Unmovable nodal points (UNP) and lines (UNL) are band crossings which positions in the Brillouin zone unaltered by symmetry preserving perturbations. Not only but also structure vicinity is determined little group of a wave vector it's irreducible (co)representations. In this paper we give full set electronic dispersions near all UNPs UNLs non-magnetic, quasi two-dimensional (2D) materials both...

Abstract. We prove that points of a finite subset Σ ⊂ P impose independent linear conditions on homogeneous forms on P of degree ⌊nλ/2 − n⌋ in the case when at most λk points of the set Σ lie on a possibly reducible curve in P of degree k and |Σ| < λ⌈λ/2⌉, where λ is a natural number and n > 3. We apply the obtained result to threefolds having at most isolated ordinary double points. In particu...

We consider the zeros on the boundary ∂Ω of a Neumann eigenfunction φλj of a real analytic plane domain Ω. We prove that the number of its boundary zeros is O(λj) where −∆φλj = λ2jφλj . We also prove that the number of boundary critical points of either a Neumann or Dirichlet eigenfunction is O(λj). It follows that the number of nodal lines of φλj (components of the nodal set) which touch the b...

Recently, the efficiency of computer modeling and simulations has been improving dramatically. Consequently, the structural analysis of welding phenomena based on thermaleelasticeplastic finite element method (FEM) can be performedwith a good accuracy in a short time. However, if themodel to be analyzed is large and it has a complex shape, problemsmight occur with preprocessing, such as themesh...

We show that the position-momentum duality offers a transparent interpretation of band geometry at topological crossings. Under this duality, with Berry connection is dual to free-electron motion under gauge field. This identifies trace quantum metric as energy in momentum space. The crossings defects thus induce quantization metric. For $\mathbb{Z}$ nodal-point and nodal-surface semimetals thr...

We analyze the topological properties of possible superconducting states emerging from a ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$-like, ${\mathcal{C}}_{4}$-symmetric Dirac semimetal, with two fourfold-degenerate points separated in ${k}_{z}$ direction. Unlike simplest Weyl semimetal for which all pairing orders are topologically obstructed and nodal, we show that obstruction semimetals crucially on...