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

Abstract

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 pseudospins in on-chip integrated valley devices. Recently, it was 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 the valley Hall effect. Then, we review recent works on nanostructures for valley-selective directional emission from 1L-TMDCs.

1. Introduction

As the growth of electronics and computing infrastructure nears the limits of the so-called Moore’s law [1], new directions in information processing and harvesting become of crucial importance in today’s technology. This issue inspired new fields of research, such as spintronics and valleytronics, in which spin or pseudospin is used as an alternative information carrier. Currently, valleytronics is of great interest due to the discovery of atomically thin single-layered (1L) transition-metal dichalcogenides (TMDCs) [2,3,4,5,6,7,8,9,10,11,12,13,14]. Monolayer TMDCs are formed (Figure 1a) by a hexagonal network of transition metal atoms (M: Mo, W) hosted between two hexagonal lattices of chalcogenide atoms (X: S, Se). Electronically, 1L-TMDCs behave as two-dimensional semiconductors, with bandgaps lying in the visible and near-infrared (IR) range. In the monolayer limit, the bandgaps of these materials are direct, enabling enhanced interactions of dipole transitions with light. An essential property of 1L-TMDCs is the broken inversion symmetry of their hexagonal 2D crystals, which, in combination with time-reversal symmetry, leads to opposite spins at the +K and −K valleys, effectively locking the spin and valley degrees of freedom (pseudospin or Berry curvature) [15,16,17]. Optical manipulation of the valley degree of freedom can be realized via exciton resonances based on the valley contrasting optical selection rules (for instance with ${\sigma }^{-}$ and ${\sigma }^{+}$ light excitation). The unique opportunity of addressing the valley index makes it possible to explore this binary quantum degree of freedom as an alternative information carrier [12,18,19,20], which may complement both classical and quantum computing schemes based on charge and spin. This possibility of using the valley degree of freedom for information processing and storage (similar to spin in spintronics) leads to conceptually new applications for valleytronics [12].

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 was demonstrated how coupling these materials to optical nanoantennas and metasurfaces can overcome this obstacle. It was demonstrated that resonant optical nanostructures and nanoantennas can effectively enhance and direct the emission from opposite valleys in 1L-TMDCs into different directions [21,22,23,24]. The proposed nanostructures for valley-selective directional emission can be divided into two groups: nanostructures for spatial separation of valley degrees of freedom using surface waves, and for separation in momentum-space, based on which photons with opposite helicity are emitted in different directions. Spatial separation of valley degrees of freedom may be accompanied by division of valley excitons in space [24], or transformation of valley exciton pseudospin to photonic degrees of freedom (e.g., transverse optical spin angular momentum) via optical spin–orbit coupling [23] (or both these processes).

This paper is devoted to reviewing state-of-the-art advances in 1L-TMDC valley degree-of-freedom separation (valley-selective directional emission and exciton sorting) mediated by nanostructures and nanoantennas. The paper is organized as follows: in Section 2, we briefly discuss the optical properties of two-dimensional (2D) TMDC materials, paying special attention to their photoluminescence/absorption spectra, dynamics of valley depolarization, and the valley Hall effect; in Section 3, we summarize recent published work devoted to nanostructures for 1L-TMDC valley separation. Special attention is devoted to our and our collaborators’ recent results in this area.

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 MoS₂, MoSe₂, WS₂, and WSe₂) 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-WS₂ (b) and 1L-MoS₂ (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_A and X_B excitons, but the PL emission from the X_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 space. 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 ~0.1–10% [25]. These low values can be significantly improved (up to ~95%) via chemical treatment with organic superacids [54,55], or via their coupling to specifically tailored resonant optical nanocavities and metasurfaces [42,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70].

