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When an optical dipole is in proximity to a metallic substrate, it can emit light into both far-field photons and surface plasmon polaritons (SPPs). Far-field emission can be measured directly via top-down optical microscopy, whereas SPP emission can be detected by converting SPPs into far-field light via engineered out-coupling structures (Fig. 1a). On a single-crystal silver film—our metal of choice due to its low loss10—SPPs are strongly polarized in the out-of-plane (z) direction in the visible frequency range (see Supplementary Section I). Consequently, the emission rate into SPPs is much greater for an out-of-plane dipole than for an in-plane dipole (Fig. 1b,c), with the enhancement factor exceeding 30 for the present device parameters (Fig 1d; for details of the analysis see Supplementary Sections II–III). At the same time, far-field emission of an in-plane dipole is strongly suppressed (Fig. 1b,d), because the in-plane electric field is close to zero near the silver surface. We note that when a point dipole is close to a metal12, non-radiative recombination due to ohmic loss can be the dominant decay mechanism. However, for delocalized excitons in quantum wells13 and two-dimensional materials, quenching of exciton luminescence by ohmic loss is significantly reduced, even when they are placed 10 nm above a silver surface (Supplementary Fig. 1 and Supplementary Section III). Combined together, the net effect of a nearby silver surface is significantly enhanced (suppressed) emission of an out-of-plane (in-plane) dipole into SPPs (the far field).

Figure 1: Probing out-of-plane electric dipole transitions in two-dimensional materials via near-field coupling to SPPs.
figure 1

a, Schematic of the experimental set-up. A TMD-based van der Waals heterostructure is placed on top of single-crystal silver with silver acting as the backgate (Vg). Optical transitions can couple to both near-field SPPs and the far field (FF). Coupling to SPPs can be detected by scattering the SPPs into the FF using nanoscale trenches etched into silver. b,c, Finite-difference time-domain simulation of the electric-field intensity radiated by an in-plane point dipole emitter (b) and an out-of-plane point dipole emitter (c). The emitter is positioned 10 nm above the silver surface. Scale bar, 1 µm. d, Emission rate γ into the FF (blue) and SPPs (red) as a function of angle θ between the transition dipole and the two-dimensional plane (0° is defined as in the two-dimensional plane). γ0 is the decay rate of the exciton population in vacuum at T = 4 K. In the analysis, the dipole emitter is 8 nm above a silver film, with 8 nm (5 nm) thick hBN below (above) the dipole to match the heterostructure geometry in the experiment. The emission wavelength is 720 nm. Far-field emission is defined as emission into an objective lens above the sample with numerical aperture of 0.75, to match the experimental measurement geometry. e, Photoluminescence spectra of WSe2 collected from the FF (blue) and from scattered SPPs (red) at T = 4 K and at zero applied gate voltage, showing the neutral exciton (X0), charged exciton (XT) and lower energy (L1) emission. In the SPP scattered spectrum, an additional peak, XD, is observed. Inset: photoluminescence intensity map with a fixed incident excitation beam overlaid with an optical image of a monolayer WSe2 device on silver. The white dashed (cyan-dashed) line indicates the region of WSe2 (electrical contacts). Scale bar, 1 µm.

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In the present experiment we used exfoliated monolayers of WSe2 or MoSe2 encapsulated between thin, insulating hexagonal boron nitride (hBN) flakes. The photoluminescence spectra of these heterostructures exhibit narrow excitonic features (linewidths of ∼2–4 meV) at 4 K. A transition metal dichalcogenide (TMD) monolayer encapsulated by hBN is placed on atomically smooth single-crystal silver10. In our devices, silver plays dual roles: it supports SPPs that can be coupled to TMD excitons and it serves as a gate electrode that can change the electrostatic potential of a TMD monolayer (Fig. 1a). The spacing between the monolayer TMD and the silver surface is determined by the bottom hBN thickness and can easily be controlled by varying this thickness. In our devices, the typical spacing was on the order of 10 nm.

