# Excitons and trions in WSSe monolayers

Katarzyna Olkowska Pucko, Elena Blundo, Natalia Zawadzka, Salvatore Cianci, Diana Vaclavkova, Piotr Kapuściński, Dipankar Jana, Giorgio Pettinari, Marco Felici, Karol Nogajewski, et al.

► To cite this version:

Katarzyna Olkowska Pucko, Elena Blundo, Natalia Zawadzka, Salvatore Cianci, Diana Vaclavkova, et al. Excitons and trions in WSSe monolayers. 2D Materials, 2022, 10 (1), pp.015018. 10.1088/2053-1583/aca915. hal-04740751

HAL Id: hal-04740751

https://hal.science/hal-04740751v1

Submitted on 16 Dec 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>
PAPER • OPEN ACCESS

# Excitons and trions in WSSe monolayers

To cite this article: Katarzyna Olkowska Pucko *et al* 2023 *2D Mater.* **10** 015018

View the [article online](#) for updates and enhancements.

## You may also like

- Rashba spin-splitting in Janus SnXY/WXY (X, Y = S, Se, Te; X, Y) heterostructures
Bhagyashri Devaru Bhat

- The mirror asymmetry induced nontrivial properties of polar WSSe/MoSSe heterostructures
Yuanyuan Wang, Wei Wei, Baibiao Huang et al.

- The in-plane metal contacted 5,1 nm Janus WSSe Schottky barrier field-effect transistors
Wei Li, Jinlei Wei, Wen Chen et al.
<figure><img src="image_2.png" /></figure>

CrossMark

OPEN ACCESS

RECEIVED

5 October 2022

REVISED

21 November 2022

ACCEPTED FOR PUBLICATION

6 December 2022

PUBLISHED

19 December 2022

Original Content from
this work may be used
under the terms of the
Creative Commons
Attribution 4.0 licence.

Any further distribution
of this work must
maintain attribution to
the author(s) and the title
of the work, journal
citation and DOI.

<figure><img src="image_3.png" /></figure>

PAPER

Excitons and trions in WS<sub>2</sub> monolayers

Katarzyna Olkowska Pucko¹,*, Elena Blundo² ID, Natalia Zawadzka¹ ID, Salvatore Cianci² ID,
Diana Vaclavkova³ ID, Piotr Kapuściński¹ ID, Dipankar Jana³, Giorgio Pettinari⁴ ID, Marco Felici² ID,
Karol Nogajewski¹ ID, Miroslav Bartos⁵ ID, Kenji Watanabe⁶ ID, Takashi Taniguchi⁷ ID, Clement Faugeras³ ID,
Marek Potemski¹,³,⁸ ID, Adam Babiński¹ ID, Antonio Polimeni¹ ID and Maciej R Molas¹,*

¹ Institute of Experimental Physics, Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland
² Physics Department, Sapienza University of Rome, 00185 Rome, Italy
³ Laboratoire National des Champs Magnétiques Intenses, CNRS-UGA-UPS-INSA-EMFL, 38042 Grenoble, France
⁴ Institute for Photonics and Nanotechnologies, National Research Council (CNR-IFN), 00133 Rome, Italy
⁵ Central European Institute of Technology, Brno University of Technology, Brno 61200, Czech Republic
⁶ Research Center for Functional Materials, National Institute for Materials Science, Tsukuba 305-0044, Japan
⁷ International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan
⁸ CENTERA Laboratories, Institute of High Pressure Physics, Polish Academy of Sciences, 01-142 Warsaw, Poland
* Authors to whom any correspondence should be addressed.

E-mail: katarzyna.olkowska-pucko@fuw.edu.pl and maciej.molas@fuw.edu.pl

Keywords: excitons, transition metal dichalcogenides, photoluminescence, g-factor, alloy, dark trion, phonon replica

Supplementary material for this article is available online

Abstract

The possibility of almost linear tuning of the band gap and of the electrical and optical properties in monolayers (MLs) of semiconducting transition metal dichalcogenide (S-TMD) alloys opens up the way to fabricate materials with on-demand characteristics. By making use of photoluminescence spectroscopy, we investigate optical properties of WS<sub>2</sub> MLs with a S/Se ratio of 57/43 deposited on SiO<sub>2</sub>/Si substrate and encapsulated in hexagonal BN flakes. Similarly to the ‘parent’ WS<sub>2</sub> and WSe<sub>2</sub> MLs, we assign the WS<sub>2</sub> MLs to the ML family with the dark ground exciton state. We find that, in addition to the neutral bright A exciton line, three observed emission lines are associated with negatively charged excitons. The application of in-plane and out-of-plane magnetic fields allows us to assign undeniably the bright and dark (spin- and momentum-forbidden) negative trions as well as the phonon replica of the dark spin-forbidden complex. Furthermore, the existence of the single photon emitters in the WS<sub>2</sub> ML is also demonstrated, thus prompting the opportunity to enlarge the wavelength range for potential future quantum applications of S-TMDs.

