Nanophotonics with 2D Transition Metal Dichalcogenides

Two-dimensional transition metal dichalcogenides (TMDCs) have recently become attractive semiconductor materials for several optoelectronic applications, such as photodetection, light harvesting, phototransistors, light-emitting diodes, and lasers. They are particularly appealing because their bandgap lies in the visible and near-IR range, and they possess strong excitonic resonances, high oscillator strengths, and valley-selective response. Coupling these materials to optical nanocavities enhances the quantum yield of exciton emission, enabling advanced quantum optics and nanophotonic devices. Here, we review state-of-the-art advances on hybrid exciton-polariton structures based on monolayer TMDCs coupled to plasmonic and dielectric nanocavities. We first generally discuss the optical properties of 2D WS2, WSe2, MoS2 and MoSe2 materials, paying special attention to their energy and photoluminescence/absorption spectra, excitonic fine structure, and to the dynamics of exciton formation and valley depolarization. We then discuss light-matter interactions in hybrid exciton-polariton structures. Finally, we focus on weak and strong coupling regimes in monolayer TMDCs-based exciton-polariton systems, envisioning research directions and future opportunities based on this novel material platform.


Introduction
In recent years, researchers all over the world have made important steps towards the development of new materials with unique optical and electronic properties. One prominent example consists of atomically thin single layered (1L) transition metal dichalcogenides (TMDCs) [1-9]. Monolayer TMDCs are formed by a hexagonal network of transition metal atoms (Mo, W) hosted between two hexagonal lattices of chalcogenide atoms (S, Se). The resulting materials have the common formula MX2 (where M is Mo or W and X is S or Se). Electronically, 1L-TMDCs behave as two-dimensional semiconductors, with bandgaps lying in the visible and near-IR range. This property profitably distinguishes them from other 2D materials, like graphene and hBN, whose bandgaps occur at longer wavelengths. In the monolayer limit, the bandgaps of these materials are direct, enabling enhanced interactions of dipole transitions with light. 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) [10][11][12][13][14], charged excitons (trions) [15][16][17], and excitonic molecules (biexcitons) [19][20][21][22][23]. Localized and dark excitonic states in 1L-TMDCs have also been demonstrated [19,24,25]. Inversion symmetry breaking and strong spin-orbital coupling in 1L-TMDCs lead to direct bandgap transitions occurring at energy-degenerate K (K') points at the edges of the 2D hexagonal Brillouin zone, enabling valley-selective circular dichroism [25][26][27][28][29][30]. This effect has become of great importance in the emerging field of valleytronics, which exploits valley pseudo-spin manipulation to transmit information [7].
Due to the monolayer nature of 1L-TMDCs, their high oscillator strength and the potential for tuning, these materials have become a unique class of 2D materials for optoelectronic applications, such as photodetection and light harvesting [ , which are very attractive for various quantum optics and nanophotonic applications. These effects benefit from squeezed states of light within plasmonic and dielectric resonators, enabled by their small mode volumes and the strong dipole moment of excitons in 1L-TMDCs. Resonant nanophotonic structures can also alter 1L-TMDCs emission properties, for example brighten the so-called dark excitons [24,51], which poorly radiate without this essential coupling with optical resonators. In addition, nanophotonic structures may improve other inherently weak properties of 1L-TMDCs, such as exciton energy transfer, which is typically limited to a short range of ~1 μm. Recently, it has been demonstrated that the exciton energy transfer range can be extended to tens of microns in hybrid structures mediated by an exciton-surface plasmon polariton-exciton conversion mechanism [67].
In the following, we provide an overview of the state-of-the-art advances of hybrid excitonpolariton structures based on 1L-TMDCs coupled to plasmonic and dielectric nanocavities. In Section 2, we discuss the optical properties of 2D WS2, WSe2, MoS2 and MoSe2 materials, with special attention to their energy spectra, photoluminescence and absorption spectra, excitonic fine structure, and dynamics of exciton formation and valley depolarization. Then in Section 3, we describe suitable optical resonances of plasmonic and dielectric nanoantennas that may be employed to enhance TMDCs. In Section 4, we provide a theoretical background to describe light-matter interactions in hybrid exciton-polariton structures, focusing on weak and strong coupling regimes of light-meter interaction. Finally, in Section 5, we discuss these regimes in 1L-TMDCs based exciton-polariton systems, emphasizing various practical realizations.
