Peer review of: Measurement of the spin-forbidden dark excitons in MoS2 and MoSe2 monolayers (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

In this work, Robert et al. studied the PL from monolayer MoS2 and MoSe2 in the in-plane 
magnetic field or tilted magnetic field. They found an emerging peak in MoS2 and MoSe2 with the 
in-plane magnetic field, which they attribute to the dark exciton. Further application of the tilted 
magnetic field also enabled authors to extract the g-factor of the dark exciton in MoS2 and the 
splitting between the dark and grey exciton. Overall, I feel this work lacks the novelty and 
importance that are required for the publication in Nature Communications. A similar method has 
been used to identify dark exciton in WSe2 in 2017 (ref. 14), and the study on dark exciton has 
developed significantly since then, by coupling the dark exciton to a plasmonic substrate (ref.15), 
AFM tip. And various methods have been developed to directly imaging the dark exciton in WSe2. 
Recently, the in-plane field method has also been used to identify the dark exciton in MoSe2 (ref. 
20). This work might be better suited for a specialized journal such as 2D materials, as the finding 
of the dark exciton in MoS2, if confirmed, will be of interest to a specific group for the completion 
of the dark exciton study in TMDs. There are also a few issues that the authors need to address. 

(1) The major one is the lack of TRPL data. Although the in-plane field dependence of the new 
peak is consistent with what has been reported for the dark exciton in WSe2, the g factor is 
significantly smaller than that in WSe2 and MoSe2. As the author discussed, the lower dark exciton 
energy than the bright exciton contradicts the temperature dependence of the PL. Lifetime 
measurement of the dark exciton would help to confirm the dark exciton nature. 

(2) The authors keep saying that the linewidth of the PL is too broad for extracting information 
directly. What is the linewidth for the dark exciton and bright exciton here? The authors reported 
PL linewidth as narrow as 2 meV in 2017 (ref. 28), and I would expect the dark exciton linewidth 
would be even smaller. 

(3) For the MoTe2 discussion, the authors attribute the absence of the dark exciton PL to the large 
energy difference between the dark and bright exciton, hence the large population difference. This 
is not entirely true, as the dark exciton typically has a much longer lifetime, which might still make 
the PL visible. 

(4) There are a few typos. In page 4, it should be “As we cannot extract the energy of the 4 lines 
at weak magnetic field due to their linewidths”. There is a missing "to". In page 6, it should be 
“CW” instead of “cw”. There are a few missing commas and extra spaces. Overall, the writing of 
the paper could be improved. For example, in the method section, this sentence reads awkwardly: 
“High-quality MoS2 and MoSe2 MLs encapsulated in hexagonal boron nitride (hBN) and transferred 
onto an SiO2 (80 nm)/Si substrate have been fabricated.” 



Reviewer #2 (Remarks to the Author): 

In their manuscript the authors present the results of a magneto-optical study of MoS2 and MoSe2 
monolayers focused on the elucidation of the exciton fine structure in these materials. The main 
observations are emerging emission signatures and characteristic splitting of the spectral features 
under strong in-plane and tilted magnetic fields. The data is further analyzed in the framework of 
an analytical model, describing the mixing of the exciton states in external magnetic fields 
accounting for the complete set of observations and allowing for the extraction of the relevant 
finestructure splitting parameters. The experimental data are very clear, the interpretations are 
strongly supported and the manuscript is overall very well presented. Moreover, the results of this 
study clarify a long-standing controversy of the exciton finestructure splitting in Mo-based 
materials and in MoS2 in particular. They are an important addition to the initial reports on W-
based systems and thus allow, for the first time, for a complete experimental and theoretical 
picture of the exciton finestructure in van der Waals monolayer semiconductors. Due to the high 
relevance for a number of optical and transport processes, including direct consequences for spin-
valley phenomena and emission efficiencies, the paper should find a broad audience in the 
community. I thus strongly recommend it for publication in Nature Communications journal. There 
are only a few points outlined in the following that the authors may consider to address. 

- While the physics determining the complex mixing behavior of the exciton states in tilted B-fields 
are clear, the presentation still leaves room for some potential misinterpretation. As the authors 
state, the labeling in the key figure 3 illustrates dominant contributions of zero-field states to the 
30T mixtures. The way it is currently phrased, however, combined with the solid lines that the eye 
then follows back to 0T in the figure, can easily imply that those are the states that the lines 
initially evolve from. Then one could, for example, think that the lower XB and XD should be 
labeled opposite (even if that is not the case as presented in SI7). The solution may be to include 
a few more details of what the solid lines mean directly into the manuscript and figure caption (+ 
potentially color the labels accordingly). May be there is even a convenient graphical way to 
indicate the mixing in the curves itself, or at least present the individual weights explicitly in the SI. 
Moreover, while the XB components in Table S1 and S2 are indeed dominant, the contributions XG 
and XD are rather similar. While mathematically correct, the small difference may not warrant the 
exclusive labeling, so that something like X_G,D and X_D,G may potentially better represent the 
actual weight distribution. Altogether, I admit to feel sufficiently confused about this part even 
writing the above, that hopefully further supports the point that the nice and interesting physics 
involved may find a slightly better representation for this subsection. 

- From the paragraphs in the discussion I understand that the authors tried to detect the XG state 
in MoS2 with high NA objectives. Would it be possible to suppress the low-NA emission from bright 
XB state for a higher chance to detect high NA luminescence from XG (may be that was tried as 
well though)? The reason is that, naively, one would expect that the observed splitting of 14 meV 
should be more than sufficient to ensure 99.99…% population of the dark state in MoS2 at 5K 
(kBT~ 0.5 meV), at least in thermal equilibrium. Then, as the authors discuss, would it mean that 
the oscillator strength of XG in MoS2 is that much lower than in W-based materials (probably by 
orders of magnitude then, considering very strong signals for WSe2, e.g.)? 

