Related papers: Umbilic Lines in Orientational Order
In many biological materials with a hierarchical structure there is an intriguing and unique mechanism responsible for the 'propagation' of order from the molecular to the nano- or micro-scale level. Here we present a much simpler molecular…
We give a combinatorial description (including explicit differential-form bases) for the cohomology groups of the space of n distinct nonzero complex numbers, with coefficients in rank-one local systems which are of finite monodromy around…
Higher-order exceptional points (EPs) in non-Hermitian systems showcase diverse physical phenomena but require more parameter space freedom or symmetries. It leads to a challenge for the exploration of high-order EP geometries in…
We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it…
Novel types of barrel-shaped chiral skyrmions can exist as isolated topological defects or as bound states in magnetic nanolayers with intrinsic and surface/interface induced chirality. The equilibrium parameters of chiral modulations…
Nonlinear electrical conduction primarily mediated by an orbital texture is observed in chiral semiconductor Te. We determine the enantiospecific sign of the nonlinear conductance and identify anomalies in its carrier-density dependence.…
Geometrical chirality is a property of objects that describes three-dimensional mirror-symmetry violation and therefore it requires a non-vanishing spatial extent. In contrary, optical chirality describes only the local handedness of…
We give a topological classification of defect lines in cholesteric liquid crystals using methods from contact topology. By focusing on the role played by the chirality of the material, we demonstrate a fundamental distinction between…
We prove that the Hilbert scheme of degeneracy loci of pairs of global sections of Omega(2), the twisted cotangent bundle on P^(n-1), is unirational and dominated by the Grassmannian of lines in the projective space of skew-symmetric forms…
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to…
We study real lines on certain Moishezon threefolds which are potentially twistor spaces of 3CP^2. Here, line means a smooth rational curve whose normal bundle is O(1)^2 and the reality implies the invariance under an anti-holomorphic…
We present theoretical and experimental results probing the rich topological structure of arbitrarily disordered finite tight binding Hamiltonians with chiral symmetry. We extend the known classification by considering the topological…
We investigate point-line geometries whose singular subspaces correspond to binary equidistant codes. The main result is a description of automorphisms of these geometries. In some important cases, automorphisms induced by non-monomial…
The assembly of filamentous bundles with controlled diameters is common in biological systems and desirable for the development of nanomaterials. We discuss dynamical simulations and free energy calculations on patchy spheres with chiral…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
This paper reviews the complex ordered structures induced by chirality in liquid crystals. In general, chirality favors a twist in the orientation of liquid-crystal molecules. In some cases, as in the cholesteric phase, this favored twist…
Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the…
In this paper we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the $3$-sphere. We also introduce the tertiary Hochschild homology corresponding to a quintuple…
We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…
The breaking of chiral and time-reversal symmetries provides a pathway to exotic quantum phenomena and topological phases. In particular, the breaking of chiral (mirror) symmetry in quantum materials has been shown to have important…