  Preserving a high degree of valley polarization of excitons in photo-excited
transition-metal dichalcogenide monolayers (TMD-MLs) is desirable for the
valley-based photonic applications, but widely recognized as a hard task
hindered by the intrinsic electron-hole exchange interaction. In this study, we
present a comprehensive investigation of valley-polarized finite-momentum
excitons in WSe$_2$-MLs over the entire Brillouin zone by solving the
density-functional-theory(DFT)-based Bethe-Salpeter equation (BSE) under the
guidance of symmetry analysis. We reveal that finite-momentum excitons are
actually in general well immune from the exchange-induced valley
depolarization, except for those with specific exciton momenta directionally
coincide with the axes associated with the $3\sigma_v$ and $3C_2'$ symmetries
in TMD-MLs. Governed by the symmetries, the valley pseudo-spin texture of the
full-zone exciton band in the momentum space is locally featured by individual
skyrmion-like structures where highly valley-polarized finite-momentum exciton
states are centred. Remarkably, we show that the high degrees of valley
polarizations of the finite-momentum exciton states are excellently well
transferable to the optical polarizations in the resulting phonon-assisted
photo-luminescences, suggesting the prospective usefulness of those
inter-valley excitons in valley-based photonics.
