  Strong Coulomb interactions in single-layer transition metal dichalcogenides
(TMDs) result in the emergence of strongly bound excitons, trions and
biexcitons. These excitonic complexes possess the valley degree of freedom,
which can be exploited for quantum optoelectronics. However, in contrast to the
good understanding of the exciton and trion properties, the binding energy of
the biexciton remains elusive, with theoretical calculations and experimental
studies reporting discrepant results. In this work, we resolve the conflict by
employing low-temperature photoluminescence spectroscopy to identify the
biexciton state in BN encapsulated single-layer WSe2. The biexciton state only
exists in charge neutral WSe2, which is realized through the control of
efficient electrostatic gating. In the lightly electron-doped WSe2, one free
electron binds to a biexciton and forms the trion-exciton complex. Improved
understanding of the biexciton and trion-exciton complexes paves the way for
exploiting the many-body physics in TMDs for novel optoelectronics
applications.
