Out-of-plane emission of trions in monolayer WSe2 revealed by whispering gallery modes of dielectric microresonators

The manipulation of light emitted by two-dimensional semiconductors grounds forthcoming technologies in the field of on-chip communications. However, these technologies require from the so elusive out-of-plane photon sources to achieve an efficient coupling of radiated light into planar devices. Here we propose a versatile spectroscopic method that enables the identification of the out-of-plane component of dipoles. The method is based on the selective coupling of light emitted by in-plane and out-of-plane dipoles to the whispering gallery modes of spherical dielectric microresonators, in close contact to them. We have applied this method to demonstrate the existence of dipoles with an out-of-plane orientation in monolayer WSe2 at room temperature. Micro-photoluminescent measurements, numerical simulations based on finite element methods, and ab-initio calculations have identified trions as the source responsible for this out-of-plane emission, opening new routes for realizing on-chip integrated systems with applications in information processing and quantum communications.


Introduction
The race to develop high-performance photonic and optoelectronic devices which take advantage of the distinctive properties and versatility of two-dimensional (2D) semiconductors 1-3 has already given rise, for example, to high-speed and highresponsivity waveguide-integrated photodetectors, 4 plasmonic nanocavities, [5][6][7] and optical resonators with enhanced light-matter interactions, [8][9][10] as the basis to construct nanolasers operating at room temperature. 11,12 Most of the optoelectronic and photonic devices developed so far are based on 2D transition metal dichalcogenide (TMD) semiconductors such as MoS2, MoSe2, WS2 and WSe2. Consequently, the characteristics of the performance of these devices strongly depend on the in-plane (IP) dipolar nature of the robust free excitons of the 2D TMDs. [13][14][15] Light from IP excitons can be easily extracted in stacked (vertical) devices. However, some emerging applications in the generation of radially polarized light in 2D TMDs 16 and integrated photonic chips can be efficiently enabled when out-of-plane (OP) excitons mediate light-matter interactions. [17][18][19][20][21][22][23][24] Although rare, OP excitons can be found in 2D semiconductors. For instance, atomically thin layers of Indium Selenide (InSe) have demonstrated, as 2D TMDs, potential applications for next generation electronics and optoelectronics [25][26][27] due to their highly tuneable band gap [28][29][30] and high electron mobility. 31 Nevertheless, unlike 2D TMDs, 2D layers of InSe have revealed to sustain luminescent free excitons with an intrinsic OP orientation. 14 This panorama puts into evidence the necessity of identify, among the different excitonic complexes existing in 2D semiconductors, those with a suitable dipole orientation for their optimal application in the emerging field of integrated photonic circuits based on 2D materials. [32][33][34][35][36][37] This question is particularly relevant for the development of novel devices based on monolayer (ML) TMDs, since strong spin-orbit coupling makes these materials offer, apart from bright and long-lived dark excitons, 38,39 high-order charge-complexes with unexplored dipolar characteristics, such as bound excitons, trions, [40][41][42][43][44] and biexcitons. 45 These complexes are technologically promising as they can manifest even at room temperature, [46][47][48] have an intrinsic charge and spin degrees of freedom that facilitate their manipulation by the application of an electric or a magnetic field, 45,49 possess a valley degree of freedom (as free-excitons), permit new optical gain mechanisms at extremely low carrier densities, 50 and can be further used as entangled photon sources. [51][52][53][54][55] Back focal plane imaging is usually considered the method-of-choice to discern the orientation of the dipole responsible for the luminescent signal emitted. 13,14,56 However, it is challenging to use this technique to discriminate contributions from different sources to the luminescent signal that may eventually have a different dipolar orientation. To overcome this limitation, more sophisticated methods have been proposed, but their application is rather limited as they require an efficient excitation of surface plasmon polaritons. 