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Optical Selection Rule based on Valley-Exciton Locking for 2D Valleytronics

Optical selection rule fundamentally determines the optical transition between energy states in a variety of physical systems from hydrogen atoms to bulk crystals such as GaAs. It is important for optoelectronic applications such as lasers, energy-dispersive X-ray spectroscopy and quantum computation. Recently, single layer transition metal dichalcogenide (TMDC) exhibits valleys in momentum space with nontrivial Berry curvature and excitons with large binding energy. However, it is unclear how the unique valley degree of freedom combined with the strong excitonic effect influences the optical excitation. Here we discover a new set of optical selection rules in monolayer WS2,imposed by valley and exciton angular momentum. We experimentally demonstrated such a principle for second harmonic generation (SHG) and two-photon luminescence (TPL). Moreover, the two-photon induced valley populations yield net circular polarized photoluminescence after a sub-ps interexciton relaxation (2p->1s) and last for 8 ps. The discovery of this new optical selection rule in valleytronic 2D system not only largely extend information degrees but sets a foundation in control of optical transitions that is crucial to valley optoeletronic device applications such as 2D valley-polarized light emitting diodes (LED), optical switches and coherent control for quantum computing.