Lie derivatives arise in studying continuous symmetries of various geometric structures on manifolds. They are also used in symmetry analysis of ordinary and partial differential equations (see [1]). In general relativity the bundle of Weyl spinors SM is a special geometric structure built over the space-time manifold M . The main goal of this paper is to clarify the procedure of applying Lie d...

The dispersion relations of magnons in ferromagnetic pyrochlores with Dzyaloshinskii-Moriya interaction are shown to possess Weyl points, i. e., pairs of topologically nontrivial crossings of two magnon branches with opposite topological charge. As a consequence of their topological nature, their projections onto a surface are connected by magnon arcs, thereby resembling closely Fermi arcs of e...

Recent discoveries on topological characterization of gapless systems have attracted interest in both theoretical studies and experimental realizations. Examples of such gapless topological phases are Weyl semimetals, which exhibit three-dimensional (3D) Dirac cones (Weyl points), and nodal line semimetals, which are characterized by line nodes (two bands touching along a line). Inspired by our...

Weyl semimetals have recently attracted enormous attention due to their unusual features. So far, this novel state has been predicted theoretically and confirmed experimentally in several materials, such as HgTe, LaPtBi, Y2Ir2O7, TaAs, TaP, NbAs, NbP and HgCr2Se4. Doping plays an important role in the research of condensed-matter materials. However, its influence on the Weyl semimetal has been ...

We study the asymptotic distribution of eigenvalues of integral operators Tk defined by kernels k which belong to Triebel-Lizorkin function space Fσ pu(F qv) by using the factorization theorem and the Weyl numbers xn. We use the relation between Triebel-Lizorkin space Fσ pu(Ω) and Besov space Bτ pq(Ω) and the interpolation methods to get an estimation for the distribution of eigenvalues in Lizo...