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In transition metal dichalcogenides layers of atomic scale thickness, theelectron-hole Coulomb interaction potential is strongly influenced by the sharpdiscontinuity of the dielectric function across the layer plane. This featureresults in peculiar non-hydrogenic excitonic states, in which exciton-mediatedoptical nonlinearities are predicted to be enhanced as compared to theirhydrogenic counterpart. To demonstrate this enhancement, we performed opticaltransmission spectroscopy of a MoSe$_2$ monolayer placed in the strong couplingregime with the mode of an optical microcavity, and analyzed the resultsquantitatively with a nonlinear input-output theory. We find an enhancement ofboth the exciton-exciton interaction and of the excitonic fermionic saturationwith respect to realistic values expected in the hydrogenic picture. Suchresults demonstrate that unconventional excitons in MoSe$_2$ are highlyfavourable for the implementation of large exciton-mediated opticalnonlinearities, potentially working up to room temperature.

Exciton-exciton interaction beyond the hydrogenic picture in a MoSe$_2$ monolayer in the strong light-matter coupling regime