We recently showed that band degeneracies in PT-symmetric systems with negligible spin-orbit coupling are characterized by a non-abelian topological charge, thus suggesting non-trivial braiding rules inside the momentum space [1]. In this seminar, I will first explain the geometric meaning of the non-abelian charge. Afterwards, I will discuss how the charge affects the description of nodal lines [2] and of Weyl points [3] in three-dimensional crystalline systems. Our first-principle calculations suggest that certain signatures of the non-abelian topology play a role in elemental scandium (Sc) under strain [1]. These signatures could be experimentally verified in photoemission experiments.
[1] Q. Wu, A. A. Soluyanov, and T. Bzdušek, arXiv:1808.07469 (2018)
[2] A. Tiwari and T. Bzdušek, arXiv:1903.00018 (2019)
[3] A. Bouhon, R.-J. Slager, and T. Bzdušek (in preparation, 2019)
