Abstract

Quantum geometry allows us to quantify the distance between quantum states. It underpins numerous phenomena in condensed matter physics, from electron transport in flat band systems to topological twists of electronic wave functions. In this talk, I will give an overview of how quantum geometry can be extended to explore the excited states of materials. Focusing on excitons, bound electron-hole pairs, I will first give an overview of the possible exciton topological phases as they arise from the underlying electron and hole states. I will next describe how quantum geometry dictates that topological excitons are larger than their trivial counterparts and show how this results in enhanced exciton diffusion. I will use a family of organic semiconductors hosting topological excitons to illustrate these ideas.