1. Introduction

Semiconducting transition metal dichalcogenides (S-TMDs) MX₂, which crystallise in the 2H phase, include only five compounds, i.e. WS₂, WSe₂, MoS₂, MoSe₂, and MoTe₂ [1]. Monolayers (MLs) of MX₂ are direct-band-gap semiconductors and can emit light more efficiently than their bulk counterparts having indirect band gaps. The fundamental optical transition in S-TMD MLs, the so-called A exciton, spans the spectral range from 1.15 eV for the MoTe₂ ML [2] up to ~2.1 eV for the WS₂ ML [3]. One possibility of adjusting the A-exciton energy is to change the layer thickness, but this is accompanied with a change in the band gap character (from direct to indirect) with

detrimental effects on the radiative efficiency [2, 4–6]. Yet another strategy is that of straining S-TMDs, thus shifting the exciton energy. However, strain also leads to direct-to-indirect exciton transitions, affecting not only the optical efficiency and carrier decay time [7], but also having huge effects on the exciton g-factor [8]. Another opportunity to adjust the energy of the optical band gap is by mixing different atoms, e.g. transition metals (Mo and W) or chalcogens (S, Se, and Te), which leads to the formation of ternary compounds (alloys), such as MoS<sub>2</sub>, WS<sub>2</sub>, MoWSe<sub>2</sub>, etc. In such materials, it is possible to tune the optical band gap by variation of the stoichiometry ratio of each element [9–12]. Using a variety of candidates, the band gap of ternary compounds can be
continuously tuned within a wide spectral range. This opens up new possibilities for absorbing and emitting light at desired wavelengths, which plays a crucial role in potential optoelectronic applications. The S-TMD MLs are known to be organised in two subgroups, i.e. *bright* and *darkish*, due to the type of the ground exciton state (bright and dark, respectively) [13]. In bright MLs, the optical recombination between spin-polarised subbands of the top valence band (VB) and the bottom conduction band (CB) is optically active (bright). In the case of darkish MLs, that transition is optically inactive (dark). $MoSe_2$ and $MoTe_2$ MLs are bright, while $MoS_2$, $WS_2$, and $WSe_2$ MLs are darkish (see [14–16]). The determination of bright or darkish character of the excitonic ground state of alloy MLs is still missing. However, in the mean field approximation, it is expected that the electronic and optical properties of alloy MLs (e.g. WSSe) are an average of those of the corresponding ‘parent’ (e.g. $WS_2$ and $WSe_2$).

In this work, we investigate the optical response of MLs of WSSe with a S/Se ratio of 57/43 encapsulated in hexagonal BN (hBN) flakes, by means of photoluminescence (PL) spectroscopy. The WSSe ML is ascribed to the family of MLs with a dark ground exciton state, like its ‘parent’ $WS_2$ and $WSe_2$ MLs. Our optical spectroscopy investigations furthermore reveal additional emission lines at energies lower than that of the bright excitons. By applying magnetic fields perpendicular and parallel to the layer plane, we are able to determine that these lines arise from bright and dark (spin- and momentum-forbidden) negatively charged excitons and to identify a phonon replica of the dark spin-forbidden charged exciton complex. We finally demonstrate WSSe MLs as a potential platform for quantum communication as these MLs, similar to $WSe_2$ or $WS_2$ [1, 17–19] host centres emitting photons one-by-one, as shown by a clear anti-bunching at zero delay in our auto-correlation measurements of their emission statistics.

## 2. Results

Low-temperature ($T = 5$ K) PL spectra of $WSe_2$, WSSe, and $WS_2$ MLs deposited on $SiO_2$/Si substrates (top) and encapsulated in hBN flakes (bottom) are shown in figure 1. The relative concentration of S and Se atoms in the WSSe crystal, from which MLs were exfoliated was determined by means of energy dispersive x-ray (EDX) analysis. The alloy was found to be homogeneous over the whole investigated crystal (~half-mm in size) with a S/Se ratio ≈ 57/43, see supplementary information (SI) for details. First, we focus on the analysis of the PL spectra measured on MLs deposited on a $SiO_2$/Si substrate, see figure 1(a). The corresponding PL spectra of the $WS_2$ and $WSe_2$ MLs display characteristic emission lines, labelled X, associated with the recombination of neutral bright

