In this talk, I will survey recent developments regarding the topological classification of symmetry-enforced band topologies in (semi)metals and magnets. These topological properties of the band structure are enforced to exist by symmetry alone, independent of the band dispersion, orbital content, and chemical composition of the material [1]. Hence, once the space group symmetries that enforce the desired band topologies have been identified, a suitable material can be found simply by browsing materials databases by space group numbers [2-4]. In this way, we have identified, among others [2-5], the topological materials ZrIrSn [2] and ferromagnetic MnSi [5], which will be discuss in detail.

 

The material ZrIrSn exhibits Weyl nodal lines near the Fermi energy, whose existence is guaranteed by a glide mirror symmetry. The topology of this nodal line is characterized by a quantized Pi-Berry phase, which leads to drumhead surface states. Ferromagnetic MnSi, on the other hand, has topological nodal planes on the BZ boundary, which are enforced by a combination of time-reversal with screw rotation symmetries. These nodal planes are sources of Berry flux, which is absorbed by single Weyl points at the center of the BZ. We discuss experimental consequences of these nodal planes in the surface spectra and de Haas-van Alphen measurements [5]. 

 

[1] Y. Zhao, A. Schnyder, Phys. Rev. B 94, 195109 (2016)

[2] J. Zhang, Y. Chan, C. Chiu, M. Vergniory, L. Schoop, A. Schnyder, Phys. Rev. Materials 2, 074201 (2018) 

[3] Y. Chan, B. Kilic, M. Hirschmann, C. Chiu, L. Schoop, D. Joshi, A. Schnyder, Phys. Rev. Materials 3, 124204 (2019)

[4] M. Hirschmann, A. Leonhardt, B. Kilic, D. Fabini, A. Schnyder, arXiv:2102.04134

[5] M. Wilde, M. Dodenhöft, A. Niedermayr, A. Bauer, C. Pfleiderer, to appear in Nature