- In the discussion/conclusion section I generally support the impact and implications of MoS2 
being a “dark” semiconductor with sizable bright-dark splitting in the overall context of quantum 
yield. However, it may be reasonable to soften at least a little bit the current phrasing considering 
the interpretation of temperature-dependent quantum yields or, in particular, the room 
temperature 100%-yield study. While there are clear implications for the bright state occupation, 
the interplay with non-radiative processes is likely to be one of the dominant factors for observed 
emission efficiency in many cases. It thus seems generally reasonable, e.g., indeed not to regard 
the decrease of PL in MoS2 as clear distinction of a “bright”/”dark” material for which the present 
study offers the most convincing clarification. Also, if the material is indeed completely free from 
non-radiative traps (which is very unlikely in most cases of course), the redistribution of excitation 
in bright and dark states would only affect the total emission rate, but still keep the yield at 100%. 

- Similar applies to the paragraph discussing spin-valley polarization in MoSe2. I agree that the 
values are usually much lower in MoSe2, but it also seems to very strongly depend on the 
excitation conditions. For resonant exciton, e.g., polarization close to 100% was in fact reported 
even for MoSe2 (Tornatzki et al. PRL 121, 167401). The arguments of faster depolarization given 
by the authors are certainly still valid, yet I would only recommend to adjust the statement 
concerning weak polarization dependence of MoSe2 to include “at non-/quasi-resonant conditions” 
and also cite the above paper for a more complete picture. 


Reviewer #3 (Remarks to the Author): 

The manuscript presents the magneto-photoluminescence measurement of the fine structures of 
exciton, including both spin-allowed bright exciton and spin-forbidden dark one, in MoS2 and 
MoSe2 monolayers with the application of very high magnetic field up to 30 Tesla that can be set 
to be in either the in-plane or titled directions. Under the orientation-controllable high magnetic 
fields, rich fine structures of exciton measured optical spectra of exciton were revealed and, with 
the fitting of model simulation, the g-factors of bright and dark exciton states can be deduced. As 
a main finding stressed by the authors, the spin-forbidden dark exciton (SFDX) states of a MoS2 
monolayer was for the first time observed and shown to be below the bright one by Delta=14meV. 
The experimental studies are interesting and significant for better knowing the low-lying exciton 
fine structures of Mo-based TMD-MLs. However, I have the following comments and questions. 

(1) To interpret the energy location of the SFDX, the authors did the analysis for fine structure 
splitting Delta, composed of the conduction band splitting Delta_so, binding energy difference 
between the SFDX and BX Delta_bind, and the e-h exchange interaction Delta_exch. With the 
estimated Delta_so~-3meV and Delta_bind ~+ 8meV, Delta_exch ~ +9meV is inferred. There 
exist however some uncertainties in the determination of the energy parameters. Beside DFT-
model-dependent Delta_so, the Delta_bind should also somehow depend on the dielectric 
screening that could be modelled in different ways and depends on the chosen parameters. With 
the fixed Delta_so, the estimated value of Delta_bind directly determines the value of e-h 
exchange interaction energy. Can the author give more concrete details on the modelling of 
dielectric screening in the estimation of Delta_bind, and explain how is the modelling way suited 
for the real measured sample? With the estimated Delta_bind~+8meV, the inferred Delta_exch is 
quite small as compared with the values reported by their previous paper, PRB 93, 121107. Can 
the authors justify the inferred e-h exchange interaction energy by comparing that with more 
other existing studies? 

(2) Fig2b and Fig3c show the bright and dark exciton levels of MoSe2-ML ordered in energy 
differently under the action of the in-plane and tilted magnetic fields, respectively. The level 
crossing around 5 T seenin Fig3c might lead to the reorder of the bright and dark exciton levels. 
Carefully examining the raw experimental data of Fig. 3a, more complex energy- and intensity-
fluctuating features are observed over the wide range from 5 to about 15 T. For more 
understanding and interpretation of the rich spectral data of Fig.3a, can the model calculation 
based on Eqs S3-S5 be extended to simulate the spectral intensities of the exciton states, and 
provide more physical insight into experimental data? 

(3) The data of MoS2 under tilted field shown in Fig4 is quite ambiguous to identify the dark 
exciton signals. In particular, the grey exciton XG signal with surrounding spectral fluctuations in 
Fig4a is hardly recognized. The ambiguity in the identification of the exciton energy levels make 
the deduced g-factor from Fig4b questionable. Also, as one of the series of data of magneto-PL of 
Mo-based TMD-MLs, Fig4a should be presented in the same fashion as Figs 1a-3a so that reader 
can have the quantitative understand of the all cases on the equal footing. In the current format, 
the spectral data of other exciton states at low field are missing to see. If the signals of the dark 
states are intrinsically weak in the case of tilted field, the model simulation should be used to 
explain it. 

(4) A schematic of experimental set-up and the complete PL spectra of the samples (even at B=0) 
over the wider spectral range showing the signals of all exciton complexes (e.g. trion, defect states, 
etc) could be added to the main article or the supplementary material to increase readers’ 
recognition on the experiment and samples. 

Overall, the manuscript presents a meaningful and interesting observation of the fine structures of 
exciton in Mo-based monolayer materials with the application of very high magnetic field. However, 
the attraction of the work mainly lies in the aspect of technology. Besides the advances in the 
employed magneto-PL technology, more physics behind the measured data should be explored 
and interpreted with more insight to increase the value of the work. The manuscript could be 
considered to be published in this journal only if the physical or conceptual aspects of the work can 
be more enriched.