Nonlinear optical selection rule based on valley-exciton locking in monolayer ws2

Optical selection rules fundamentally determine the optical transitions between energy states in a variety of physical systems, from hydrogen atoms to bulk crystals such as gallium arsenide. These rules are important for optoelectronic applications such as lasers, energy-dispersive X-ray spectroscopy, and quantum computation. Recently, single-layer transition metal dichalcogenides have been found to exhibit valleys in momentum space with nontrivial Berry curvature and excitons with large binding energy. However, there has been little study of how the unique valley degree of freedom combined with the strong excitonic effect influences the nonlinear optical excitation. Here, we report the discovery of nonlinear optical selection rules in monolayer WS2, an important candidate for visible 2D optoelectronics because of its high quantum yield and large direct bandgap. We experimentally demonstrated this principle for second-harmonic generation and two-photon luminescence (TPL). Moreover, the circularly polarized TPL and the study of its dynamics evince a sub-ps interexciton relaxation (2p -> 1s). The discovery of this new optical selection rule in a valleytronic 2D system not only considerably enhances knowledge in this area but also establishes a foundation for the control of optical transitions that will be crucial for valley optoelectronic device applications such as 2D valley-polarized THz sources with 2p-1s transitions, optical switches, and coherent control for quantum computing.