Direct band gap transitions in 1L-TMDCs occur at the energy-degenerate K (K') points, at the edges of the 2D hexagonal Brillouin zone. 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 [25][26][27][28][29][30]. This effect is key for valleytronics applications, which focus on the manipulation of valley pseudo-spins to encode signals and information [7]. Despite a tremendous interest in this area, valleytronics faces the obstacle of short valley depolarization times, only ~5 ps for 1L-TMDCs at cryogenic temperatures and sub-picosecond at room temperatures. Inversion symmetry breaking and strong spin-orbital coupling also lead to so-called spin-forbidden dark excitons polarized along the out-of-plane direction, which can be brightened by strong static magnetic fields [72] or tipenhanced Purcell effect [24].
Below we review the optical properties of 1L-TMDCs with focus on WS2 and WSe2, which are very often used for LED and laser technologies. Almost any conclusion drawn in the following is also applicable to other 1L-TMDC materials, because of their similar nature. We must stress that the optical properties of 1L-TMDCs (PL spectra, Raman spectra, transmission/absorption spectra) may slightly vary as a function of several factors, including fabrication techniques (mechanical exfoliation or chemical vapor deposition), type of substrate, defects and others.

Optical properties of 2D WS2, photoluminescence tuning and excitonic fine structure
1L-tungsten disulfide (WS2) is one of the most studied 2D transition-metal dichalcogenide semiconductors [19,22,64,[73][74][75][76][77]. 1L-WS2 has been attracting growing interest due to its unique properties, such as large spin-orbit coupling, high emission quantum yield [78], large exciton/trion binding energies [13,79], and demonstrated nonblinking photon emission [69]. Additionally, this material is attractive because it enables strong-coupling with excitons [57,64,75] and trions [17], as discussed in more detail in Section 5 in the context of tuning PL spectra and excitonic fine structure (trions, biexcitons). 1L-WS2 contains a single layer of W atoms with 6-fold coordination symmetry, hexagonally packed between two trigonal atomic layers of S atoms. The energy band diagram (energy versus wavevector k) of 1L-WS2, as well as its absorption spectra (orange curve) and photoluminescence (blue curve), are shown in Figs. 1(a), (b). The direct bandgap of 1L-WS2 is ~2.1 eV [45,81]. Inversion symmetry breaking of the crystal lattice combined with strong spin-orbit coupling results in a large valence band splitting (~427 meV) at the K (K') points in the first Brillouin zone, Fig. 1(a). This phenomenon gives rise to two different valley excitons (XA and XB excitons), which are associated with optical transitions from the upper and the lower valence band to the bottom of the conduction band, respectively. The XA exciton binding energy was demonstrated to be equal ~0.71 eV [79]. Note that the exciton binding energy may strongly depend on TMDC fabrication technique, as well as the defect and exciton concentrations [82]. It causes an appearance of two resonances in the absorption spectrum, Fig. 1(b). The PL spectrum also consists of two resonances corresponding to XA and XB excitons, but the PL emission from XB exciton is very weak [right inset in Fig. 1(b)]. It has been demonstrated that WS2 PL spectrum can be tuned in various ways, including chemical doping [74], mechanical strain [83], type of substrate [84], surrounding dielectric environment [85], electrical doping [18,73], laser intensity [18,82,86], and interaction with optical cavities [17,87,88]. For example, in [18] tunable emission in 1L-WS2 was demonstrated by controlling the electrical doping strength. Fig. 1(c) shows the PL spectra of 1L-WS2 at room temperature for different gate voltages, ranging from -40 to 40 V, continuously modulating the charge carrier density. These results demonstrate that the exciton peak has two components, the neutral exciton XA and the charged exciton XA -(trion), located at lower energy. At cryogenic temperatures, trions can contribute significantly to the PL emission spectra [17]. Note that the doping by free charge carriers can occur because of WS2 interaction with the dielectric environment (for example, the substrate) [89].
