## Introduction

Transition metal dichalcogenide (TMD) monolayers are direct-bandgap semiconductors of which the conduction and valence band extrema consist of two valleys1,2. The broken inversion symmetry of the lattice gives rise to optical selection rules that enable valley-selective, inter-band excitation of electrons using circularly polarized light3,4,5. A strong Coulomb interaction results in the subsequent formation of excitons6, which maintain a valley polarization that is determined by the ratio between the intervalley scattering time and the exciton lifetime3,7. Such valley-polarized excitons have been proposed as carriers of information and play a central role in the field of valleytronics8,9. As such, understanding the processes that govern the exciton lifetime and associated valley polarization is important for assessing the potential applicability of valley-polarized excitons in devices.

Under optical excitation, a charge-density-controlled chemical equilibrium between neutral and charged excitons (trions) forms in a TMD monolayer10,11,12. The conversion into trions reduces the exciton lifetime13 and may therefore be expected to lead to a large valley polarization of excitons that are created via valley-selective optical pumping, but demonstrating this effect has thus far remained elusive.

The charge density of TMD monolayers can be controlled via electrostatic gating or chemical doping10,11,14,15,16,17,18,19,20. While electrostatic gating is a flexible technique that allows a continuous change of the charge density10,11,14, chemical doping provides a convenient alternative that requires no microfabrication and is well suited for achieving high doping levels15,16,17,18,19,20. Here, we study the valley polarization of excitons and trions in monolayer $$\text {WS}_{2}$$ and show that chemical doping via aromatic anisole (methoxy-benzene) quenches the exciton photoluminescence and causes the spectrum to become dominated by trions with a strong valley polarization. A spatial study of the remaining exciton emission shows that also the excitons attain a strong valley polarization, which we attribute to the rapid doping-induced conversion into trions. We extend a rate equation model describing exciton-trion conversion10 to include the two valleys and use it to explain the observed valley polarization in terms of the doping-controlled chemical equilibrium between excitons and trions.

## Results

When doping a TMD monolayer using aromatic molecules such as anisole, Hard Soft Acid Base (HSAB) theory allows predicting whether the dopant will be n- or p-type16. Electrons hop between the adsorbed molecules (A) and the monolayer (B) to compensate for the difference in chemical potential $$\mu$$ between both systems21. The chemical hardness $$\eta$$ of the materials determines how quickly an equilibrium is reached, leading to an average number of transferred electrons per molecule $$\Delta N$$:

\begin{aligned} \Delta N=\frac{\mu _A-\mu _B}{\eta _A+\eta _B}. \end{aligned}
(1)

For both anisole and monolayer $$\text {WS}_{2}$$, the chemical potential and chemical hardness has been calculated using density functional theory22,23. Using these values (Supplementary Section S1) we find $$\Delta N=0.22$$, such that we expect the monolayer to be n-doped upon physisorption of anisole molecules (Fig. 1a).

To study the effect of chemical doping with anisole on the valley polarization properties of $$\text {WS}_{2}$$, we start by characterizing the photoluminescence of exfoliated $$\text {WS}_{2}$$ monolayers on 280 nm Si/$$\text {SiO}_{2}$$ substrates. The emission spectrum of an as-prepared monolayer shows the characteristic bright exciton resonance at 2.01 eV (Fig. 1b, black line)24. After chemical doping by a 2-h treatment in liquid anisole at $$70\,^{\circ }\hbox {C}$$, the bright exciton resonance is strongly quenched and only a weak emission peak that is red-shifted by $$\Delta E=23\,\hbox {meV}$$ remains (Fig. 1b, red line). Because the increased binding energy of trions compared to excitons should lead to such a red shift14 and the expected n-type doping by the anisole molecules should favour trion formation, we attribute this peak to emission associated with trions. This conclusion is further supported by spatial studies of emission spectra showing both exciton and trion components that we will describe below. As expected, the trion emission is weak due to its long radiative lifetime and strong non-radiative decay attributed to Auger recombination10,25,26.

Doping by adsorbed carbon-hydrogen groups27 was previously shown to result in an increase of the longitudinal acoustic LA(M) and LA(K) modes in the Raman spectrum of $$\hbox {WS}_2$$ monolayers. Our treatment causes a similar increase of the LA(M) Raman mode (Fig. 1c), which we therefore attribute to the adsorption of anisole molecules. We do not observe an associated increase of the LA(K) mode at about $$190\, \hbox {cm}^{-1}$$, which may be due to the different nature of the adsorbates resulting in different lattice deformations and/or defects in the monolayer. We note that a similar behaviour was observed in previous work on $$\hbox {WS}_2$$ monolayers7, which showed an increasing intensity of the LA(M) Raman mode without an associated increase in the LA(K) mode as a function of the defect concentration. In addition, we find that the double-resonance 2LA(M) mode remains unaffected by the doping, indicating that our treatment does not significantly change the monolayer’s electronic structure28.

