LSM Webinar: Non-Abelian topology of electron energy bands

by Dr Tomas Bzdusek

Thursday 13 Aug 2020, 14:00 → 15:00 Europe/Zurich

Join Zoom Meeting
https://uzh.zoom.us/j/91765424583?pwd=eHJpb3BvOWVTSCs2SkFVUVNQVlY0dz09

Meeting ID: 917 6542 4583
Passcode: 898673

Abstract:
The energy bands of electrons inside the momentum space of crystalline matter are characterized by topological invariants, which cannot change as long as the energy gap between the bands remains open. Such a description applies both to fully gapped insulators and superconductors, as well as to various types of band degeneracies (so-called `nodes') in semimetals and metals. Topological invariants are usually captured by Abelian groups, such as the Kane-Mele $Z_2$ invariant of time-reversal-symmetric topological insulators, or the integer Chern number that stabilizes Weyl nodes.

In this seminar, I will reflect on our recent discovery of a non-Abelian topological invariant that arises in certain space-time-inversion symmetric crystals. I will first explain the origin and the geometric meaning of its non-commutative behaviour, which suggests the possibility of non-trivial braiding of nodes inside the momentum space. Afterwards, I will outline how the non-Abelian band topology enters the mathematical characterization and how it affects the observable properties of chain nodes in elementary Sc [1], of Weyl nodes in ZrTe [2], and of triple-point nodes in Li2NaN [3].

References:
[1] Q.S. Wu, A. A. Soluyanov, and T. Bzdušek, "Non-Abelian band topology of non-interacting metals", Science 365, 1273--1277 (2019)
[2] A. Bouhon, Q.S. Wu, R.-J. Slager, H. Weng, O. V. Yazyev, and T. Bzdušek, "Non-Abelian reciprocal braiding of Weyl points and its manifestation in ZrTe", Nature Physics (2020)
[3] P. M. Lenggenhager, X. Liu, S. S. Tsirkin, T. Neupert, and T. Bzdušek, "Multi-band nodal links in triple-point materials under strain" (in preparation, 2020)