A excitons comprising carriers from the $K^±$ points of the Brillouin zone (BZ) [1]. The determined X energies for the $WS_2$ and $WSe_2$ MLs are equal to about 2.090 eV and 1.745 eV, respectively. By analogy, we ascribe the emission line apparent at about 1.909 eV in the WSSe ML to the A exciton. Its energy is very close to 1.942 eV, as expected for the alloy ML from the linear dependence of the X energy with the S/Se relative concentration. As can be seen in figure 1(b), the encapsulation of MLs in hBN redshifts the X energies. This results from the reduction of both the band gap energies and the binding energies of excitons in the hBN-encapsulated MLs, as compared to MLs deposited on a $Si/SiO_2$ substrate. This reduction is due to the different dielectric environments of the MLs (hBN encapsulation versus vacuum and $Si/SiO_2$ substrate) [20]. Note that a series of low-energy emission lines can be observed in figure 1. Their attribution for $WS_2$ and $WSe_2$ MLs was discussed in the literature [3, 4, 6, 21], while the corresponding analysis for the WSSe ML was missing and will be presented in the following. The most well-known effect of the hBN encapsulation is a significant reduction in the inhomogeneous broadening of the spectral lines, leading to linewidths that approach the radiative decay limit [22]. To study the hBN influence in our case, we fitted the X lines, seen in figure 1, with Lorentzian functions. Their extracted linewidths, i.e. full width at half maximum, decrease substantially from 13 meV (16 meV) for the $WSe_2$ ($WS_2$) MLs deposited on a $Si/SiO_2$ substrate to a few meV for MLs encapsulated in hBN flakes (3.5 meV for $WSe_2$ and 5.2 meV for $WS_2$). Interestingly, the linewidth reduction for the WSSe ML (from 23 meV for $Si/SiO_2$ to 18 meV for encapsulated ML) is not as large. The main difference may come from the intrinsic quality of the WSSe alloy crystal compared with the pure $WS_2$ and $WSe_2$ crystals. While the S/Se composition in our WSSe crystal is relatively homogeneous at the macroscale, local variations of the chalcogen concentration are expected at the nanoscale. The alloy disorder as the main source of intrinsic scattering strongly limits the exciton lifetime in alloy MLs, leading to a broadening of the lines. Consequently, it is expected that hBN-encapsulation is not able to yield to a sizeable reduction of the X linewidth.

The assignment of the lower-in-energy features, labelled T, $T^I$ and $T_{E''(Γ)}^D$ in figure 2(a), requires a more detailed analysis. The T line can be ascribed to the negatively charged exciton (negative trion) according to the following evidence: (a) the energy separation between the X and T lines is of 32 meV, which is very close to the corresponding separation between the neutral exciton and the negative trion reported in the $WSe_2$ (32 meV) [21, 23] and $WS_2$ MLs (34 meV) [16, 20]; (b) the T emission line can be observed up to room temperature (see SI for details),
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Low-temperature (T = 5 K) PL spectra of WSe₂, WS₂, and WSSe MLs (a) deposited directly onto a SiO₂/Si substrate and (b) encapsulated in hBN flakes. The spectra were measured under excitation energy of 2.41 eV and power of 50 µW.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** (a) Power dependence of low-temperature (T = 5 K) PL spectra measured on a WSSe monolayer with 2.41 eV laser light excitation. (b) The intensity evolution of the emission features with excitation power. The dashed black line indicates the linear dependence as a guide to the eye. (c) The low-temperature PL spectrum of a single photon emitter, denoted as LX, measured on a WSSe ML. Note that the presented spectrum was measured on a specific region of a WSSe ML different from the ML displayed in panel (a). (d) The photon autocorrelation histogram recorded for the LX line.</figcaption></figure>
which is typical of the negative trion lines in W-based
MLs [4, 13, 20]; (c) the sign of free carriers can be
revealed indirectly due to the apparent double struc-
ture of the T lines at the highest magnetic fields,
as discussed later (see figure 5(a)), which is a sig-
nature of negatively charged excitons in WSe₂ and
WS₂ MLs [3, 20, 21, 24]. The assignment of the T¹
and T<sup>D</sup><sub>E''(Γ)</sub> lines to the correspondingly intervalley
momentum-forbidden negative dark trion and the
phonon replica of the intravalley spin-forbidden dark
trion, requires the use of external magnetic fields
applied in different configurations with respect to the
ML plane (parallel or perpendicular), which is dis-
cussed below. To confirm the origin of the aforemen-
tioned emission lines, we investigated their intensity
evolution as a function of the excitation power. The
low-temperature PL spectra of a WS<sub>Se</sub> ML encap-
sulated in hBN flakes measured with four differ-
ent excitation powers are presented in figure 2(a),
while the obtained power dependences of the stud-
ied emission lines are shown in figure 2(b). Note
that the power evolution of the T<sup>D</sup><sub>E''(Γ)</sub> line could
not be resolved for an excitation power greater than
300 µW. The integrated intensities of all investigated
lines are characterised by an almost linear evolution
with the excitation power. To analyse quantitatively
the power evolutions of the line intensities, we fit-
ted the corresponding dependences using the follow-
ing formula I ∝ P<sup>β</sup>, where I is integrated intensity of
lines, P is the excitation power, and β is a power coef-
ficient. The extracted values for the slopes of these lin-
ear evolutions range from about 1 for the X, T, and
T<sup>D</sup><sub>E''(Γ)</sub> lines to 1.2 for the T<sup>I</sup>, which is expected in
the case of excitonic complexes composed of a single
electron-hole (e-h) pair (in contrast to biexcitons,
whose intensities increase quadratically with excita-
tion power) [25].

