# Valley-Selective Response of Nanostructures Coupled to 2D Transition-Metal Dichalcogenides
## 2 Optical Properties of 1L-TMDCs  
In this section, we briefly discuss the optical properties of 2D-TMDCs, addressing the interested reader to more detailed review papers on the topic [4; 7; 9; 25; 26; 27]. Single-layered TMDCs (like MoS\({}_{2}\), MoSe\({}_{2}\), WS\({}_{2}\), and WSe\({}_{2}\)) behave as two-dimensional semiconductors, with their bandgaps lying in the visible and near-infrared (IR) ranges [7]. In the monolayer limit, TMDCs are particularly interesting because their bandgaps become direct, thus enabling enhanced interactions of dipole transitions with light [28]. The evolution of the band structure of 2D-TMDCs was calculated from first principles (density functional theory) in Reference [13]. The transition to a direct bandgap semiconductor makes it easier for photons with an energy equal to the bandgap to be absorbed or emitted, without requiring additional phonons to be absorbed. As a result, the resonant excitonic absorption of a single TMDC monolayer can be as large as 5-20%, which is one order of magnitude larger than, for instance, that of quantum well systems [29]. Experimentally, researchers verified the monolayer nature of chemical vapor deposition (CVD)-grown or exfoliated TMDCs using atomic force microscopy and photoluminescence (PL) spectroscopy [30]. For example, Figure 1b-e demonstrate the band structures of 1L-WS\({}_{2}\) (b) and 1L-MoS\({}_{2}\) (d), as well as their absorption spectra and photoluminescence (Figure 1c,e) at room temperature. The PL spectrum consists of two resonances corresponding to \(X_{\rm A}\) and \(X_{\rm B}\) excitons, but the PL emission from the \(X_{\rm B}\) exciton is very weak. We note that the optical properties of 1L-TMDCs (PL spectra, Raman spectra, and transmission/absorption spectra) may slightly depend on several factors, including fabrication techniques (mechanical exfoliation or chemical vapor deposition), type of substrate, defects, and others. Reduced dielectric screening and strong Coulomb interactions between charged particles (electrons and holes) result in strong excitonic resonances in the visible and near-IR range with large binding energies. Strong Coulomb interactions in these materials lead to the formation of strongly bound excitons (binding energies of 0.2 to 0.8 eV) [31; 32; 33], charged excitons (trions) [34; 35], and excitonic molecules (biexcitons) [36; 37; 38; 39; 40]. Localized and dark excitonic states in 1L-TMDCs were also demonstrated [36; 41; 42]. Due to the monolayer nature of 1L-TMDCs, their high oscillator strength, and their potential for tuning, these materials become a unique class of 2D materials for optoelectronic applications, such as photodetection and light harvesting [43; 44; 45; 46], phototransistors and modulation [47; 48], and light-emitting diodes [49; 50; 51]. Operation of 1L-TMDCs in a single-photon emission regime was also reported [52; 53]. The enhancement of the exciton transition dipole in 1L-TMDCs can be understood assuming that it is proportional to the electron-hole overlap in real psec. Recently, it was demonstrated that the bright-exciton dipole moment can be further enhanced via the dielectric screening effect in high-dielectric-constant solvents (like ethanol and water), which gives rise to asymmetric Fano resonance and strong coupling effects [30]. The quantum yield of emission of these materials depends on many factors, including fabrication techniques (mechanical exfoliation or chemical vapor deposition), type of substrate, defects, and so on. Typically, as-prepared 1L-TMDCs have a relatively low quantum yield of \(\sim\)0.1-10% [25]. These low values can be significantly improved (up to \(\sim\)95%) via chemical treatment with organic superacids [54; 55], or via their coupling to specifically tailored resonant optical nanocavities and metasurfaces [42; 56; 57; 58; 59; 60; 70]. A variety of new optical effects stemming from the interaction of 1L-TMDCs with plasmonic (i.e., made of noble metals) and high-index dielectric (Si, Ge, GaP) nanocavities was demonstrated.