Valley-selective chiral phonon replicas of dark excitons and trions in monolayer WSe_{2}

We observe a set of three replica luminescent peaks at ∼21.4 meV below the dark exciton, and negative and positive dark trions (or exciton polarons) in monolayer WSe_{2}. The replica redshift energy matches the energy of the zone-center E^{′′}-mode optical phonons. The phonon replicas exhibit a parallel gate dependence and the same g-factors as the dark excitonic states, but follow the valley selection rules of the bright excitonic states. While the dark states exhibit an out-of-plane transition dipole and valley-independent linearly polarized emission in the in-plane directions, their phonon replicas exhibit an in-plane transition dipole and valley-dependent circularly polarized emission in the out-of-plane directions. Our results and symmetry analysis show that the K-valley dark exciton decays into a left-handed chiral phonon and a right-handed photon, whereas the K^{′}-valley dark exciton decays into a right-handed chiral phonon and a left-handed photon. Such valley selection rules of chiral phonon replicas can be utilized to identify the valleys of the dark excitonic states and explore their chiral interactions with phonons.