It is important to mention that in addition to
the free exciton and trion lines, a zoo of states res-
ulting in a broad band below 1.8 eV can also be
observed in figure 2(a). These emission lines fea-
ture a sublinear behaviour with power and are thus
attributed to defect-related emissions. Interestingly,
at some specific locations where the ML is wrinkled
or blistered (and thus strained [26, 27]) due to the
trapping of contaminants or close to the edges, isol-
ated narrow lines show up from the broad defect-
related band, like those in figure 2(c). These lines
can be attributed to localised excitons (LXs), sim-
ilar to what was reported for WSe₂ [1, 19]. To verify
their quantum nature, we performed autocorrela-
tion measurements on the LX line, see figure 2(c).
As shown in figure 2(d), a clear antibunching beha-
viour is observed, resulting in a second-order auto-
correlation function g(0) = 0.388 ± 0.081, thus prov-
ing the single-photon emitter nature of the LXs. Our
result confirms the promise of WS<sub>Se</sub> for quantum

applications and calls for a deeper investigation of the
LX properties and of the role played by strain, which
will be the object of future studies.

From the analysis presented so far, we can con-
clude that the low-temperature PL spectra of the
WS<sub>Se</sub> ML encapsulated in hBN flakes comprise emis-
sion lines due to excitonic complexes composed of an
e–h pair. Figure 3 shows possible spin configurations
for the bright and dark excitons formed in the vicin-
ity of the A exciton. The neutral bright exciton in the
K<sup>±</sup> valley is composed of an electron from the higher-
lying level of the CB and a hole from the top level
of the VB from the same K<sup>±</sup> point, see figure 3(a).
The negatively charged exciton (negative trion) is a
three-particle complex composed of an e–h pair and
an excess electron. There are four negative trions in
darkish MLs based on tungsten (W) atoms (WS<sub>2</sub> or
WS<sub>Se</sub><sub>2</sub>) [3, 21, 23], i.e. two bright and two dark states.
These states can be formed at the K<sup>+</sup> and K<sup>−</sup> points
due to the location of a hole, leading to two possible
configurations of a given complex. Note that only a
single configuration of a specific complex is shown in
panels (b), (c), and (d) of figure 3. Due to the spin
conservation rule for S-TMD MLs, the bright (optic-
ally active) negative trion can be found in both the
intravalley singlet (T<sup>S</sup>), involving two electrons from
the same valley, and the intervalley triplet (T<sup>I</sup>), com-
prising two electrons from different valleys [20]. For
dark (optically inactive) negative trions, the corres-
ponding electrons are located in different valleys and
characterised by antiparallel alignment of their spins.
This configuration leads to two complexes, depend-
ing on the state of electron associated with the recom-
bination process: intravalley spin-forbidden (T<sup>D</sup>) and
intervalley momentum-forbidden (T<sup>I</sup>), which cannot
recombine optically due to spin and momentum con-
servation, respectively [3, 16, 28]. One of the pos-
sibilities to fulfil the spin and momentum conserva-
tion rules during optical recombination of dark trions
is phonon emission from the Γ and K points of the
BZ, respectively [3, 21, 23, 29]. Figure 3(d) presents
the schematic illustration of a possible recombina-
tion pathway of dark negative trions involving optical
phonon emission from the Γ point of the BZ, T<sup>S</sup><sub>E''(Γ)</sub>.
To verify the assignment of the T, T<sup>I</sup>, and T<sup>D</sup><sub>E''(Γ)</sub> lines,
we measured PL spectra as functions of in-plane and
out-of-plane magnetic fields up to 30 T, see figures 4
and 5.

To investigate the effect of the in-plane mag-
netic field (B_‖) on the emission of the WS<sub>Se</sub> ML,
we measured the evolution of the low-temperature
(T = 4.2 K) PL spectra under fields up to B_‖ = 30 T.
Figure 4(a) presents the PL spectra at selected
magnetic fields, B_‖ = 0, 10, 20, and 30 T. With
increasing B_‖, the intensity of the T¹ line increases
significantly, while the intensities of the other
emission lines, seen in the PL spectra, remain almost
<figure><img src="image_6.png" /></figure>

**Figure 3.** Schematic illustration of possible spin configurations for (a) the neutral exciton (X), (b) the bright singlet and triplet negative trions (T$^S$ and T$^I$, respectively), (c) the dark intravalley and intervalley negative trions (T$^D$ and T$^I$, respectively), and (d) the dark trion emission assisted by the optical phonon $E''$ from $\Gamma$ point of the BZ ($T_{E''(\Gamma)}^D$) formed in the vicinity of optical band gap of WSSe ML. Note that, except for the X complex, we draw only complexes for which a hole is located at the K$^+$ point of the BZ.

