Non-Abelian Statistics in Momentum Space

We develop a general theory describing the stability and conversions of a wide range of band-structure nodes. The technique readily applies to a plethora of nodes existing in semimetals and superconductor, while it also reveals various previously unknown nodal features. Especially, we find that band-structure nodes in PT-symmetric systems with negligible spin-orbit coupling carry a non-Abelian charge, thus suggesting non-trivial braiding rules in momentum space. The non-Abelian charge also poses constrains on admissible nodal-line composition in 3D systems, and on the topological transitions between various such compositions. We emphasize that the non-Abelian property arises without the need of electron interactions.

In this talk, I motivate our description of band-structure nodes based on homotopy theory, and demonstrate its power on several simple examples. Afterwards, I clarify the meaning of the non-Abelian charge arising in PT-symmetric systems, and show how it constraints nodal compositions in a simple metal, namely elemental scandium (Sc) under strain. Our predictions could be experimentally tested in photoemission experiments.