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. Examples include the observation of strong plasmon–exciton coupling [63,70,71,72], pronounced Fano resonances [58], and plasmon-induced resonance energy transfer [73], which are very attractive for various quantum optics and nanophotonic applications. These effects benefit from the 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 bandgap 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 [15,17,74,75,76,77]. This effect is key for valleytronics applications, which focus on the manipulation of valley pseudo-spins to encode signals and information [12,23,77,78]. The operation principles of valleytronics are mainly based on the valley Hall effect [75], which refers to the opposite Hall currents for carriers located in opposite valleys (Figure 1f). Excitation of 1L-TMDCs by ${\sigma }^{+}$ and ${\sigma }^{-}$ light causes a nonequilibrium population of the +K or −K valley. These carriers have opposite Berry curvature, which acts like an effective magnetic field in the momentum space. As a result, these two sorts of valley particles (+K or −K) propagate in different directions. If the particles are electrically charged (electrons, holes, or trions), this effect gives rise to the Hall voltage. If the particles are neutral, the Hall effect can be detected by measuring the circularly polarized components of the emitted photoluminescence (PL) intensity. In this case, the effect can be characterized by the degree of valley polarization:

$$\rho (\omega )=\frac{I_{+}(\omega )-I_{-}(\omega )}{I_{+}(\omega )+I_{-}(\omega )},$$

(1)

where $I_{+}(\omega )$ and $I_{-}(\omega )$ refer to the PL intensity with ${\sigma }^{+}$ and ${\sigma }^{-}$ polarization, respectively. The Hall effect can also be detected in reflectance experiments via so-called Kerr rotation spectroscopy, when a system illuminated by linearly polarized light causes a rotation of polarization in a scattered signal [79,80,81]. By spatially resolving the Kerr signal, the valley polarization can be mapped out in a sample, and accumulation of the +K and −K valley polarizations can be observed.

A general scheme for generating and detecting valley polarization was first proposed and realized in another 2D material—graphene—with broken inversion symmetry [82,83]. Then, a free-carrier valley Hall effect in monolayer MoS₂ was demonstrated using electric readout methods [75] in the form of transverse motions of valley-polarized carriers in the presence of an in-plane electric field. More recently, an exciton valley Hall effect was reported for a monolayer MoS₂ where the exciton motion was driven by a temperature gradient [77]. Moreover, other factors such as uncontrolled strain can also lead to the separation of valley-polarized excitons [12]. More recently, the valley-polarized exciton dynamics in a 2D semiconductor van-der-Waals heterostructure was also studied and was proven to be a versatile platform for valleytronics [84].

For a full description and understanding of 1L-TMDC behavior, it is important to know the exciton and coherence lifetimes. The exciton lifetime describes the average time for 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) [85]. If the system is excited by ${\sigma }^{+}$ or ${\sigma }^{-}$ light, the coherence lifetime says how long the +K or −K valley is 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 [86]. The dynamics of photoexcited electron−hole pairs in 1L-WSe₂ at room temperature and ambient conditions was directly traced in Reference [87]. It was shown that, after highly nonresonant interband excitation by a femtosecond laser pulse, the concentration of free carriers increased, reaching its maximum after 0.5 fs. This excitation was followed by a rapid carrier relaxation toward the respective band minima. More than half of the carriers are already bound into excitons 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 decaying, and it 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 binding energies (~0.5 eV) of excitons, which are well above the thermal energy (~50 meV).

The valley-polarization degree dynamics of 1L-WSe₂ was experimentally studied in Reference [79] using the pump–probe Kerr rotation technique. It was demonstrated that the exciton valley depolarization time decreased significantly from ~6 ps to ~1.5 ps when the lattice temperature increased from 4 K to 125 K, which is in good agreement with theoretical estimations [88]. In Reference [81], these results were obtained from ab initio calculations, which took into account all possible mechanisms of valley depolarization. Similar results were demonstrated in Reference [41]. At room temperature, the valley depolarization times are considerably shorter than 1 ps, which is much shorter than the exciton lifetime. Thus, all previously reported carrier and exciton valley Hall effects relying on nonzero valley polarization were observed at low temperatures. At room temperature, the valley-polarization lifetime is too short to be utilized in real applications. However, since the binding energy 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 are reviewed in the next section.

3. Nanostructures for Valley-Selective Directional Emission

3.1. Single Nanoantennas

As mentioned in the introduction, the proposed nanostructures for valley-selective response can perform spatial separation of the valley degree of freedom with surface waves or separation in K-space when photons with opposite helicity are emitted in different directions. Moreover, spatial separation of the valley degree of freedom may be accompanied by real dividing of valley excitons [24] or the transformation of valley exciton pseudospin to photonic degrees of freedom via optical spin–orbit coupling [21,23,89,90,91,92] (or both these processes). Below, we describe all these possibilities with various examples from the recent literature.