57 In this work, we propose a versatile and simple method to spectroscopically elucidate the existence of an OP component in the photoluminescent response of a dipole which, at the same time, puts into evidence its feasibility to promote light coupling to a planar device. The proposed method relies on the different selective ability of IP and OP dipolar emission to excite whispering gallery modes of SiO2 microspheres deposited on top of the emitting layers. We have applied this method to study the orientation of dipoles related to the different light contributions observed in ML WSe2 at room temperature, these from trions and excitons. By microphotoluminescence (µ-PL) measurements, numerical simulations based on the finite element method (FEM), and ab-initio calculations of the excitonic states we have found a non-negligible OP dipolar component of trions in ML WSe2, which contrasts to the well-established IP nature of its free bright excitons. These results establish that exciton complexes are excellent candidates for light manipulation in planar optoelectronic devices and photonic chips.  Figure 1b shows µ-PL spectra acquired in a bulklike (16 nm thick) InSe nanosheet deposited on a SiO2/Si substrate and partly covered with SiO2 microspheres (see optical image at the inset of Figure 1b). The µ-PL spectrum measured in a bare region of the InSe nanosheet shows an emission peak located at 1.24 eV, corresponding to the radiative free-exciton recombination processes occurring at energies reported for bulk InSe. 14,30 Although it is almost negligible in this spectrum, it is worth mentioning that a weak broad emission is detected at energies higher than 1.45 eV, which stems from the amorphous SiO2 substrate. Compared to the µ-PL spectrum measured in the bare InSe nanosheet, the one acquired in a point of sample covered with SiO2 microspheres shows a strong enhancement of the signal intensity (see Figure 1b and the µ-PL map in its inset) that makes visible even the weak luminescence coming from the SiO2 substrate. This lensing effect, promoted by the microspheres, is not restricted to bulklike InSe nanosheets. In fact, the use of dielectric microspheres seems to provide for a tool to enhance the usually low-intensity PL signal of atomically-thin InSe nanosheets without damaging the sample, as it has been demonstrated for a 2D InSe nanosheet 6.5 nm-thick with an noticeable blueshift of its PL signal due to quantum-confinement effects (See Supplementary Figure S1). 30 A similar lensing effect is observed in other 2D semiconductors. Figure 1c shows the µ-PL spectra acquired in a ML of WSe2 deposited on a SiO2/Si substrate, on which a SiO2 microsphere has been placed (see the optical image at the inset of Figure 1c). In the bare region of the ML of WSe2, the PL spectrum shows a double-peak structure whose deconvolution has been performed by assuming gaussian-like components. 48,58 In this way, deconvolution processes have allowed to resolve a main PL peak centered at 1.666 eV, coming from optical recombination of the X 0 neutral exciton, and a second and broad PL peak centered at 1.640 eV. Such low-energy feature has been usually attributed to recombination of trions, whose observation is hard at room temperature but possible in doped samples (as those used in this work) due to the higher probability of forming charged excitons in these samples than in intrinsic ones. 48,57,59,60 In line with that observed for InSe nanosheets, the µ-PL spectrum measured in the region of the WSe2 nanosheet under the SiO2 microsphere (see also the PL map inserted in Fig. 1c) shows an enhanced intensity signal, compared to that of the bare ML.

Results and discussion
Clearly, the lensing effect described above is promoted by the difference between air and the microsphere refractive index, 61 The lensing effect is not only restricted to the excitation process but extends also to the light-collection process (Figure 2a, bottom panel). Importantly, this effect tends to enhance the collection of light within the numerical aperture of our optical objective that would be eventually lost in the absence of the microsphere, as the far-field emission from OP dipoles. 64 Besides the lensing effect, the presence of the microspheres also promotes the appearance of strong resonances in the PL spectrum (see Fig. 1   has an associated trion family (X C and , respectively) that inherits the selection rules (see Fig. 4c), 73 whose recombination results in a broad PL-band at the energy of the peak around 1.640 eV, as shown in Fig. 1c, due to the coupling of light to both to IP and OP dipoles. These facts arise trions as the main source of OP light able to excite WGMs of dielectric microspheres.