To study the valley polarization of chemically-doped $$\hbox {WS}_2$$ monolayers, we use near-resonant excitation with a 594 nm circularly polarized, continuous-wave laser that is focused to a diffraction-limited spot. The resulting photoluminescence is polarization filtered and collected using a home-built confocal microscope (see “Methods” section). Before detecting the emission with an avalanche photodiode (APD), we apply a spectral bandpass filter with a transmission window centred around the exciton and trion resonances (see the shaded area in Fig. 1b).

We quantify the valley polarization $$\rho$$ via polarization-resolved photoluminescence measurements according to

\begin{aligned} \rho =\frac{I_{\sigma ^+}-I_{\sigma ^-}}{I_{\sigma ^+}+I_{\sigma ^+}}. \end{aligned}
(2)

Here, $$I_{\sigma ^+}$$ and $$I_{\sigma ^-}$$ represent the intensities of the right- and left-handed emission by the sample under $$\sigma ^+$$ excitation and the total photoluminescence is given by $$I=I_{\sigma ^+}+I_{\sigma ^-}$$. By scanning the sample while detecting its emission using the APD, we make photoluminescence and valley-polarization maps of our flakes, before and after treating them.

Before the anisole treatment, the photoluminescence is characterized by bright exciton emission (Fig. 2a, left panel) with no valley polarization (Fig. 2b, left panel). Strikingly, the trion emission that remains after chemical doping (Fig. 2a, right panel) has a valley polarization of about 25% (Fig. 2b, right panel). We consistently observe the emergence of strong valley polarization after anisole treatment in multiple samples (Supplementary Section S2).

Next, we demonstrate the substrate independence of the effect of our treatment by repeating the measurements on an yttrium iron garnet (YIG) substrate. YIG is a magnetic insulator that was shown to effectively negatively dope $$\text {MoS}_{2}$$ monolayers at low temperatures, possibly due to dangling oxygen bonds at the YIG surface29. As such, the total level of doping could be larger for monolayers on YIG due to additional doping from the substrate.

We exfoliated monolayers $$\text {WS}_{2}$$ onto polydimethylsiloxane (PDMS) stamps and deposited them onto the YIG substrates30. As before, the emission of the monolayers is strongly quenched after chemical doping and a valley polarization of about 20–40% emerges (Fig. 3, Supplementary Section S2). Compared to the monolayers on Si/$$\hbox {SiO}_2$$ substrates we conclude that these data do not indicate significant additional doping from the YIG substrate.

To assess the spatial homogeneity of the doping, we characterize the photoluminescence and valley polarization of a relatively large-area monolayer flake on YIG (Fig. 3a,b). In most parts of the flake, we observe a valley polarization of about 40%. In addition, at multiple spots in the monolayer, we observe an enhanced photoluminescence and reduced valley polarization. A comparison with an atomic force microscope topography image (Fig. 3c) shows that these spots are associated with wrinkles in the flake. Spectrally, the spots are characterized by the simultaneous presence of an exciton resonance and a trion resonance, with the exciton resonance rapidly vanishing as we move off the spot and the trion resonance remaining approximately constant (Fig. 3d). We extract the valley polarization and brightness of the exciton and trion resonances by fitting similar emission spectra near multiple wrinkles with an exciton and trion component (Supplementary Section S3). The extracted trion brightness and valley polarization is independent of the local exciton emission (Fig. 3e), highlighting their spatial homogeneity. In particular, the trion valley polarization of about 40% is similar to that in the flat areas of the flake (Fig. 3b,f). The stronger exciton emission at wrinkles indicates that the doping is less effective, possibly resulting from the restricted physical access to the monolayer at wrinkles or from a decreased substrate-induced doping due to the increased substrate-monolayer distance. In addition, the exciton and trion formation could be altered at the wrinkles as a result of local strain31.

Strikingly, the excitons at the wrinkles also attained a strong valley polarization, as can be seen from the spectra in Fig. 3d. We extend an existing rate equation model10 to argue that this is the result of the doping-induced conversion of excitons into trions (Fig. 4a). This conversion acts as a decay channel for the excitons, enhancing their valley polarization and quenching their photoluminescence. The model predicts that the excitonic valley polarization starts to increase strongly when the conversion rate into trions $$\Gamma _{\text {T}\leftarrow \text {X}}$$ becomes comparable to the intervalley scattering rate $$\Gamma _{\text {iv,X}}$$ (Fig. 4b, green line). Since $$\Gamma _{\text {T}\leftarrow \text {X}}$$ is proportional to the electron density as described by a law of mass-action11,12, indeed an emergent exciton polarization is expected when doping is strong.

