Valley-Selective Response of Nanoantennas Coupled to 2D Transition Metal Dichalcogenides

Monolayer (1L) transition metal dichalcogenides (TMDCs) are attractive materials for several optoelectronic applications because of their strong excitonic resonances and valley-selective response. Valley excitons in 1L-TMDCs are formed at opposite points of the Brillouin zone boundary, giving rise to a valley degree of freedom that can be treated as a pseudospin and may be used as a platform for information transport and processing. However, short valley depolarization times and relatively short exciton lifetimes at room temperature prevent using valley pseudospin in on-chip integrated valley devices. Recently it has been demonstrated how coupling these materials to optical nanoantennas and metasurfaces can overcome this obstacle. Here, we review the state-of-the-art advances in valley-selective directional emission and exciton sorting in 1L-TMDC mediated by nanostructures and nanoantennas. We briefly discuss the optical properties of 1L-TMDCs paying special attention to their photoluminescence/absorption spectra, dynamics of valley depolarization and valley Hall effect. Then, we review recent works on nanostructures for valley-selective directional emission from 1L-TMDCs.


Introduction
New directions in information processing and harvesting is of crucial importance in today's technology, giving rise to new fields of research, such as spintronics and valleytronics, in which spin or pseudospin are used as alternative information carriers. Currently, valleytronics is of great interest due to the discovery of atomically thin single layered (1L) transition metal dichalcogenides Section 3 we summarize recent work devoted to nanostructures for 1L-TMDC valley separation published. Special attention is devoted to our and our collaborators' recent results in this area. which gives rise in asymmetric Fano resonance and strong coupling effects [45]. The quantum yield of emission of these materials depend 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 ~0.1-10% [46]. These low values can be significantly improved (up to ~95%) by chemical treatment by organic superacids [47,48] or by coupling them to specifically tailored resonant optical nanocavities and metasurfaces [33, [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63].
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 has been demonstrated. Examples include the observation of strong plasmon-exciton coupling [56,[63][64][65], pronounced Fano resonances [51] and plasmon-induced resonance energy transfer [66], which are very attractive for various quantum optics and nanophotonic applications. These effects benefit from localization of light within plasmonic and dielectric resonators, enabled by their small mode volumes and the strong dipole moment of excitons in 1L-TMDCs.
Direct band gap transitions in 1L-TMDCs occur at the energy-degenerate K (K') points at the edges of the 2D hexagonal Brillouin zone (schematically shown in Figure 1a). Due to inversion symmetry breaking and strong spin-orbital coupling in 1L-TMDCs, the electronic states of the two valleys have different chirality, which leads to valley-selective circular dichroism [13,[67][68][69][70][71] where the exciton motion is driven by a temperature gradient [71]. Moreover, other factors such as uncontrolled strain can also lead to the separation of valley-polarized excitons.
For a full description and understanding of the 1L-TMDCs behavior, it is important to know the exciton and coherence lifetimes [76]. The exciton lifetime describes the average time during which an exciton exists, and it usually defines the excitonic spectral linewidth. This time also limits the propagation distance of excitons. The coherence time defines the time during which an exciton remembers the state of the excitation field (for example, polarization). If the system is excited by  σ or  σ light, the coherence lifetime says how long the +K or -K valley are inequivalently polarized (nonzero valley polarization). In 1L-TMDCs the coherence time is usually less than the exciton lifetime (at room temperature) and it is key for valleytronics and quantum optics applications [77].
The dynamics of photoexcited electron−hole pairs in 1L-WSe 2 at room temperature and ambient conditions has been directly traced in Ref. [78]. It has been shown that after highly nonresonant interband excitation by the femtosecond laser pulse, the concentration of free carriers increases, reaching its maximum after 0.5 fs. This excitation is followed by a rapid carrier relaxation towards the respective band minima. More than half of the carriers are bound into excitons already 0.4 ps after the excitation. The ratio between excitons and unbound electron-hole pairs increases up to 0.5 ps.
Interestingly, the exciton concentration grows even after 0.5-0.6 ps, when the free carrier concentration starts to decay, and continues up to 1 ps. Then, both concentrations decay on a time scale of a few picoseconds, while a significant fraction of free carriers is still observed after 5 ps. We note that the results for cryogenic temperatures are similar because of strong bounding energies (~0.5 eV) of excitons, which are well above the thermal energy (~50 meV).
The valley polarization degree dynamics of 1L-WSe 2 has been experimentally studied in Ref. of excitons is very large in 1L-TMDCs, it is therefore both feasible and highly desirable to design a photonic device to manipulate valley excitons at room temperature even without valley polarization.
These structures will be reviewed in the next section.

Metasurfaces
Metasurfaces for valley-selective response of 2D transition-metal dichalcogenides at room temperature have been proposed in Refs. [17,19]. The metasurface proposed in Ref. [17] consists  Another realization of a metasurface for valley exciton sorting and routing in a 1L-MoS2 has been proposed in Ref. [19]. The metasurface consists of asymmetrically shaped grooves on a silver (Ag) film arranged in a subwavelength 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. As already mentioned, the +K and -K valley excitons in a 1L-TMDCs can be modeled as in-plane circularly polarized dipoles oscillating with opposite helicity.
However, their in-plane oriented dipoles cannot asymmetrically excite conventional SPPs, since they do not engage the required out-of-plane chirality. Moreover, the efficiency of 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 in-plane electric field, and it enables chirality dependent coupling between TMDs and metasurfaces. Figure  Concluding this section, we note that the proposed solutions to separate valley index is rather general, and it can be applied to a wide range of layered materials. Moreover, no exciton valley polarization is required, as is the case for MoS2 at room temperature, which allows utilizing this approach in valleytronics applications at room temperature.

Conclusions
In this paper, we have reviewed state-of-the-art advances in 1L