TRR 360 Seminar:

Topology in multi-level systems and braiding of band singularities

F. Nur Ünal

Topology in multi-level systems and braiding of band singularities

Dr. F. Nur Ünal

TCM Group, Cavendish Laboratory, University of Cambridge, United Kingdom

Recent years have witnessed the discovery of novel multi-gap topologies that go beyond all previously-known classifications, arising from intricate non-Abelian braiding procedures. I will talk about non-Abelian charges that can be associated with band singularities in certain multi-level systems and discuss their braiding procedures. I will introduce new non-Abelian topological phases, some of which come with no static counterparts, highlighting new topological invariants required to characterise these phases. The underlying non-Abelian charges can be however quite elusive, and consequently direct measurement of these charges and topological invariants has been challenging. To this end, I will identify observable signatures within reach of state-of-the-art experiments and present concrete protocols with first experimental verifications. Finally, I will go beyond these non-Abelian topological considerations and introduce visually powerful geometric descriptions that arise for multi-level systems (qudits) with more general applications.

arXiv:2511.03894

arXiv:2603.04489

Nat. Comm. 15, 1144 (2024)

Phys. Rev. Lett. 133, 093404 (2024)

Phys. Rev. Research 4, 023120 (2022)