At low temperatures, other electron-hole states can be observed. Fig. 1(d) presents the integrated PL emission intensities of XA(excitons), XA -(negatively charged trions), XAXA (biexcitons), and LS (localized excitons) from 1L-WS2 as a function of the excitation power at 4.2K [18]. At low excitation intensities, LS, XA, and XAgive the main contribution to PL emission. The emission from exciton and trion states increases linearly ( 1.0  ) with the excitation power, whereas the emission from LS shows a sublinear dependence ( 0.6  ). On the contrary, the integrated intensity of biexcitons XAXA grows quadratically with the excitation power ( 1.9  ), as expected. Similar results for biexciton emission from edges of triangular 1L-WS2 have been demonstrated in [22]. Thus, biexciton PL emission dominates for highpower excitation, and it has been observed only at cryogenic temperatures (~4K). We note that the trion state can also have a finite structure with triplet and singlet trions, which can be observed in PL spectra at a temperature of 4K [90].

Optical properties of 2D WSe2. Dynamics of exciton formation and valley depolarization
The second 1L-TMDCs material that we discuss is WSe2, which has also been very well studied [11,[91][92][93][94]. As applications of this material, in the following we will describe dynamics of exciton formation and valley depolarization. This material is also attractive for enabling strong-coupling regimes of light-matter interaction [50]. Also in this case, the conclusions about this material can be applied to other 1L-TMDC materials, except specific aspects of exciton-phonon interactions [76].
Figs. 2(a), (b) show the energy structure of 1L-WSe2 [ Fig. 2(a)] and the corresponding absorption spectra (orange curve) and photoluminescence (blue curve) [ Fig. 2(b)]. The direct bandgap is ~1.6 eV. As in the case of 1L-WS2, this material supports XA and XB excitons, which are associated with optical transitions from the upper and the lower valence band to the bottom of the conduction band. Accordingly, the absorption spectrum has two resonances corresponding to XA and XB excitons. For the full description of the temporal behavior of 1L-TMDCs like WSe2, it is important to know their exciton and coherence lifetimes [99]. The exciton lifetime describes the average time during which an exciton exists, and it usually defines the excitonic spectral linewidth. The coherence time defines the time during which an exciton remembers the state of the excitation field (for example, polarization). The coherence time is usually less than the exciton lifetime and it is key for valleytronics and quantum optics applications [100].
In Ref. [91], a femtosecond optical-pump/mid-IR-probe (with probe energy ∼170 meV, which coincides with the difference between exciton eigenstates) was used to directly monitor the dynamics of photoexcited electron−hole pairs in 1L-WSe2, Fig. 2(c). After highly nonresonant interband excitation (3.04 eV) 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 (Fig. 2(c), grey curve). The ratio between excitons and unbound electron−hole pairs increases up to 0.5 ps (Fig. 2(c), blue curve). 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. These experiments have been performed at room temperature and ambient conditions. These relatively short characteristic times loss  of exciton dynamics in 1L-TMDCs (1-5 ps) are caused by nonradiative processes, like exciton dissociation by defects and phonons, as well as possible four-body interactions [101], whereas the radiative exciton recombination is characterized by much longer times ( rad~0 .1 1   ns) [102]. The mismatch between these times causes a low quantum yield in emission, which can be defined as

Optical properties of 2D MoS2 and MoSe2
For the sake of completeness, we also summarize the fundamental optical properties of 1L-MoS2 and MoSe2 materials. Figs. 3(a),(c) show energy structure of 1L-MoS2 and 1L-MoSe2, respectively. Figs. 3(b),(d) show the absorption spectra (orange curve) and photoluminescence spectra (blue curve) of 1L-MoS2 and 1L-MoSe2, respectively. These materials also have XA and XB exciton resonances in their absorption spectra.  Fig. 3(b). The binding energies of excitons and trions in 1L-MoS2 were extracted to be around 900 and 40 meV, respectively. Notably, the trion/exciton PL peaks in 1L-MoS2 materials can be tuned by different dielectric environments, with blue shifts of up to 40 meV and significant enhancement in PL emission intensities [108]. Relatively high exciton decay times of ~100 ps can be significantly reduced (up to ~10ps) by strong excitation [101].