Excitons were created using off-resonant 660 nm laser excitation, and the photoluminescence (PL) spectra were collected either from the same spot excited by the laser via far-field imaging (FF-PL), or from scattered SPPs at the out-coupling structures (SPP-PL, inset of Fig. 1e). At 4 K, the FF-PL spectrum of WSe2 displays several commonly observed spectral features, assigned previously to neutral exciton emission (X0), charged exciton emission (XT) and the lower-energy emission (L1) often attributed to defects14. Both X0 and XT are known to have only in-plane transition dipole moments15. The SPP-PL spectrum, however, exhibits an additional large peak (XD) at 731 nm that is absent in the far-field spectrum, with a narrower linewidth (∼2 meV) than the other spectral features. In contrast, neither the FF-PL nor SPP-PL spectra of monolayer MoSe2 exhibit the feature corresponding to XD in WSe2 SPP-PL (Supplementary Fig. 2). These observations suggest that the WSe2-specific XD feature is associated with an out-of-plane transition dipole moment that preferentially couples to SPPs.

To further explore the nature of excitonic species in monolayer TMDs, we compared the FF-PL and SPP-PL spectra for monolayer WSe2 and MoSe2 as we tuned the carrier density by means of a gate voltage. It is well known that the neutral exciton emission (X0) of TMD monolayers only exists inside the bandgap16. Once electrons or holes are added to the conduction band (CB) or valence band (VB) of the TMD monolayers via electrostatic doping by a gate voltage, the emission from X0 vanishes, and the photoluminescence spectra are dominated by the charged exciton emission, XT. In Fig. 2a–d and in Supplementary Figs 2 and 3, such trends are evidenced by the simultaneous disappearance of X0 and the onset of in-plane conduction outside the bandgap region (−2.5V < Vg < 0 V)17. The gate-dependent SPP-PL spectra of a WSe2 monolayer in Fig. 2b show that emission from XD exists only within the same voltage range as the bright neutral exciton X0.

Figure 2: Gate-dependent far-field and SPP-coupled photoluminescence spectra in WSe2 and MoSe2.
figure 2

a–d, Gate-voltage (Vg)-dependent FF-PL (a) and SPP-PL (b) spectra of WSe2, and FF-PL (c) and SPP-PL (d) spectra of MoSe2. The intensity is plotted on a linear scale from low (dark blue) to high (yellow). The photoluminescence intensity of a is normalized with respect to that of b (c is normalized with respect to d) so that the intensity of the charged exciton XT at zero gate voltage is equal. Dashed lines correspond to boundaries where the neutral exciton X0 exists in FF-PL, and correspond to the chemical potential being inside the bandgap region (i). In b, a new feature XD emerges in the same Vg range as the neutral exciton. Negative (positive) gate voltages correspond to p (n) doping. The BN gate dielectric thickness is 8 nm for the WSe2 sample and 10 nm for the MoSe2 sample.

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Outside the bandgap region, additional optical transitions with an out-of-plane dipole orientation emerge. Figure 3a,b presents the FF-PL and SPP-PL spectra of WSe2 at different gate voltages. We normalized both FF-PL and SPP-PL spectra using the intensity of a charged exciton peak XT, because it is known to involve a purely in-plane transition dipole moment15. The ratio of SPP-PL intensity to the FF-PL intensity after normalization provides a direct measure of the orientation of the transition dipole for each luminescent species: the unity ratio represents a purely in-plane dipole, and a value larger than one indicates that the transition dipole has some out-of-plane components. Based on our theoretical calculations presented in Fig. 1d and Supplementary Fig. 4, an optical transition with a purely out-of-plane transition dipole should have a normalized coupling ratio of 7 in our device geometry. The experimental results for XD yield a value of 16: this discrepancy between theory and experiment is probably due to small, yet non-negligible, absorption of SPPs by charged excitons as they propagate through the WSe2, which increases the apparent coupling ratio of XD after normalization. Indeed, Supplementary Fig. 5 shows that there can be sizeable absorption of SPPs due to charged excitons when SPPs propagate through several micrometres of the WSe2 channel. When SPPs propagate through a minimal distance (less than 1 µm) within WSe2 (Supplementary Fig. 6), the normalized coupling ratio determined by experiment is close to 7, in good agreement with the theoretical calculations. Figure 3b shows that the value of the normalized coupling ratio in WSe2 is large not only for the neutral exciton peak XD at 731 nm, but also for the L1 peak at 740 nm. Specifically, in the bandgap region (−2.5 V < Vg < 0 V), the normalized coupling ratio of L1 is ∼3, but increases significantly and reaches a value of ∼16 just when the Fermi level reaches the VB maximum (Vg ≈ −2.5 V) and the CB minimum (Vg ≈ 0 V). A plot of normalized coupling ratios for MoSe2 does not show a comparable feature (Supplementary Fig. 7).