<figure><img src="image_7.png" /></figure>

**Figure 4.** (a) Low-temperature ($T = 4.2$ K) PL spectra of a WSSe monolayer encapsulated in hBN flakes measured at selected magnetic fields applied in the ML's plane. The PL spectra are normalised to the intensity of the X line. (b) The corresponding magnetic-field dependence of the relative intensity of the dark trion line to the neutral exciton line, $I_{T^D/T^I}$. The solid black curve represents a quadratic fit according to the equation described in the text. The spectra were measured under excitation energy of 2.41 eV and power of 50 µW.

unchanged. The energy separation between the X and T$^I$ lines of approximately 57 meV is very similar to the reported energy separations between the bright neutral exciton and the spin-forbidden negative trion in both WSe$_2$ (54–60 meV) [21, 21, 23, 30] and WS$_2$ (57 meV) [3]. Consequently, the brightening of the emission line in the in-plane field, labelled T$^D$, is ascribed to the intravalley spin-forbidden dark negative trion. To support further our attribution, we analyse the magnetic field evolution of the T$^{D/I}$ intensity. The $B_\parallel$ evolution of the intensity of the dark trion T$^D$ is expected to be quadratic $I = \alpha B_\parallel^2$ [3, 13, 31]. Figure 4(b) displays the $B_\parallel$ dependence of the relative intensities of the T$^{I/D}$ and X lines in magnetic fields

up to 30 T. Note that the division by the X intensity allows us to eliminate the variation of the signal intensity during measurements, e.g. the measured signal in the magnetic field setup is affected by the Faraday effect. The extracted data are accompanied by quadratic fits with the formula $I = I_0 + \alpha B_\parallel^2$, where $I_0$ corresponds to the T$^I$ intensity at zero field. As can be appreciated in figure 4(b), the obtained data can be described well by the proposed formula with the $\alpha$ parameter equal to $9.1 \times 10^{-3} \text{T}^{-2}$.

The last part of this work is devoted to the effects of out-of-plane magnetic fields ($B_\perp$) on the properties of the studied lines. Figure 5(a) demonstrates the helicity-resolved PL spectra measured
<figure><img src="image_8.png" /><figcaption>**Figure 5.** (a) Helicity-resolved PL spectra of an hBN-encapsulated WSSe monolayer at $T = 4.2$ K measured at selected values of the applied out-of-plane magnetic field. The red (blue) colour corresponds to the $\sigma^+$ ($\sigma^-$) polarised spectra. The spectra are vertically shifted for clarity. (b) Energy difference between the two circularly polarised split components of the X, T, $T^1$, and $T_{E''(\Gamma)}^D$ transitions as a function of out-of-plane magnetic field. The solid lines represent fits according to the equation described in the text. The spectra were measured under excitation energy of 2.41 eV and power of 50 µW.</figcaption></figure>

on the hBN-encapsulated WSSe ML in magnetic fields up to 30 T oriented perpendicularly to the ML plane. Due to both the large binding energies of free excitons and their huge reduced masses in S-TMD MLs [32–34], applying the out-of-plane magnetic field results mostly in the exciton Zeeman effect [35] (the diamagnetic shift of the ground excitonic states can hardly be seen in magnetic fields as high as 70 T [32, 33]), which manifests itself as a splitting of the two counter-circularly-polarised components of a given transition ($\sigma^\pm$). As can be seen in figure 5(a), all the observed emission lines split into two $\sigma^\pm$ components, but the magnitude of the Zeeman splittings differs, providing us with a tool to distinguish between the different complexes. Note that a double structure of the $\sigma^+$ component of the T line can be appreciated at 30 T with the determined energy separation between the $T^S$ and $T^T$ components of about 6 meV (see SI for details), which is in very good agreement with the previously reported corresponding energy splitting of the spin-singlet and spin-triplet negative trions in the WS$_{0.6}$Se$_{1.4}$ [36], WSe$_2$ (6–7 meV) [37–39], and WS$_2$ (7–8 meV) [20, 40] MLs. The energy separation of the $\sigma^\pm$ components in the $B_\perp$ field, $\Delta E(B_\perp) = E_{\sigma^+} - E_{\sigma^-}$ can be expressed as $\Delta E(B_\perp) = g\mu_B B_\perp$, where g denotes the effective g-factor of the considered excitonic complex and $\mu_B$ is the Bohr magneton. The magnetic field evolutions of $\Delta E$ with linear fits to the experimental data for the X, T, $T^1$, and $T_{E''(\Gamma)}^D$ lines are shown in figure 5(b). The extracted g-factors for both the X and T lines are about –3.7. Simultaneously, the g-factors found for the $T^1$ and $T_{E''(\Gamma)}^D$ lines are

