Theory of exciton–exciton interactions in semiconductors and topological insulators

Understanding the mutual interactions between excitons—bound electron–hole pairs in semiconductors—is an important but challenging problem due to the exciton’s composite nature. I will present an analytical approach deriving a two-exciton Schrödinger equation that yields an effective, spin-dependent potential between two excitons. This potential incorporates all exchange processes between identical particles, thus avoiding the common perfect-boson approximation. In the Born–Oppenheimer limit, where the holes are taken to be much heavier than the electrons, it exactly reproduces the Heitler–London theory for the dihydrogen molecule, and thus constitutes a generalization of this well-known result to the case of arbitrary mass ratios. The effect of virtual excited states can be systematically introduced in our theory and in particular delivers the expected van der Waals 1/r⁶ attraction at large separations. Extending our framework to include band topology and geometry provides a unified description of interacting excitons in systems with general electronic Hamiltonians. Specific model examples show how these ingredients can significantly influence the spectrum of bound exciton pairs. Our results advance the understanding of excitonic interactions in semiconductors and topological insulators and can be applied to the study of biexciton spectra, correlated excitonic matter, and beyond.