CPM Seminar

Towards Topological Diagnosis of Correlated Electron Systems

Maia Vergniory

Département de physique
Université de Sherbrooke

Topological quantum chemistry (TQC) has provided a complete descrip on of the universal proper es of all possible atomic band insulators across all space groups by taking crystalline unitary symmetries into account. It links the chemical and symmetry structure of a given material with its topological proper es. While this formalism has lled the gap between mathema cal classi ca on and the prac cal diagnosis of topological materials, an obvious limita on is that it only applies to weakly interac ng systems. It remains an open ques on to what extent this formalism can be generalized to correlated systems that exhibit symmetry-protected topology, such as Kondo or Mo insulators.

In this talk, I will rst introduce TQC and its applica on to correlated systems. We will then analyze the topology of SmB₆ Kondo insulators and compare our ndings with many-body results. Building on this insight, we will present a new family of experimentally grown Kondo materials and discuss their topological properties.

For Mo insulators, we have developed a general framework to address this outstanding ques on, and we illustrate its power by applying it to these systems. In our approach, the concept of Green's func on Berry curvature-- which is frequency-dependent-- is introduced. We apply this concept to a system that features symmetry-protected nodes in its noninterac ng band structure. Here, strong correla ons drive the system into a Mo insula ng state, crea ng contours in frequency-momentum space where the Green's func on vanishes. The Green's func on Berry ux associated with these zeros is found to be quan zed, serving as a direct probe of the system's topology. Our framework enables a comprehensive search for strongly correlated topological materials characterized by Green's func on topology. Finally, we will discuss a recent experiment on the correlated Mo insulator NiS₂.

References:
[1] All topological bands of all stoichiometric materials, Maia G Vergniory, Benjamin J Wieder, Luis Elcoro, Stuart SP Parkin, Claudia Felser, B Andrei Bernevig, Nicolas Regnault, Science 376 (6595), eabg9094 (2022)
[2] Mikel Iraola, Niclas Heinsdorf, Apoorv Tiwari, Dominik Lessnich, Thomas Mertz, Francesco Ferrari, Mark H Fischer, Stephen M Winter, Frank Pollmann, Titus Neupert, Roser Valen , Maia G Vergniory, Physical Review B 104 (19), 195125 (2021)
[3] Mikel Iraola, Iñigo Robredo, TItus Neupert, Juan L Mañes, Roser Valen , Maia G Vergniory, Physical Review Research 6 (3), 033195
[4] Chandan Se y, Fang Xie, Shouvik Sur, Lei Chen, Silke Paschen, Maia G Vergniory, Jennifer Cano, Qimiao Si, arXiv preprint arXiv:2311.12031
[5] Mikel Iraola, Haojie Guo, Fabio Orlandi, et al. arXiv:2504.02063