  Transition-metal dichalcogenide bilayers exhibit a rich exciton landscape
including layer-hybridized excitons, i.e. excitons which are of partly intra-
and interlayer nature. In this work, we study hybrid exciton-exciton
interactions in naturally stacked WSe$_2$ homobilayers. In these materials, the
exciton landscape is electrically tunable such that the low-energy states can
be rendered more or less interlayer-like depending on the strength of the
external electric field. Based on a microscopic and material-specific
many-particle theory, we reveal two intriguing interaction regimes: a
low-dipole regime at small electric fields and a high-dipole regime at larger
fields, involving interactions between hybrid excitons with a substantially
different intra- and interlayer composition in the two regimes. While the
low-dipole regime is characterized by weak inter-excitonic interactions between
intralayer-like excitons, the high-dipole regime involves mostly
interlayer-like excitons which display a strong dipole-dipole repulsion and
give rise to large spectral blue-shifts and a highly anomalous diffusion.
Overall, our microscopic study sheds light on the remarkable electrical
tunability of hybrid exciton-exciton interactions in atomically thin
semiconductors and can guide future experimental studies in this growing field
of research.
