Non-Abelian band topology in non-interacting metals

Tomáš Bzdušek

Stanford University

We show that non-Abelian topological structure arises inside the momentum space of semimetals and metals under various symmetry settings [1], including PT-symmetric systems with negligible spin-orbit coupling, and C2T-symmetric systems with or without spin-orbit coupling. This results in non-Abelian topological charges of band-structure nodes, similar to those that describe disclinations in biaxial nematics, implying non-trivial braiding phenomena inside the momentum space [2]. We discuss how the non-Abelian band topology can be captured using various mathematical techniques, including homotopy groups, characteristic classes, and Wilson-loop Pfaffians [3]. We conclude the talk by briefly commenting on the interplay of this newly discovered topological structure with space-group symmetry.

[1] Q.S. Wu, A. A. Soluyanov, T. Bzdušek, arXiv:1808.07469 (2018)
[2] A. Tiwari and T. Bzdušek, arXiv:1903.00018 (2019)
[3] A. Bouhon, R.-J. Slager, T. Bzdušek, arXiv:1907.10611 (2019)