Figure 3: Gate-dependent enhancement of the neutral and charged dark exciton state.
figure 3

a, FF-PL (blue) and SPP-PL (red) spectra of WSe2 normalized to the intensity of the charged exciton XT at different gate voltages. X0 and XD represent neutral bright and dark excitons. The L1 peak also brightens up in SPP-PL. b, Normalized coupling ratio, defined as the SPP-PL intensity divided by the FF-PL intensity, both normalized by the bright charged exciton intensity, as a function of gate voltage.

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The origin of optical transitions with an out-of-plane dipole moment (XD and L1) in WSe2 can be understood by examining the band structure of monolayer TMDs. At the CB minimum and VB maximum of monolayer TMDs, that is, the K and K′ points in reciprocal space, the electronic wavefunctions can be characterized by their transformation properties under a 120° rotation (R) about the surface normal (z axis) and a reflection (P) in the TMD plane (x–y plane, Fig. 4a). Each orbital wavefunction carries a magnetic quantum number m (only m modulo 3 matters because of the reduced rotational symmetry) and a parity p (odd: p = −1; even: p = 1). Selection rules dictate that light circularly polarized in the x–y plane (σ±) can only induce transitions between states with the same parity and with magnetic quantum numbers differing by one. By contrast, light polarized linearly along the z axis couples states with opposite parity and identical magnetic quantum numbers.

Figure 4: Band structure and optical transitions in WSe2 and MoSe2 in the presence of spin–orbit coupling.
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a, Crystal structure of TMDs (MX2) and two of its symmetries (three-fold rotation axis R and reflection plane P). b,c, Allowed transitions at the K point for WSe2 (b) and MoSe2 (c). For the K valley, the allowed transition (black solid arrow) is circularly polarized (σ+). Coloured arrows indicate the dominant direction of the electronic spin. Due to spin–orbit coupling, spin is not an exact quantum number. In WSe2 (b), the spin-flip transition between the upper VB and the lower CB is weakly allowed and has a transition dipole polarized in the out-of-plane (z) direction. The transition between the lower VB and the upper CB is strictly dipole forbidden. In MoSe2 (c), the spin splitting of the CB is opposite, leading to different band ordering.

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Monolayer TMDs exhibit strong spin–orbit coupling proportional to L · S, where L and S are the orbital and spin angular momentum, respectively. The spin–orbit interaction leads to a large spin splitting in the VBs (on the order of several hundred meV18,19) and a much smaller splitting in the CBs. The latter is because the spin degeneracy in the CB is only lifted to second order5,6,8 by the SOC term L+S− + L−S+, which mixes different orbital and spin wave functions. Notably, the splitting is of opposite sign for WSe2 and MoSe2 (refs 5, 6, 8) (the band orderings for WSe2 and MoSe2 are shown in Fig. 4b,c). Owing to the SOC mixing term, spin is no longer an exact quantum number and nominally spin-forbidden transitions, associated with dark exciton states, are in principle possible, albeit weakly. We note that the spin directions in Fig. 4b,c only denote the dominant spin direction. Two of the four possible transitions at the K point are between bands with the same dominant spin directions and are therefore optically ‘bright’. For the remaining two transitions that are nominally ‘dark’, the transition dipole moment should be along the z direction because SOC only couples states with opposite parity. Including magnetic quantum numbers, group theoretic considerations dictate that only the transition connecting to the upper VB is allowed with z-polarized light9,20. The strength of the out-of-plane dipole moment is predicted to be weak, approximately a hundred times smaller than the in-plane bright exciton dipole moment9. However, because the energy scale associated with the sample temperature (∼0.4 meV at 4 K) is much smaller than the bright/dark exciton energy splitting of ∼40 meV, the exciton population at thermal equilibrium is almost entirely in the dark exciton state7 and the dark exciton emission should be visible as long as the z-polarized light can be collected, as in the case of SPP-PL.

These band structure and SOC considerations strongly suggest that the XD feature we observe in SPP-PL of WSe2 (Figs 2b and 3), with its z-polarized dipole orientation, corresponds to the dark exciton described in Fig. 4b. In contrast, in MoSe2 SPP-PL (Fig. 2d), the corresponding feature is absent (Supplementary Figs 2 and 7), because the dark exciton has a higher energy than the bright exciton5,6,7,8,21 and thus should not be observed in our experiment. We note that the XD feature in WSe2 lies 42 meV below the bright exciton transition (X0), similar to recently observed dark excitons22,23 under the application of a large (up to 30 T) in-plane magnetic field. The small difference in bright/dark exciton energy splitting (42 meV in our case versus 47 meV in magnetic-field studies22,23) probably originates from different experimental conditions that can modify the dielectric environment and the band structure of WSe2 (refs 24,25): hBN encapsulated WSe2 on top of silver in our measurements versus unpassivated WSe2 on SiO2 (refs 22,23).

