Topological materials science
Topology, a mathematical concept, recently became a hot and truly transdisciplinary topic in condensed matter physics, solid state chemistry and materials science. Since there is a direct connection between real space: atoms, valence electrons, bonds and orbitals, and reciprocal space: bands, Fermi surfaces and Berry curvature, a simple classification of topological materials in a single particle picture should be possible. Beyond Weyl and Dirac, new fermions can be identified in compounds that have linear and quadratic 3-, 6- and 8- band crossings that are stabilized by space group symmetries. Crystals of chiral topological materials CoSi, AlPt and RhSi were investigated by angle resolved photoemission and show giant unusual helicoid Fermi arcs with topological charges of ±2. In agreement with the chiral crystal structure two different chiral surface states are observed. Recently magnetic materials were investigated in the context of topology. In magnetic materials the Berry curvature and the classical anomalous Hall (AHE) and spin Hall effect (SHE) helps to identify potentially interesting candidates. As a consequence, the magnetic Heusler compounds have already been identified as Weyl semimetals: for example, Co 2 YZ, and Co 3 Sn 2 S 2. The Anomalous Hall angle also helps to identify materials in which a QAHE should be possible in thin films. Heusler compounds with non-collinear magnetic structures also possess real-space topological states in the form of magnetic antiskyrmions, which have not yet been observed in other materials.