# Valley-Selective Response of Nanostructures Coupled to 2D Transition-Metal Dichalcogenides
## 3 Nanostructures for Valley-Selective Directional Emission
### Metasurfaces  
Metasurfaces for valley-selective response of 2D transition-metal dichalcogenides at room temperature were proposed in References [21; 24]. The metasurface proposed in Reference [21] consists of an array of rectangular nanoapertures in a 200-nm film of gold arranged with a grating period, \(\Lambda\), rotated per column by an angle, \(\pi/6\) (Figure 3a). The resulting metasurface is covered by a mechanically exfoliated monolayer of WS\({}_{2}\). The metasurface chirality in plane allows valley-selective  
Figure 2: (**a**) Conceptual illustration of the directional emission of valley-polarized exciton in WS\({}_{2}\). The valley pseudospin and photon path are coupled by the means of spin-orbit coupling of light [23]. (**b**,**c**) Measured directional coupling efficiency, \(K_{\text{exp}}=(I_{L}-I_{R})/(I_{L}+I_{R})\), of the guided emission as a function of the position of the excitation 594-nm laser in the transverse direction (y) with (**b**) left- and (**c**) right-handed circular polarization. Gray lines represent fitting results obtained using the calculated directional coupling efficiency. Purple dotted lines correspond to the total photoluminescence (PL) intensity measured from the ends of the nanowire as a function of the excitation position. (**d**) Array of double-bar plasmonic antennas for valley-selective directional emission from a 1L-TMDC. (**e**) Polar plots of the radiated power in the far field; \(\Delta\varphi=\pm 90^{\circ}\) denotes right and left circularly polarized excitons [22]. spin-momentum-locked propagation of the PL signal (Figure 3b). Moreover, it was shown that the proposed resonant metasurface shows a coupling regime, which is very close to the strong coupling regime [72; 94] with Rabi splitting energy of 40 meV at the crossing point (A-exciton emission energy, 2.01 eV) between the uncoupled exciton and the surface mode of the metasurface. As a result, the entire structure forms hybrid exciton-photon quasiparticles (referred to as chiralitons). In this case, the spatial separation of the valley degree of freedom is accompanied by real dividing of valley excitons in space in the form of polaritons. The difference between PL dispersions obtained with left and right circularly polarized excitations is displayed in Figure 3c, showing the net flows of chiralitons with spin-determined momenta. The hybrid structure also shows resonant reflection with pronounced asymmetry in differential white-light reflectivity maps (Figure 3d). Another realization of a metasurface for valley-exciton sorting and routing in 1L-MoS\({}_{2}\) was proposed in Reference [24]. The metasurface consists of asymmetrically shaped grooves on a silver (Ag) film arranged in a sub-wavelength period, Figure 4a. The SEM image of the cross-section of the realized asymmetric grooves is shown in Figure 4b. The spatial separation of valley excitons of opposite chirality is enabled by coupling to surface plasmon polaritons (SPPs) propagating along the asymmetrically shaped grooves. The operation principles of this approach are described below. As already mentioned, the +K and \(-\)K valley excitons in 1L-TMDCs can be modeled as in-plane circularly polarized dipoles oscillating with opposite helicity. However, the in-plane-oriented dipoles cannot asymmetrically excite conventional SPPs in a metasurface with symmetrically shaped grooves. Moreover, the efficiency of  
Figure 3: (**a**) Chiral coupling of valley excitons in a 1L-TMDC with spin-momentum-locked surface plasmons on a surface with an array with \(\varphi\)-rotated rectangular apertures [21]. (**b**) Real-space leakage radiation microscope images of the surface plasmons launched by \(\sigma^{-}\) and \(\sigma^{+}\) excitations. (**c**) Differential PL dispersion spectrum for left and right circularly polarized excitations. The shaded regions in all panels are removed by the laser line filter, and the cross-cuts are taken at 2 eV. (**d**) Differential angle-resolved reflection spectrum for left and right circularly polarized light.