# Valley-Selective Response of Nanostructures Coupled to 2D Transition-Metal Dichalcogenides
## 3 Nanostructures for Valley-Selective Directional Emission
### Metasurfaces
in-plane dipoles coupling to TM polarized SPPs is very small. These challenges require metasurfaces with asymmetric grooves, where the effective coupling between 1L-TMDC excitons and SPP waves is possible on the side walls. This crucial concept extends the photonic spin Hall effect to planar metasurfaces with only an in-plane electric field, and it enables chirality-dependent coupling between TMDs and metasurfaces. Figure 4c shows the experimentally observed degree of the valley-polarization (left) pattern over the metasurface. These results demonstrate the asymmetry of the measured PL signal from 1L-MoS\({}_{2}\) on metasurfaces away from the laser excitation spot. The right plot shows the results from 1L-MoS\({}_{2}\) on an Ag homogeneous substrate, where a vanishing degree of valley polarization is observed. A valley-exciton dividing of \(\sim\)2 \(\upmu\)m is demonstrated. Figure 4d demonstrates a line profile, \(\Delta I(y)=I_{+}(y)-I_{-}(y)\), measured (left) and simulated (right) along the groove. The black dashed curve shows the fitting by subtracting two Gaussian curves. Figure 4: Routing valley excitons in 1L-MoS\({}_{2}\) with a metasurface made of monocrystalline silver (Ag) [24]. (**a**) Illustration of valley excitons in a monolayer TMD controlled by a metasurface consisting of asymmetric grooves. Not only are valley-polarized excitons spatially separated, but photons with opposite helicity are also emitted in different directions, serving as a valley–photon interface mediated by excitons. (**b**) SEM image of the cross-section of the asymmetric grooves. (**c**) Illustration of valley-exciton separation caused by the metasurface. Real-space color plot of valley polarization obtained from the (left) MoS\({}_{2}\) metasurface and (right) MoS\({}_{2}\) flat silver film under 532-nm laser excitation. (**d**) A line profile, \(\Delta I(y)=I_{+}(y)-I_{-}(y)\), along the groove. The black dash curve is a fitting by subtracting two Gaussian curves (**left**). A line profile from the simulation (**right**). (**e**) Illustration of the helicity-dependent directional emission of the valley excitons (**left**). Numerically simulated far-field emission pattern from valley excitons with opposite helicity (**right**). (**f**) Set-up for the K-space mapping of PL. (**g**) Experimental \(\rho(k_{||})\) distribution in photon momentum space obtained from (**left**) the MoS\({}_{2}\) metasurface and (**right**) the MoS\({}_{2}\) flat silver film. It was also demonstrated that the metasurface emits photons with opposite helicity in different directions, dividing the valley degree of freedom in the far-field pattern (Figure 4e). Numerical results (Figure 4e, right panel) show that the \(\sigma^{+}\) and \(\sigma^{-}\) polarized photons preferentially emit toward the upper and lower hemisphere, respectively. The experimental results of measurement of the valley degree of freedom in the K-space, obtained with the set-up sketched in Figure 4f, are summarized in Figure 4g. These results clearly show the ability of the metasurface to divide the \(+\)K and \(-\)K valley exciton emissions into different radiation directions. Concluding this section, we note that the proposed solutions for separating valley index are rather general, and they can be applied to a wide range of layered materials. Moreover, no exciton valley polarization is required, as is the case for MoS\({}_{2}\) at room temperature, which allows utilizing this approach in valleytronics applications at room temperature.