The emergence of L1, a z-polarized transition outside the bandgap region, may indicate the formation of dark charged excitons. Once the Fermi level reaches the band edge of either the CB or VB, features corresponding to the bright and dark neutral excitons disappear, suggesting that these neutral excitons bind with free carriers to form charged excitons (trions26,27 or polarons28). The peak L1 may thus originate from charged dark excitons that form when neutral dark excitons bind with free electrons and holes. It should be noted that similar suggestions have been made using the observation of L1 brightening under an in-plane magnetic field22. The band structure of WSe2 dictates that a dark charged exciton should form through the binding of a dark neutral exciton with an electron/hole in the other valley. Bright charged excitons are formed, on the other hand, by the binding of a bright neutral exciton with an electron/hole from the same or opposite valley29. Figure 3b also shows significant brightening of the L1 feature as the Fermi level reaches the VB maximum (Vg ≈ −2.5 V) and the CB minimum (Vg ≈ 0 V): this observation may suggest the reorientation of a transition dipole moment at those points or alternatively a change in the relative population of states with in-plane versus out-of-plane transition dipole moments. The exact reasons for the observation is not understood at the moment, and requires further experimental and theoretical analyses.

We have demonstrated a new method for SPP-assisted near-field spectroscopy that enables measurement of the dipole orientation of two-dimensional excitons. The technique does not require a high magnetic field and can be easily integrated with other devices, making it easily accessible, versatile and technologically relevant. We use this method to observe nominally spin-forbidden dark excitonic states in monolayer WSe2 with out-of-plane dipole orientation, thus directly probing the SOC physics in TMD monolayers.

Our method opens up avenues for controlling the fundamental properties of atomically thin materials and the realization of new potential applications. It should enable detailed studies of indirect dark excitons30 and the interaction between out-of-plane excitons and phonons in van der Waals heterostructures31. Due to the negligible coupling to free-space electromagnetic modes, the near-field coupling to tightly confined nanophotonic and plasmonic modes should play the dominant role in radiative interactions of dark excitons under a wide variety of experimental conditions. These can be used to realize active metasurfaces based on spatial modulation of exciton lifetimes and to explore schemes for chiral photonics10 and quantum optics11. Finally, the dark excitons can have a long lifetime7,9, which may be used to study transport and electrostatic manipulation of excitonic matter in two-dimensional systems28,32,33, with potential applications for information processing and on-chip communication.

Methods

Single-crystal silver films (250 nm thick) were grown via sputtering on the (0001) face of 4H-SiC substrates at 350 °C with a buffer layer of Ti (90 nm thick), grown at 500 °C. Typical silver films show a root-mean-square roughness of less than 1 nm and exhibit a long propagation length for SPPs10. Trenches that served as in- and out-coupling structures for SPPs were made using electron-beam lithography and argon ion etching. Thin layers of hBN and monolayers of WSe2 and MoSe2 were mechanically exfoliated from bulk crystals onto Si wafers coated with 285-nm-thick SiO2. Monolayer TMDs were then identified under an optical microscope and verified via photoluminescence measurements. The thicknesses of hBN layers were measured by atomic force microscopy. The hBN/TMD/hBN heterostructures were then assembled and transferred by a dry transfer method34 onto the patterned single-crystal silver substrates. Afterwards, thin layers of SiN (160 nm; via plasma-enhanced chemical vapour deposition at room temperature) and alumina (30 nm; via atomic layer deposition at 90 °C) were deposited, with the pattern defined by electron-beam lithography. These served as an insulating barrier between the silver substrate and the electrical contacts to the TMDs. Finally, electrical contacts were deposited by electron-beam evaporation of Cr (10 nm)/Au (90 nm) followed by sputtering of another 40 nm of Au, with the dimensions defined by electron-beam lithography. Optical measurements were carried out in a home-built confocal microscope using an objective with a numerical aperture of 0.75 in a 4 K cryostat (Montana Instruments). Two galvo mirrors were used to scan the excitation and collection spots independently on the sample.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Additional information

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