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The recent emergence of electromagnetic topological defects has attracted wide interest in fields from topological photonics to deep-subwavelength light-mater interactions. Previously, much of the research has focused on constructing…
Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the…
We propose and analyze an effective free energy describing the physics of disclination defects in particle arrays constrained to move on an arbitrary two-dimensional surface. At finite temperature the physics of interacting disclinations is…
Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behavior of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable…
The results of ultra-high vacuum low-temperature scanning-tunneling microscopy (STM) and spectroscopy (STS) of atomically clean (111) surface of the topological insulator Bi$_2$Se$_3$ are presented. We observed several types of new…
The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are…
The influence of the space charge of ions emitted from the surface of a conical spike on its shape has been studied. The problem of the calculation of the spatial distributions of the electric field, ion velocity field, and the space charge…
We report appearance of non-trivial zero energy corner modes in the form of topological defects (trimers) in a carefully designed 2D crystalline topological insulator. The proposed scenario is developed via an unconventional stacking of 1D…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
We introduce topological defect to a square lattice of elliptical cylinders. Despite the broken translational symmetry, the long-range positional order of the cylinders leads to residual photonic bandgap in the density of optical states.…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…
Nontrivial properties of electronic states in topological insulators are inherent not only to the surface and boundary states, but to bound states localized at structure defects as well. We clarify how the unusual properties of the…
Most of the half-Heusler RPtBi compounds (R=rare earth) host various surface states due to spin-orbit coupling driven topological band structure. While recent ARPES measurements ubiquitously reported the existence of surface states in…
Various types of topological defects in graphene are considered in the framework of the continuum model for long-wavelength electronic excitations, which is based on the Dirac--Weyl equation. The condition for the electronic wave function…
Higher-order topological insulators host gapless states on hinges or corners of three-dimensional crystals. Recent studies suggested that even topologically trivial insulators may exhibit fractionally quantized charges localized at hinges…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
Biological surfaces, such as developing epithelial tissues, exhibit in-plane polar or nematic order and can be strongly curved. Recently, integer (+1) topological defects have been identified as morphogenetic hotspots in living systems.…
Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the…
Topological crystalline insulators (TCIs) can exhibit unique, quantized electric phenomena such as fractional electric polarization and boundary-localized fractional charge. This quantized fractional charge is the generic observable for…
Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex…