets floating in an isotropic environment or cavities carved out of a…
Topology can manifest itself in colloids when quantified by invariants like Euler characteristics of nonzero-genus colloidal surfaces, albeit spherical colloidal particles are most often studied, and colloidal particles with complex…
The progress of realizing colloidal structures mimicking natural forms of organization in condensed matter is inherently limited by the availability of suitable colloidal building blocks. To enable new forms of crystalline and…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
Toroidal structures are a common feature in a wide variety of astrophysical objects, including dusty tori in AGNs, rings in galaxies, protoplanetary disks, and others. The matter distribution in such structures is not homogeneous and can be…
The mechanical properties of crystals on curved substrates mix elastic, geometric and topological degrees of freedom. In order to elucidate the properties of such crystals we formulate the low-energy effective action that combines metric…
Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical…
One of the central experimental efforts in nematic colloids research aims to explore how the interplay between the geometry of particles along with the accompanying nematic director deformations and defects around them can provide a means…
Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable…
Topological phases usually are unreachable in molecular solids, which are characteristic of weakly dispersed energy bands with a large gap, in contrast to topological materials. In this work, however, we propose that nontrivial electronic…
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…
By using topological current theory, we study the inner topological structure of the topological defects in two-dimensional (2D) crystal. We find that there are two elementary point defects topological current in two-dimensional crystal,…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
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…
Topological defects are crucial to the thermodynamics and structure of condensed matter systems. For instance, when incorporated into crystalline membranes like graphene, disclinations with positive and negative topological charge…
This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical…
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…
Using tools and concepts from contact topology we show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This leads to a number of additional topological invariants for cholesteric…
The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…
Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic…