How can topology and geometry of electrons alter optical properties of quantum matter?
In solid state materials, collections of quantum states can be viewed as vector bundles [1].
These bundles can be topologically non-trivial, similarly to the famous Möbius band. Moreover, the bundles of electrons in crystals enjoy a Riemannian structure, i.e., they encode quantum metrics [2], which can be loosely viewed as spanning background geometries over momentum spaces.
In topological semimetals, such metrics also host singularities analogous to the metric singularities in general relativity, the black holes. We predict a range of smoking-gun probes for singular and higher-order, e.g., torsional, geometric tensors realised by the electronic states in topological materials [3-5].
In this seminar, I will show how these can be rooted in the theory of optical responses [6], in multiple topological quantum matter guises. In the realm of strongly interacting electrons, I will further conclude with our recent discovery of topological excitons realising non-trivial quantum geometry within excitonic state bundles in organic semiconductors [7].
[1] A. Kitaev, AIP Conf. Proc. 1134, 22-30 (2009).
[2] J.P. Provost, and G. Vallee, Commun. Math. Phys., 76, 289-301 (1980).
[3] W.J. Jankowski, et. al., Phys. Rev. B. 111, L081103 (2025) [Editor's suggestion].
[4] W.J. Jankowski, and R.-J. Slager, Phys. Rev. Lett. 133, 186601 (2024).
[5] W.J. Jankowski, et. al., Phys. Rev. B. 110, 075135 (2024).
[6] J. Ahn, et. al., Nat. Phys. 18, 290-295 (2022).
[7] W.J. Jankowski, et. al., Nat. Commun. 16, 4661 (2025).
Wojciech is a PhD student at the University of Cambridge, in the group of Prof. Robert-Jan Slager.
About the qGAP meeting series
Welcome to qGAP, our seminar series on Quantum Physics and Quantum Technology.
The series of seminars/lectures are meant to cover broadly activities at UiO and elsewhere related to quantum physics and technologies, mainly from a theoretical perspective, though we also welcome experimental talks.
We aim at having regular seminars, discussions of recent articles, presentations by master and PhD students and more. We aim for this series to be a combination of research talks and journal clubs.
Educational topics are also most welcome.
Please feel free to suggest speakers, yourself included!
Get in touch with Gunnar Lange to suggest a speaker or if you would like to be included in the mailing list.
All are welcome!
Upcoming
- Hsuan-Yin Lin (Simula UiB) June 6