much larger and correspond to approximately –13.8 and –7.9. The $T_{E''(\Gamma)}^D$ assignment to the phonon replica of the $T^D$ line is due to its g-factor of about –8, which is a characteristic value of spin-forbidden transitions (see [3, 23, 29] for details). As this type of transition requires spin-flip process of an electron in the CB (see figure 3(d)), it can be only achieved by a chiral phonon of a specific symmetry, that is $E''$ from the $\Gamma$ point of the BZ. [3, 23, 29] Moreover, the attribution of the $T_{E''(\Gamma)}^D$ to the emission of the $E''(\Gamma)$ phonon allows us to determine its energy to be about 28 meV. Note that the $E''(\Gamma)$ phonon can not be observed in a typical experimental backscattering geometry [41, 42], which requires that the electric field of the incident wave is perpendicular to the ML plane. Moreover, due to the identification of the phonon replica involving the $E''$ phonon from the $\Gamma$ point of the BZ, its energy was determined to be about 28 meV. If we consider the corresponding $E''(\Gamma)$ energies in WS$_2$ (36 meV) [3] and WSe$_2$ (21 meV) [30] MLs, the determined value is very close to the estimate of 30 meV obtained by making the assumption of a linear dependence of the phonon energy on the S/Se relative concentration in the ML alloys. Consequently, as reported in the literature, excitonic complexes in S-TMD MLs can be arranged into three groups due to their Zeeman splitting magnitude [3, 21, 23, 35]: (a) g-factors around –4 for bright transitions (X and T: –3.7); (b) spin-forbidden dark transitions are described by the g-factor equal to around –8 ($T_{E''(\Gamma)}^D$: –7.9); and (c) values of g-factors of about –14 are characteristic for momentum-forbidden dark transitions ($T^1$: –13.8).
### 3. Summary

To conclude, we presented a PL-based investigation of the optical response of MLs of WS<sub>Se</sub> with a S/Se ratio of 57/43 deposited on Si/SiO<sub>2</sub> substare and encapsulated in hBN flakes. We found that the WS<sub>Se</sub> ML was characterised by a dark ground exciton state, like its ‘parent’ WS<sub>2</sub> and WSe<sub>2</sub> MLs. Moreover, the existence of single photon emitters in the WS<sub>Se</sub> ML was also demonstrated. Through the application of in-plane and out-of-plane magnetic fields, the four main emission lines apparent in the low-temperature PL spectra were ascribed to the neutral bright exciton, the bright and dark (spin- and momentum-forbidden) negatively charged excitons, and the phonon replica of the dark spin-forbidden trion. Our results show that alloyed S-TMD MLs can represent a powerful material platform to widen the spectral range of operation of 2D crystals for optoelectronics and quantum technology applications.

### 4. Methods

MLs of WS<sub>Se</sub> were mechanically exfoliated from the bulk crystals grown by the Flux zone method and purchased from 2D semiconductors. The MLs were exfoliated with a scotch tape onto polydimethylsiloxane (PDMS). Relatively thick hBN flakes were exfoliated mechanically onto SiO<sub>2</sub>/Si substrates (300 nm thick SiO<sub>2</sub> on top of a 500 µm thick Si). The WS<sub>Se</sub> MLs were then deterministically transferred from the PDMS to the hBN flake. Thin hBN flakes were exfoliated onto PDMS and deposited on the WS<sub>Se</sub> ML to encapsulate it. After each deposition step, the sample was annealed in high vacuum (10<sup>-6</sup> mbar) at ~120 °C for several hours to induce the coalescence of the contaminants, thus improving the adhesion of the sample. For the WS<sub>Se</sub> MLs on SiO<sub>2</sub>/Si substrates, the MLs were first isolated onto PDMS and then deposited on the substrate. The investigated MLs of WSe<sub>2</sub> and WS<sub>2</sub> ML encapsulated in hBN flakes were fabricated in an analogue way by mechanical exfoliation based on PDMS, but the whole structure was deposited on a bare Si substrate. The WSe<sub>2</sub> and WS<sub>2</sub> MLs on SiO<sub>2</sub>/Si substrates were fabricated by simple exfoliation of the bulk crystals onto the substrates.

The WS<sub>Se</sub> alloy was examined by EDX analysis using a ZEISS-Sigma300 scanning electron microscope equipped with an Oxford Instruments X-Act 100 nm energy-dispersive spectrometer. Data were acquired with an acceleration voltage of 28 kV and analysed by INCA software. The spatial resolution was in the 10–15 µm range.

The PL experiments at zero magnetic field were performed using a λ =514.5 nm (2.41 eV) continuous wave (CW) laser diode. The studied samples were placed on a cold finger in a continuous flow cryostat mounted on x-y motorised positioners. The

excitation light was focused by means of a 100× long-working-distance objective with a 0.55 numerical aperture producing a spot of about 1 µm diameter. The signal was collected via the same microscope objective, sent through a 0.75 m monochromator, and then detected using a liquid nitrogen cooled charge-coupled device (CCD) camera.