In contrast, 1L MoSe2 is a direct-gap semiconductor with a bandgap of ~1.65 eV [109]. Fig. 3(d) shows that the band-edge (XA) exciton in the PL emission spectrum appearing at ~1.6 eV. At cryogenic temperatures, two features at ~1.65 and ~1.62 eV in this spectrum are attributed to the exciton and negative trion [21,110]. Trions and biexcitons in 1L MoSe2 (at cryogenic temperatures) with large binding energies of 30meV (trions) and 50−70 meV (biexcitons) can be also resolved [16,111] Fig. 4 shows as an example the optical features of typically sized plasmonic and dielectric NCs. The resonant behavior of a dielectric NC strongly depends on its size, which may be used to tune its resonance to the response of an excitonic subsystem. For example, Figs. 4(a) and (b) demonstrate the optical properties of two spherical dielectric NCs (c-Si) with radius of 80 nm and 100 nm, respectively. These NCs have an MD resonance (blue solid curve) tuned to the PL maximum of, respectively, 1L-WS2 and WSe2. The scattering efficiency ( sct  ) reaches 90% for an 80 nm-particle and increases up to 95% for the 100 nm-particle.

Optical resonances of plasmonic and dielectric nanocavities
On the contrary, the plasmonic resonance (ED) of a plasmonic (Ag) NC weakly depends on the particle size, as it is mostly affected by the interface between metal and the surrounding material, and its curvature. Fig. 4(c) shows that an increase in particle radius from 10 nm to 30 nm redshifts the resonance only by ~10 nm, with associated decrease in its Q-factor from ~30 to ~10. The size increase turns the particle from mainly-absorptive (scattering efficiency ~5%) to mainly-scattering (scattering efficiency ~60%). The plasmonic resonance depends strongly on the permittivity of the dielectric environment, Fig. 4(d). For instance, an increase of h  from 1 to 4 leads to a large redshift in the resonance peak from 370 nm (air) to 500 nm ( 4 with an increase of efficiency (up to 90%) for the R=30 nm particle, and a corresponding reduction in Q-factor to ~5. The shape and arrangements of NCs are other convenient ways to tune their resonant properties. It has been demonstrated that the plasmonic resonance frequency can be engineered on demand by controlling these design parameters [145][146][147]. This mechanism for tunability is particularly important for 1L-TMDCs, since their absorption and PL peaks are usually significantly divided. In this case, the shape tunability of plasmonic NCs allows to adjust two (or even more) resonances to the absorption peak (for high excitation rate) and to the PL peak (high emission rate), simultaneously [53]. In the case of dielectric NCs, the shape tunability paves a way to control the total emission intensity through destructive interference in farfield of the radiation of two (or more) neighboring modes of different nature, with the realization of an almost nonradiative field configuration [148-150], leading to a large increase of Q factor and enhanced light-matter interactions.

Weak and strong coupling regimes
Coupling of an excitonic subsystem, such as 1L-TMDCs, with a NC can be described in the Jaynes-Cummings formalism [151] by the following matrix element of the coupling Hamiltonian: being the transition dipole moment of a two-level exciton subsystem, e and being the elementary charge and reduced Planck constant, and r being the radius-vector operator. The quantity v0 () Er is the vacuum electric field (the field per one photon) of the resonator mode at an exciton position. Thus, the coupling strength of the exciton and NC is described by the coupling constant (g), which defines two characteristic regimes of interaction and, hence, spontaneous emission. If the condition g   , the system instead is strongly coupled. In this regime, the system is characterized by energy exchange between exciton and cavity (Rabi oscillations), resulting in a more complex behavior of spontaneous emission and splitting of the scattering spectrum (Rabi splitting) [65,152]. To describe the coherent scattering spectra of the system, the coupled harmonic oscillator model can be used [59,153]. This model considers a cavity driven by an external field, which is coupled to the exciton resonance with a coupling constant g.
