Ten-valley excitonic complexes in charge-tunable monolayer WSe$_2$

Excitons dominate the optical response of two-dimensional (2D) semiconductors. Strong interactions produce peculiar excitonic complexes, which provide a testing ground for exciton and quantum many-body theories. Here, we report a hitherto unobserved many-body exciton that emerges upon filling both the K and Q valleys of WSe$_2$. We optically probe the exciton landscape using charge-tunable devices with unusually thin dielectrics that facilitate doping up to several $10^{13}$ cm$^{-2}$. We observe the emergence of the thermodynamically stable complex when 10 valleys are electrostatically filled. We gain insight into its physics using magneto-optical measurements. Our results are well-described by a model where the number of distinguishable Fermi seas interacting with the photoexcited electron-hole pair defines the complex's behavior. In addition to expanding the repertoire of excitons in 2D semiconductors, this complex could probe the limit of exciton models and answer open questions about screened Coulomb interactions in 2D semiconductors.