Two-dimensional pentagonal structures based on the Cairo tiling are basis of a family layered materials with appealing physical properties. In this work we present theoretical study symmetry-based electronic and optical properties these materials. We provide complete classification space groups that support for binary ternary systems. By means first-principles calculations, their band local spi...

This is of nonlinear an exposition of the variational and differential properties spline curves, based on the Euler-Bernoulli theory for the bending of thin beams or elastica. For both open and closed splines through prescribed nodal points in the euclidean plane, various types --. of nodal constraints are considered, and the corresponding algebraic and differential equations relating curvature...

We study the topological properties of magnon excitations in a wide class of three dimensional (3D) honeycomb lattices with ferromagnetic ground states. It is found that they host nodal ring magnon excitations. These rings locate on the same plane in the momentum space. The rings can be gapped by Dzyaloshinskii-Moriya (DM) interactions to form two Weyl points with opposite charges. We explicitl...

We describe a detailed computational procedure which, given data values at arbitrarily distributed points in the plane, determines if the data are convex and, if so, constructs a smooth convex surface that interpolates the data. The method consists of constructing a triangulation of the nodes (data abscissae) for which the triangle-based piecewise linear interpolant is convex, computing a set o...

Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d(x(2)-y(2)) superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into seven distinct cases (including cases with nematic order) and anal...

We prove new patchworking theorems for singular algebraic curves, which state the following. Given a complex toric threefold Y which is fibred over C with a reduced reducible zero fiber Y0 and other fibers Yt smooth, and given a curve C0 ⊂ Y0, the theorems provide sufficient conditions for the existence of one-parametric family of curves Ct ⊂ Yt, which induces an equisingular deformation for so...

Giant anomalous Hall effect (AHE) and magneto-optical activity can emerge in magnets with topologically nontrivial degeneracies. However, identifying the specific band-structure features such as Weyl points, nodal lines, or planes which generate response is a challenging issue. Since low-energy interband transitions govern static AHE, we addressed this question prototypical magnetic semimetal $...