Excitonic topology and quantum geometry in organic semiconductors.

Excitons drive the optoelectronic properties of organic semiconductors which underpin devices including solar cells and light-emitting diodes. Here we show that excitons can exhibit topologically non-trivial states protected by inversion symmetry and identify a family of organic semiconductors realising the predicted excitonic topological phases. We also demonstrate that the topological phase can be controlled through experimentally realisable strains and chemical functionalisation of the material. Appealing to quantum Riemannian geometry, we predict that topologically non-trivial excitons have a lower bound on their centre-of-mass spatial spread, which can significantly exceed the size of a unit cell. Furthermore, we show that the dielectric environment allows control over the excitonic quantum geometry. The discovery of excitonic topology and excitonic Riemannian geometry in organic materials brings together two mature fields and suggests many new possibilities for a range of future optoelectronic applications.