Interplay of non-Abelian band topology with crystalline symmetry

We discuss the recently discovered non-Abelian topological invariant that characterizes band nodes inside the momentum space of certain non-interacting metals. This non-Abelian topology prominently arises in systems with PT symmetry (space-time inversion) or with C₂T symmetry (composition of π-rotation with time-reversal). Given the prevalence of these symmetries in most space groups, one expects important implications of the non-Abelian invariant for real materials.

In this talk, we first introduce the quaternion formulation of this topological invariant as obtained by Ref. [1]. We subsequently reformulate the topology using frame rotations and Euler class [2] as developed recently by Ref. [3]. We finally present new results concerning the interplay of the non-Abelian band topology with point-group symmetry. We find that this interplay implies non-trivial conversions between Weyl points, nodal lines, and nodal chains as the system parameters (such as strain or tight-binding coefficients) are tuned.

[1] Q.-S. Wu, A. A. Soluyanov, and T. Bzdušek, Science 365, 1273 (2019)
[2] J. Ahn, S. Park, and B-J Yang, Phys. Rev. X 9, 021013 (2019)
[3] A. Bouhon, R.-J. Slager, and T. Bzdušek, arXiv:1907.10611 (2019)