James C. McGroddy Prize for New Materials Talk: 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 [1]. One important criterion for the identification of the topological material is, in the language of chemistry, the inert pair effect of the s-electrons in heavy elements, and the symmetry of the crystal structure. Binary phosphides are an ideal material class for a systematic study of Dirac, Weyl and new Fermion physics, since these compounds can be grown as high-quality single crystals. A new class of topological phases that have Weyl points was also predicted in the family that includes NbP, NbAs. TaP, MoP and WP₂ [2-5]. In magnetic materials the Berry curvature and the classical anomalous Hall and spin Hall effect helps to identify potentially interesting candidates. As a consequence, the magnetic Heusler compounds have already been identified as Weyl semimetals: for example, Co₂YZ, Mn₃Sn and Co₃Sn₂S₂ [6]. The Anomalous Hall angle also helps to identify materials in which a quantum anomalous Hall effect should be possible in thin films. Even beyond this reciprocal Berry curvature, 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 [7].
[1] Bradlyn et al., Nature 547 298, (2017)
[2] Shekhar et al., Nat. Phys. 11, 645 (2015)
[3] Liu et al., Nat. Mat. 15, 27 (2016)
[4] Gooth et al., Nature 547, 324 (2017)
[5] Kumar et al., Nat. Com. 8 (2017) 1642
[6] Manna et al., Nat. Mat. Rev. 3 244 (2018)
[7] Nayak et al., Nature 548, 561 (2017)