To increase g and achieve strong coupling, we can increase the dipole moment of the exciton subsystem and/or reduce the effective mode volume eff V , which can be defined in the low loss limit as [154,155] where () Er is the electric field of mode, () r  is the permittivity distribution, and integration runs over the entire space including the NC and surrounding space.
As we discussed above, 1L-TMDCs have very strong dipole moment of excitons because of their direct bandgap and 2D nature. The effective mode volume is usually less than the physical volume of the resonant cavity and it strongly depends on its nature (plasmonic or dielectric This equation says that the quantum yield can be enhanced by Purcell factor, which is important for 1L-TMDCs, because of their low radiation efficiency and decay times mismatch ( rad loss ex ex  ).

Weak coupling regime
Weak coupling regime in 1L-TMDCs based nanostructures manifests itself in increasing of the PL intensity without noticeable change in the spectrum. This increase relies on Purcell effect, which leads to quantum yield enhancement. The Purcell effect is caused by the mode volume (2) shrinking, and it depends on the NC Q-factor through its geometry and arrangement, as in Eq. (3). The so-called gap plasmonic modes, arising between nearby plasmonic particles, are of special interest because of their small mode volumes. In Ref.
[54], monomer and dimer (supporting gap modes) Au NCs of four different sizes were examined for PL intensity enhancement from CVD-synthesized WS2 flakes, Fig. 5(a). The figure shows that relatively small dimer NC formed by closely placed Au particles (75 nm) cause the largest enhancement of PL emission, whereas larger dimers have effects comparable to a single monomer. Another exciting way to enhance the PL emission intensity is based on NCs designed to support two resonant (gap) modes at both 1L-TMDC PL emission and absorption maxima. In Ref. [53], a NC consisting of a silver (Ag) nanocube (~75 nm edge length) located over a gold film divided by a dielectric nanoscale spacer (<10 nm) has been studied [see the inset in Fig.  5(b)]. The dielectric spacer was filled by 1L-MoS2. The NC supports two split modes at wavelengths 420 nm and 660 nm, with ultrasmall effective mode volumes of  As we discussed in Section 2, 1L-TMDCs are of special interest because of their valleyselective circular dichroism, caused by lattice inversion symmetry breaking and strong spinorbital coupling. Thus, the coupling of excitons belonging to different valleys in chiral NC, which interact differently with left (   ) and right (   ) circularly polarized light is of major interest for practical applications. An interesting geometry is a spiral ring resonant structure (Au) on SiO2/Au/SiO2/Si substrate, as presented in Fig. 5(c), inset. The 1L-MoS2 is placed between spiral rings and the first SiO2 spacer. The structure demonstrates strong dependence of PL intensity on the circular polarization handedness of the laser excitation. For example, for a left-handed 2-turn spiral rings the structure demonstrates 10-fold enhancement in PL intensity for   excitation at 633 nm wavelength, whereas the   excitation causes only a slight enhancement, Fig. 5(c).
