In this seminar, we explore the effects of local electron-electron repulsion on the single- and two-particle properties of a quantum spin Hall insulator, using a consistent mean-field approach. Specifically, we examine the Bernevig, Hughes, and Zhang model and find that the interaction between electrons leads to the emergence of an insulating and magnetoelectric phase that breaks inversion and time-reversal symmetries, but not their product. We observe that the softening of two exciton branches, each possessing finite and opposite Chern numbers, signals the approach to this phase from both topological and nontopological sides. Furthermore, we discuss the implications of these excitons, including their surface counterparts, on various physical observables. Overall, our study sheds light on the role of electron-electron repulsion in quantum spin Hall insulators and highlights the emergence of a novel phase that could be seen as a condensate of topological excitons.
