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A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…
The geometric shape, symmetry, and topology of colloidal particles often allow for controlling colloidal phase behavior and physical properties of these soft matter systems. In liquid crystalline dispersions, colloidal particles with low…
We propose an experimental scheme to construct an optical lattice where the atoms are confined to the surface of a torus. This construction can be realized with spatially shaped laser beams which could be realized with recently developed…
On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models,…
Chiral condensed matter systems, such as liquid crystals and magnets, exhibit a host of spatially localized topological structures that emerge from the medium's tendency to twist and its competition with confinement and field coupling…
Theoretical calculations, computer simulations and experiments indicate the possible existence of a ferromagnetic liquid state. Should such a state exist, demagnetization effects would force a nontrivial magnetization texture governed by…
The Hopf fibration is an important object in mathematics and physics. A landmark discovery in topology and a fundamental object in the theory of Lie groups, the Hopf fibration has a wide variety of physical applications including magnetic…
We study composed map germs with respect to their local fibrations. Under most general conditions, inspired by the tameness condition that was introduced recently, we prove the existence of singular tube fibrations, and we determine the…
We construct two-band topological semimetals in four dimensions using the unstable homotopy of maps from the three-torus $T^3$ (Brillouin zone of a 3D crystal) to the two-sphere $S^2$. Dubbed ``Hopf semimetals'', these gapless phases…
In this note we study logarithmic transformations in the sense of differential topology on two fibers of the Hopf surface. It is known that such transformations are susceptible to yield exotic smooth structures on four-manifolds. We will…
In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross section sculpted on a chemically…
Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime…
The anchoring of nematic liquid crystals on surfaces with grafted liquid crystalline chain molecules is studied by computer simulations and within a mean field approach. The computer simulations show that a swollen layer of collectively…
Hopfions, as three-dimensional topologically nontrivial structures described by poloidal and toroidal winding numbers, hold promise as robust information carriers in spintronics, functional materials, and optical communications. Although…
Abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because…
We report a molecular-dynamics simulation of a single-component system of particles interacting via a spherically symmetric potential that is found to form, upon cooling from a liquid state, a low-density porous crystalline phase. Its…
In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the…
Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose…
Much recent progress has been made in the study of nematic solids, both glassy and elastomeric, particularly in the realm of stress-free, defect-driven deformation in thin sheets of material. In this paper we consider a subset of texture…
Structured light fields embody strong spatial variations of polarisation, phase and amplitude. Understanding, characterization and exploitation of such fields can be achieved through their topological properties. Three-dimensional (3D)…