Interaction-Induced Crystalline Topology of Excitons

• Topological band theory has celebrated various successes over the last few years, such as the recent classifications of crystalline materials based on their space group symmetry. We are currently witnessing a drive to generalise this theory to the case where interactions between electrons become relevant, with much work focused on ground states. In this talk, I will present an alternative approach by exploring the topology of interaction-induced excitations. Specifically, I will discuss how the topological theory of symmetry indicators can be applied to exciton band structures in centrosymmetric semiconductors. An important distinction will be made between topological invariants inherited from the electron and hole bands and those intrinsic to the exciton wave function. Focusing on the latter, I will introduce a class of exciton bands for which the maximally localized exciton Wannier states are shifted with respect to the electronic Wannier states by a quantized amount. We refer to these excitons as “shift excitons”. Our analysis explains how the exciton spectrum can be topologically nontrivial and sustain exciton edge states in open boundary conditions even when the underlying noninteracting bands have a trivial atomic limit. Finally, I will demonstrate the presence of shift excitons as the lowest energy neutral excitations of the Su-Schrieffer-Heeger model in its trivial phase when supplemented by local two-body interactions.