Microscopic modelling of exciton-exciton interactions in atomically thin semiconductors

The successful isolation and characterization of the technologically promisingmaterial graphene in 2004 has spurred huge interest in other two-dimensionalmaterials. Transition-metal dichalcogenides (TMDs), being one such class ofmaterials, display intriguing properties from both a fundamental and techno-logical point of view. In particular, they constitute a platform for studyingnovel physical phenomena such as many-body correlations and exotic statesof matter. The exceptionally strong Coulomb interaction in these materialsgives rise to tightly bound excitons, i.e., electron-hole pairs, which are nei-ther of purely fermionic nor purely bosonic character. In the weak excitationregime, it is sufficient to treat excitons as pure bosons, but as the density ofexcitons increases their fermionic substructure becomes important, resultingin highly non-trivial scattering characteristics between excitons.In this work we have developed a microscopic theory of exciton-exciton in-teractions in TMD monolayers and van der Waals heterostructures. Thelatter are formed when stacking two monolayers on top of each other andthis extends the rich exciton landscape to include also spatially separated in-terlayer excitons, consisting of electrons and holes located in different layers.We find that intralayer and interlayer excitons interact in fundamentally dif-ferent ways – while intralayer excitons interact primarily through quantum-mechanical exchange interactions, interlayer excitons can be viewed as re-pelling dipoles. We demonstrate the crucial role of these strong repulsivedipole-dipole interactions for exciton transport and diffusion. Moreover, weshed light on the particular importance of dark excitons in the context ofexciton-exciton annihilation, which crucially governs the efficiency of TMD-based optoelectronic applications. The microscopic insights gained in thiswork can be used to study more exotic quantum phenomena such as strongcorrelations or exciton-exciton interactions between hybridised exciton statesin moire materials