Conclusions
To summarize, we have demonstrated a spectroscopic method that enables the

Materials and methods
InSe and WSe2 2D nanosheets have been micromechanically exfoliated using the well-  The optical absorption of monolayer WSe2 has been computed within the framework of the Bethe-Salpeter Equation, as implemented in Yambo code. 74 The input of the BSE are the electronic states of WSe2, calculated using density functional theory within the local-density approximation with the code Quantum Espresso. 75 We use fully relativistic pseudopotentials with semicore electrons for W. The simulations of the excitonic states have been performed in a 15x15x1 k-grid including 2 valence and 2 conduction bands.
The vacuum distance between two periodic images is 30 Bohr.

AUTHOR INFORMATION
Corresponding Author

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding authors upon reasonable request. Correspondence and requests for materials should be addressed to J.F.S.R.    Figure  1b and 1c, respectively. Middle panels: Intensity ratio between the PL spectra shown in their respective top plots, which evidence the coupling of emitted light to the WGMs of dielectric microspheres. Bottom panels: Spectral response calculated for a dipolar emission coupled to the WGMs of a spherical microresonator of 4.69 µm in diameter, when these emitting dipoles are IP (purple curve) or OP (orange curve) oriented. The TM or TE character of each WGMs has been indicated on each resonance peak. The position of the hole is fixed (pink sphere) near the W atom and we represent the electronic density. The maximum is set to 1 and we fix the isosurface value to 0.1 for both wave functions.

2
Effects of the microsphere parameters on the WGMs observed in 2D nanosheets Figure S1. WGMs in 2D InSe nanosheets. (a) Micro-PL spectra acquired in two points of a 6.5 nm thick InSe nanosheet deposited on a SiO 2 /Si substrate, which is shown in the optical image in the inset as a dark nanosheet [S5]. The A and B µ-PL spectra were acquired in bare region of the nanosheet and in a point covered by a microsphere, which correspond to the positions labelled on the optical image, respectively. (b) top plot: Intensity ratio between the PL spectra shown in (a). Bottom plots: Spectral response calculated for a dipolar emission coupled to the WGMs of a spherical microresonator of a diameter of 4.80 µm, when these emitting dipoles are IP (purple curve) or OP (orange curve) oriented. The TM or TE character of each WGMs has been indicated on each resonance peak.

Symmetry analysis of optical selection rules of monolayer WSe 2
The main properties of the photoluminescence spectra of monolayer WSe2 are determined by the optical selection rules at the K point. Figure S5 shows the bands at K, labelled with the symmetry representation. The up and down arrow indicates the dominant spin projection. At the opposite K point (K'), the spin of each band is reversed.
In absence of spin-orbit interaction, the optical selection rules only allow absorption for inplane light. The out-of-plane transition is possible only due to the spin-orbit interaction and the resulting mixing of valence bands of opposite spin projection. We have also marked the magnitude of the spin-orbit splitting at the conduction and valence bands ( Figure S5). It is a common trend in transition metal dichalcogenides a larger magnitude in the valence band [S6].
The OP transition at one of the two K-points involves the Γ 10 (↑) from the CB and Γ 8 (↓) from the VB, where Γ n are the irreducible representations, and the product is Γ 10 (↑)xΓ 8 (↓).
The spin-orbit interaction induces a band mixing among the valence band Γ 8 (↓) and deeper ones (not shown here). These deeper valence bands ( ′) transform with the same representations but with reversed spin. Therefore, states at the top valence band can be expressed as U Γ 8 (↓) + U ′(↑) . The coefficient β depends on the strength of the spin-orbit interaction. Due to this mixture, z-polarized (i.e., OP) optical transitions become possible between the valence and conduction band with opposite spin, as the band ′(↑) has the same spin orientation than the conduction band Γ 10 , and therefore the total angular momentum (including valley, spin, and orbital component) is strictly conserved. Nevertheless, the oscillator strength is much weaker than in the case of IP transitions. A derivation based in group theory is presented in the Supplementary Information of Ref. 64.