Microscopic modelling of exciton-exciton interactions in atomically thin semiconductors

Licentiate thesis, 2022

The successful isolation and characterization of the technologically promising
material graphene in 2004 has spurred huge interest in other two-dimensional
materials. Transition-metal dichalcogenides (TMDs), being one such class of
materials, display intriguing properties from both a fundamental and techno-
logical point of view. In particular, they constitute a platform for studying
novel physical phenomena such as many-body correlations and exotic states
of matter. The exceptionally strong Coulomb interaction in these materials
gives rise to tightly bound excitons, i.e., electron-hole pairs, which are nei-
ther of purely fermionic nor purely bosonic character. In the weak excitation
regime, it is sufficient to treat excitons as pure bosons, but as the density of
excitons increases their fermionic substructure becomes important, resulting
in 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. The
latter are formed when stacking two monolayers on top of each other and
this 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 repulsive
dipole-dipole interactions for exciton transport and diffusion. Moreover, we
shed light on the particular importance of dark excitons in the context of
exciton-exciton annihilation, which crucially governs the efficiency of TMD-
based optoelectronic applications. The microscopic insights gained in this
work can be used to study more exotic quantum phenomena such as strong
correlations or exciton-exciton interactions between hybridised exciton states
in moire materials.