In addition to conventional bright excitonic states, as discussed in Section 2, 1L-TMDCs possess spin-prohibited dark excitons with polarization in the out-of-plane direction, characterized by ultrahigh radiative lifetimes because of their low radiation loss. These states are particularly interesting for quantum information processing applications. It has been demonstrated that in 1L-TMDCs dark excitons can be excited through two-photon excitation spectroscopy [13] and in-plane magnetic field [72]. Additionally, emission from dark excitons can be detected if a 1L-TMDC is excited by a field with vanishing in-plane component, as it has been realized with SPP waves [157]. In Ref. [24], it was shown that ultrahigh Purcell effect can be used for dark exciton spectroscopy even at room temperature. Fig. 5(d) shows results from tip-enhanced PL spectroscopy of 1L-WSe2 arranged on Au substrate. In-plane side excitation (field distribution is shown in the right inset) demonstrates enhancement in PL intensity (blue curve) over emission for high tip distances (black curve) with peak at the right exciton (X0). More interestingly, out-plane side excitation (field distribution shown in the left inset) results in strong optical field confinement in the gap between the tip and the Au substrate. In this case, the PL peak is shifted to the dark exciton emission (XD), with PL intensity enhancement 5

Strong coupling regime
Although structures supporting gap plasmons possess small effective mode volumes, they suffer from high dissipative losses, hindering the achievement of strong coupling regimes. Thus, for this purpose more carefully designed structures with low mode volumes and lower dissipative losses must be used [17,50,57,75,158]. Fig. 6(a) shows a possible layout, consisting of an individual gold nanorod placed on 1L-WS2 (substrate is SiO2/Si). Fig. 6(b) shows darkfield scattering spectra from different individual gold nanorods coupled to the same 1L-WS2 flake for different nanorod aspect ratios, which allow to estimate the Rabi splitting energy for various frequency detunings. The resulting colored normalized scattering spectra from the hybrid structure with different detunings between plasmon resonances and the exciton is shown in Fig. 6(c). Splitting of high-energy and low-energy branches, with Rabi splitting energy of 106 meV, which satisfies the strong coupling condition, can be observed. Active control over strong coupling via temperature has also been observed.
As we discussed in Section 2, charged excitons (trions) can also be observed in 1L-TMDCs PL spectra at cryogenic temperatures or under 1L-TMDCs doping. The strong coupling with trions is of special interest because they form charged exciton-polaritons, which can be actively controlled by an external electrical bias. Charged exciton polaritons have been demonstrated in Ref. [17] at low temperatures. The structure is composed of Ag nanoprisms placed on 1L-WS2 (substrate is SiO2/Si). In this case, the electrical doping from the substrate was insignificant, hence only neutral (X 0 ) have been observed in PL spectra at room temperature, whereas the trion (X + ) has manifested itself at low temperatures, Fig. 6(e). The enhancement of trion coupling strength up to ~50 meV (the Rabi splitting is ~100 meV) at 77 K has been observed, Fig. 6(f). The observed reduction in exciton coupling strength with temperature increase can be explained by trion dissociation to excitons and free carriers.

Outlook and conclusion
We have reviewed state-of-the-art advances of hybrid exciton-polariton structures based on 1L-TMDCs coupled to plasmonic and dielectric nanocavities. First, we have discussed the optical properties of 1L-WS2, WSe2, MoS2 and MoSe2 materials, with special emphasis on their energy spectra, photoluminescence and absorption spectra, excitonic fine structure, and dynamics of exciton formation and valley depolarization. Then, we have provided a theoretical background to describe light-matter interaction in such hybrid exciton-polariton structures, and we have applied it to discuss weak and strong coupling regimes in 1L-TMDCs-based exciton-polariton systems.
This research area is still very young, yet full of exciting promises and opportunities. Several more studies and experiments are needed to fully understand the nature of this new material platform, and its potential for new technology. We envision several future research directions in this context. First, although all-dielectric NCs [131] possess attractive properties, like low dissipative losses and strong optical magnetic response (Section 3), there are only preliminary results in the area of their interaction with 1L-TMDCs [75]. Interaction of 1L-TMDCs with anopole-like [150] field configurations and non-radiating resonant eigenstates and bound states in the continuum [159,160] can offer exciting opportunities. Second, various applications require light emitting systems containing 1L-TMDCs to have highly directive (and even steerable) spontaneous emission patterns, for instance, for the emission collection enhancement. This issue is addressed in only a few recent papers [61,161] and it requires additional studies. In this context, suitably designed resonant nanostructures or metasurfaces can spatially separate valley polarized excitons, which may bring valleytronics to real-life applications [162].