Effects of quantum geometry on exciton condensation

The interplay between electronic correlations and quantum geometry has emerged as a central theme in modern condensed matter physics. Motivated by recent discoveries of topological excitonic insulators, we investigate how the band topology and quantum geometry influence exciton formation and condensation. Using a prototypical three-band model, we show that distinct exciton modes can be stabilized by tuning the underlying band geometry. Remarkably, we find that the condensation gap of the excitonic insulator differs significantly between topologically trivial and nontrivial bands, even when their dispersions are made identical. This result demonstrates that quantum geometric effects play a non-negligible role in determining the stability and gap magnitude of excitonic condensates beyond what is captured by the band dispersion alone. Our work highlights the need to extend the standard BCS–BEC crossover framework to explicitly incorporate the geometric character of Bloch bands.