Photons as information carriers are more robust and controllable than excitons, especially at room temperature. Thus, nanostructures supporting the coupling of valley pseudospin to photonic degrees of freedom (e.g., transverse optical spin angular momentum, t-OSAM) are desirable for on-chip integrated valley devices. The optical spin–orbit coupling effect provides a robust one-to-one transformation of the valley degree of freedom into t-OSAM because of spin-momentum locking. One realization of this idea was implemented in Reference [23] (Figure 2a).

The structure consists of a single silver nanowire placed on top of a TMD flake (WS₂), consisting of five layers, which is an indirect semiconductor, but still preserves valley-polarization properties [93]. The silver nanowire supports guided modes possessing t-OSAM in the out-plane direction. Spin-momentum locking of these plasmonic modes allows the transformation of valley polarization into directional emission: the system, excited by circularly polarized light in the center of the nanowire, launches plasmonic modes carrying t-OSAM in the left or right direction as a function of their valley polarization. Note that, because of the structure symmetry, this operation can be achieved under asymmetric-laser-spot excitation in the transverse direction (y). This effect can be described by the coupling efficiency, $K_{\exp }=(I_L-I_R)/(I_L+I_R)$, where $I_L$ and $I_R$ are the light intensities directed to the left and right side, respectively. Thus, when this value is zero, the structure shows the same coupling on both sides. The measurement results of the coupling efficiency for 594-nm ${\sigma }^{+}$ and ${\sigma }^{-}$ light excitation as a function of the laser-spot coordinate in the transverse direction are shown in Figure 2b,c. The purple dotted lines show the total PL intensity measured from the ends of the nanowire as a function of the excitation position.

Plasmonic (Au) nanoantennas for valley-dependent far-field emission (separation in K-space) when photons with opposite helicity are emitted in different directions were theoretically proposed in Reference [22] (Figure 2d). The antenna consists of two closely arranged plasmonic bars different in their lengths. The short bar possesses electric-dipole resonance, while the longer one has quadrupole resonance at the same operation wavelength. The entire nanoantenna being excited by a circularly polarized dipole (modeled as two orthogonal short dipoles with a relative phase of $\Delta \phi =\pm {90}^{°}$) emits in different directions. The asymmetry originates from the constructive or destructive interference of fields from dipole and quadrupole resonances. Thus, when the coupled 1L-TMDC–nanoantenna system is excited by light of different circular polarizations, the emission from the two valleys (+K and −K) is emitted in opposite directions (Figure 2e). The nanoantennas in Figure 2d are assumed to be located far enough from each other such that the response of the system is defined with good approximation by the response of the isolated nanoantenna.

3.2. 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, $\mathsf{\Lambda }$, rotated per column by an angle, $\pi /6$ (Figure 3a). The resulting metasurface is covered by a mechanically exfoliated monolayer of WS₂. The metasurface chirality in plane allows valley-selective 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-MoS₂ 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 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-MoS₂ on metasurfaces away from the laser excitation spot. The right plot shows the results from 1L-MoS₂ on an Ag homogeneous substrate, where a vanishing degree of valley polarization is observed. A valley-exciton dividing of ~2 µm 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.

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 MoS₂ at room temperature, which allows utilizing this approach in valleytronics applications at room temperature.

4. Conclusions

In this paper, we reviewed state-of-the-art advances in 1L-TMDC valley degree-of-freedom separation, accompanied by valley-selective directional emission or real exciton dividing, mediated by resonant plasmonic nanostructures and nanoantennas. These works are aimed at overcoming a significant obstacle in the field of valleytronics related to short valley depolarization times and relatively short exciton lifetimes at room temperature, which prevent using valley pseudospin in on-chip integrated valley devices. The observed nanostructures for valley-selective directional emission allow either the spatial separation of the valley degree of freedom with surface waves, or separation in K-space when photons with opposite helicity are emitted in different directions. The existing works show that spatial separation of the valley degree of freedom may be accompanied by real dividing of valley excitons in space, or a transformation of valley exciton pseudospin into a photonic degree of freedom (e.g., transverse optical spin angular momentum) via optical spin–orbit coupling (or both these processes). This analysis was supported by a brief review of the optical properties of 2D TMDC materials, with attention paid to their photoluminescence/absorption spectra, dynamics of valley depolarization, and the valley Hall effect.