Quentin MARSAL : Probing the robustness of topological phases with nonlocal topological markers

Space-resolved markers of quantum geometry such as the local Chern marker or the Bott index have opened the way to characterization of topological phases from the perspective of position space, which has been particularly useful to diagnose amorphous topological phases.

In this presentation, I will focus on the nonlocal part of quantum geometric indicators and demonstrate that it behaves as correlation functions independently of the material’s structure, showing sharp variations in the vicinity of topological transitions and exhibiting a unique pattern in real space for each transition. Those patterns enable a refined, class-internal probe of topological stability. As such, nonlocal quantum geometric indicators provide a more efficient and versatile tool to understand and predict the stability of topological phase transitions.

Marsal et al., ArXiv:2511.09664