Low-temperature micro-magneto-PL experiments were performed in the Voigt and Faraday geometries, i.e. magnetic field orientated parallel and perpendicular with respect to ML's plane, respectively. Measurements (spatial resolution ~1 µm) were carried out with the aid of a resistive magnetic coil producing fields up to 30 T using a free-beam-optics arrangement. The sample was placed on top of a x-y-z piezo-stage kept at T = 4.2 K and was excited using a CW laser diode with 515 nm wavelength (2.41 eV photon energy). The emitted light was dispersed with a monochromator of a 0.5 m focal length and detected with a CCD camera. The combination of a quarter-wave plate and a linear polariser was used to analyse the circular polarisation of signals (the measurements were performed with a fixed circular polarisation, whereas reversing the direction of magnetic field yielded the information corresponding to the other polarisation component due to time-reversal symmetry).

Autocorrelation measurements were performed in a Hanbury-Brown-Twiss setup by using a frequency-double Nd:YAG CW laser emitting at λ = 532.2 nm.

### Data availability statement

The data that support the findings of this study are available upon reasonable request from the authors.

### Acknowledgment

The work has been supported by the National Science Centre, Poland (Grants No. 2017/27/B/ST3/00205 and 2018/31/B/ST3/02111), EU Graphene Flagship Project, and the CNRS via IRP '2DM' project. We acknowledge the support of the LNCMI-CNRS, member of the European Magnetic Field Laboratory (EMFL). The Polish participation in EMFL is supported by the DIR/WK/2018/07 Grant from Polish Ministry of Education and Science. We acknowledge support by the European Union's Horizon 2020 research and innovation programme through the ISABEL Project (No. 871106). E B acknowledges support from La Sapienza through the grant Avvio alla Ricerca 2021 (Grant No. AR12117A8A090764). This project was funded within the QuantERA II Programme that has received funding from the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 101017733, and with funding organisations Ministero dell'Università e della Ricerca
(MUR) and Consiglio Nazionale delle Ricerche (CNR). M B acknowledge support by the ESF under the project CZ.02.2.69/0.0/0.0/20_079/0017 436. C F acknowledges support from Graskop project ANR-19-CE09-0026. K W and T T acknowledge support from JSPS KAKENHI (Grants No. 19H05790, 20H00354 and 21H05233).

## Author Contributions

K O-P, E B, N Z, S C, D V, P K, D J, G P, M F, C F, M P, A P, A B, and M R M performed the experiments. E B, K N, and M B fabricated the samples K W and T T grew the hBN crystals. K O-P, E B, A P, and M R M wrote the manuscript with inputs from the all co-authors.

## Conflicts of interest

There are no conflicts to declare.

## ORCID iDs

Katarzyna Olkowska Pucko

https://orcid.org/0000-0002-6036-7096

Elena Blundo https://orcid.org/0000-0003-0423-4798

Natalia Zawadzka https://orcid.org/0000-0002-3282-9513

Salvatore Cianci https://orcid.org/0000-0003-4020-369X

Diana Vaclavkova https://orcid.org/0000-0003-3116-2224

Piotr Kapuściński https://orcid.org/0000-0003-0241-0583

Giorgio Pettinari https://orcid.org/0000-0003-0187-3770

Marco Felici https://orcid.org/0000-0002-0977-2301

Karol Nogajewski https://orcid.org/0000-0001-8839-5032

Miroslav Bartoš https://orcid.org/0000-0002-5923-0260

Kenji Watanabe https://orcid.org/0000-0003-3701-8119

Takashi Taniguchi https://orcid.org/0000-0002-1467-3105

Clement Faugeras https://orcid.org/0000-0002-9615-8739

Marek Potemski https://orcid.org/0000-0001-8881-6618

Adam Babiński https://orcid.org/0000-0002-5591-4825

Antonio Polimeni https://orcid.org/0000-0002-2017-4265

Maciej R Molas https://orcid.org/0000-0002-5516-9415

## References

[1] Koperski M, Molas M R, Arora A, Nogajewski K, Slobodeniuk A O, Faugeras C and Potemski M 2017 *Nanophotonics* **6** 1289

[2] Lezama I G, Arora A, Ubaldini A, Barreteau C, Giannini E, Potemski M and Morpurgo A F 2015 *Nano Lett.* **15** 2336–42

[3] Zinkiewicz M et al 2021 *Nano Lett.* **21** 2519–25

[4] Arora A, Koperski M, Nogajewski K, Marcus J, Faugeras C and Potemski M 2015 *Nanoscale* **7** 10421

[5] Arora A, Nogajewski K, Molas M, Koperski M and Potemski M 2015 *Nanoscale* **7** 20769

[6] Molas M R, Nogajewski K, Slobodeniuk A O, Binder J, Bartos M and Potemski M 2017 *Nanoscale* **9** 13128