Strongly valley-polarized excitons are expected in the limit of large doping (Fig. 4b). For our flakes, doping is strongest in the flat areas away from the wrinkles as reflected by the low photoluminescence in these areas. Because we are unable to spectrally distinguish the weak exciton emission from the dominant trion emission in these areas, we analyse the valley polarization of the integrated photoluminescence spectrum using our APD. When plotting the local valley polarization against the local photoluminescence (Fig. 4c), we observe a non-monotonous behaviour with a maximum at low photoluminescence. According to our model, this maximum occurs because the exciton valley polarization (green line in Fig. 4b) increases with doping while the exciton photoluminescence vanishes. As a result, the trion contribution (red line) starts to dominate the total signal (black line). These results highlight that the exciton valley polarization becomes large because of the rapid conversion into trions.

On wrinkles, we observe that the excitons have a lower valley polarization than the trions (Fig. 3d). In contrast, our model predicts that the local valley polarization of the trions cannot exceed that of the excitons even at low doping (Fig. 4b, Supplementary Section S4). This indicates that the observed spectra on wrinkles are a result of spatial averaging over less-doped, wrinkled areas with a strong exciton contribution and strongly-doped surrounding areas with a dominant trion emission (Supplementary Section S5). Such averaging is expected from the diffraction-limited optical spotsize of our confocal microscope (diameter: $$\sim 500\,\hbox {nm}$$).

In summary, we have demonstrated that chemical doping with anisole is an effective method to generate highly valley-polarized excitons and trions in monolayer $$\text {WS}_{2}$$ at room temperature. The emission spectrum of as-prepared monolayers is characterized by a bright exciton resonance that exhibits no valley polarization. After chemical doping, a trion resonance appears with a polarization up to 40%. The doping is less efficient at wrinkled areas, which are marked by the simultaneous presence of exciton and trion resonances. The excitons have a robust valley polarization, which we attribute to the rapid conversion into trions induced by the doping. A rate equation model captures the quenching-induced valley polarization, indicating the presence of excitons with a higher polarization than trions in the limit of maximal quenching. Our results shed light on the effect of the doping-controlled conversion between excitons and trions on the valley polarization in single layers of $$\text {WS}_{2}$$ and highlight that valley polarization by itself does not necessarily reflect optovalleytronic potential, since a strongly-quenched carrier lifetime and emission may constrain its application in devices.

## Methods

### Experimental setup

A schematic overview of the setup is presented in Supplementary Section S6. Our samples are excited by a lowpass-filtered 594 nm OBIS laser (Coherent) of which we control the polarization using achromatic half- and quarter-wave plates (Thorlabs). A 50 $$\times$$, $$\hbox {NA}=0.95$$ (Olympus) objective focuses the laser to a diffraction-limited spot and collects the emission from the sample. The emission is separated from the excitation by a 10:90 beam splitter (R:T, Thorlabs). The handedness of the excitation and detection is controlled by a second quarter-wave plate, which projects both circular polarizations of the photoluminescence onto two orthogonal linear polarizations of which we select one with the polarizer. The emission is longpass filtered (2 $$\times$$ Semrock, BLP01-594R-25) to eliminate the laser reflection. We use a mirror on a computer-controlled flipmount to switch between a fiber-coupled spectrometer (Kymera 193 spectrograph with a cooled iVac 324 CCD detector) and an avalanche photodiode (APD, Laser Components) for the detection of the photoluminescence. Before the emission is detected by the APD, it is filtered with a pinhole and bandpass filter (Semrock, FF01-623/32-25). The sample is mounted on an xyz-piezo stage (Mad City Labs, Nano-3D200FT) to allow nanoscale positioning of the sample. An ADwin Gold II was used to control the piezo stage and read out the APD. The grating in the Raman microscope (Renishaw inVia Reflex, 514 nm laser) had 1600 lines per mm, giving a spectral resolution of $$\sim 2 \,\hbox {cm}^{-1}$$ per pixel. All measurements were performed at room temperature.

### Sample fabrication

The $$\text {WS}_{2}$$ monolayers were exfoliated from commercially-purchased bulk crystals (HQ Graphene) on PDMS stamps, and were transferred to Si/$$\text {SiO}_{2}$$ and YIG chips. The 245 nm thick YIG films were grown on a gadolinium gallium garnet (GGG) substrate via liquid phase epitaxy and were purchased at Matesy gmbh. YIG samples were sonicated in acetone and cleaned in IPA before stamping.