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

Abstract

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 WS 2 , 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 R 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.

Nonlinear optics of two‐dimensional transition metal dichalcogenides

“…Hu et al demonstrated that SHG valley photons of monolayer WS 2 could be routed to the desired direction in free space by using a metasurface which imposed phase and spin modulation to SHG valley photons (Figure C) . Apart from SHG, the valley selective TPA luminescence was also reported by Xiao et al A valley polarization degree of 35% was reported when the two‐photon excitation was in resonance with 2 p exciton (Figure D) . For the valley selective SHG, the total angular momentum should be conserved, including valley angular momentum, exciton angular momentum, lattice angular momentum, and photon spin angular momentum .…”

“…The excitonic‐enhanced SHG may explain why χ (2) deviated so much in different literatures. Please be noted that the excitonic effect‐enhanced SHG can only occur in s state because there is no excitonic angular momentum change and the SHG selection rule is satisfied …”

“…Copyright 2019, Nature Publishing Group. D, Valley polarized TPL of monolayer WS 2 . Copyright 2015, Nature Publishing Group.…”

“…Please be noted that the excitonic effect-enhanced SHG can only occur in s state because there is no excitonic angular momentum change and the SHG selection rule is satisfied. 66,148 The exciton energy can be actively tuned by electron doping, 149 which renders that SHG can be actively tuned by applying a bias for a fixed excitation wavelength. Seyler et al observed that SHG of monolayer WSe 2 could change four times when the gate voltage was swept from −80 to 80 V. 64,150 Figure 4C shows that the dominated exciton in WSe 2 can be tuned from positive trion (X + ), neutral exciton (X 0 ) to negative trion (X − ) by varying the gate voltage.…”

“…176 Apart from SHG, the valley selective TPA luminescence was also reported by Xiao et al A valley polarization degree of 35% was reported when the two-photon excitation was in resonance with 2p exciton ( Figure 8D). 148 For the valley selective SHG, the total angular momentum should be conserved, including valley angular momentum, exciton angular momentum, lattice angular momentum, and photon spin angular momentum. 148 The SHG and TPA selection rule is different.…”