[7] Blundo E, Felici M, Yildirim T, Pettinari G, Tedeschi D, Miriametro A, Liu B, Ma W, Lu Y and Polimeni A 2020 *Phys. Rev. Res.* **2** 012024

[8] Blundo E et al 2022 *Phys. Rev. Lett.* **129** 067402

[9] Sun Y, Fujisawa K, Lin Z, Lei Y, Mondschein J S, Terrones M and Schaak R E 2017 *J. Am. Chem. Soc.* **139** 11096–105

[10] Xie L M 2015 *Nanoscale* **7** 18392–401

[11] Zhao Y, Zhang Z and Ouyang G 2018 *Appl. Phys. A* **124** 1432–0630

[12] Nugera F A, Sahoo P K, Xin Y, Ambardar S, Voronine D V, Kim U J, Han Y, Son H and Gutiérrez H R 2022 *Small* **18** 2106600

[13] Molas M R, Faugeras C, Slobodeniuk A O, Nogajewski K, Bartos M, Basko D M and Potemski M 2017 *2D Mater.* **4** 021003

[14] Molas M R et al 2019 *Phys. Rev. Lett.* **123** 096803

[15] Robert C et al 2020 *Nat. Commun.* **11** 4037

[16] Zinkiewicz M et al 2020 *Nanoscale* **12** 18153–9

[17] Palacios-Berraquero C et al 2016 *Nat. Commun.* **7** 12978

[18] Chakraborty C, Vamivakas N and Englund D 2019 *Nanophotonics* **8** 2017–32

[19] Cianci S, Blundo E, Felici M, Polimeni A and Pettinari G 2022 *Opt. Mater.* **125** 112087

[20] Vaclavkova D, Wyzula J, Nogajewski K, Bartos M, Slobodeniuk A O, Faugeras C, Potemski M and Molas M R 2018 *Nanotechnology* **29** 325705

[21] Liu E, van Baren J, Liang C T, Taniguchi T, Watanabe K, Gabor N M, Chang Y C and Lui C H 2020 *Phys. Rev. Lett.* **124** 196802

[22] Cadiz F et al 2017 *Phys. Rev. X* **7** 021026

[23] He M et al 2020 *Nat. Commun.* **11** 618

[24] He Y M 2015 *Nat. Nanotechnol.* **10** 497–502

[25] Klingshirn C F 2012 *Semiconductor Optics* (Berlin: Springer)

[26] Blundo E, Yildirim T, Pettinari G and Polimeni A 2021 *Phys. Rev. Lett.* **127** 046101

[27] Di Giorgio C, Blundo E, Pettinari G, Felici M, Bobba F and Polimeni A 2022 *Adv. Mater. Interfaces* **9** 2102220

[28] Liu E, van Baren J, Lu Z, Altaiary M M, Taniguchi T, Watanabe K, Smirnov D and Lui C H 2019 *Phys. Rev. Lett.* **123** 027401

[29] Liu E, van Baren J, Taniguchi T, Watanabe K, Chang Y C and Lui C H 2019 *Phys. Rev. Res.* **1** 032007

[30] Yang M, Ren L, Robert C, Van Tuan D, Lombez L, Urbaszek B, Marie X and Dery H 2022 *Phys. Rev. B* **105** 085302

[31] Zinkiewicz M, Grzeszczyk M, Kipczak L, Kazimierczuk T, Watanabe K, Taniguchi T, Kossacki P, Babiński A and Molas M R 2022 *Appl. Phys. Lett.* **120** 163101

[32] Stier A V, Wilson N P, Clark G, Xu X and Crooker S A 2016 *Nano Lett.* **16** 7054–60

[33] Goryca M et al 2019 *Nat. Commun.* **10** 4172

[34] Molas M R, Slobodeniuk A O, Nogajewski K, Bartos M, Bala L, Babiński A, Watanabe K, Taniguchi T, Faugeras C and Potemski M 2019 *Phys. Rev. Lett.* **123** 136801
[35] Koperski M, Molas M R, Arora A, Nogajewski K, Bartos M, Wyzula J, Vaclavkova D, Kossacki P and Potemski M 2019 2D Mater. **6** 015001

[36] Meng Y et al 2019 Nano Lett. 19 299–307

[37] Courtade E et al 2017 Phys. Rev. B **96** 085302

[38] Chen S Y, Goldstein T, Taniguchi T, Watanabe K and Yan J 2018 Nat. Commun. **9** 3717

[39] Li Z et al 2018 Nat. Commun. **9** 3719

[40] Jakubczyk T, Nogajewski K, Molas M R, Bartos M, Langbein W, Potemski M and Kasprzak J 2018 2D Materials **5** 031007

[41] Duan X et al 2016 Nano Lett. **16** 264–9

[42] Jalouli A, Kilinc M, Marga A, Bian M, Thomay T, Petrou A and Zeng H 2022 J. Chem. Phys. **156** 134704