Valley depolarization in downconversion and upconversion emission of monolayer WS2 at room temperature

Han Li 1 , Yating Ma 1 , Yizhen Sui 1 , Yuxiang Tang 1 , Ke Wei 1 , Xiang’ai Cheng 1 , and Tian Jianghttp://orcid.org/https://orcid.org/0000-0003-3343-5548 1
  • 1 College of Advanced Interdisciplinary Studies, National University of Defense Technology, 410073, Changsha, China
Han Li
  • College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, 410073, China
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, Yating Ma
  • College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, 410073, China
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, Yizhen Sui
  • College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, 410073, China
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, Yuxiang Tang
  • College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, 410073, China
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, Ke Wei
  • College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, 410073, China
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, Xiang’ai Cheng
  • College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, 410073, China
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and Tian JiangORCID iD: https://orcid.org/0000-0003-3343-5548

Abstract

Benefiting from strong photon–exciton and phonon–exciton interactions in atomic thickness, transition metal dichalcogenides (TMDCs) are viewed as one promising platform for exploring elementary excitonic photoluminescence (PL) and intrinsic spin–valley properties at the monolayer limit. Despite well-studied Stokes downconversion (DC) PL, the anti-Stokes upconversion (UC) PL has been recently reported in TMDC monolayers, which mainly focus on UC mechanisms while detailed valley-related dynamical processes are unwittingly less concerned. Here, we carry out an in-depth investigation on both DC and UC emission features of monolayer WS2 at room temperature, where UC PL persists with energy gain up to 190 meV. The PL excitation and power-dependent experiments clearly distinguish the origins of DC PL and UC PL, which refer to saturated absorption and phonon-assisted transition from charged trions to neutral A-excitons. And contrast valley properties are observed in DC and UC scenarios with polarization-resolved PL and pump–probe measurements. According to the experimental facts, phenomenological dynamical DC and UC scenarios are modeled with intervalley depolarization taken into consideration, in which intermediates from spontaneous intervalley depolarization account for the observed emission and valley properties. This work can help understand the light–matter interactions and valley properties in monolayer TMDCs.

1 Introduction

Photoluminescence (PL) is an elementary light–matter interaction process, in which downconversion (DC) PL is the general Stokes process in emission of semiconductors, resulting in the energy or frequency of an emitted photon smaller than that of the absorbed one. In contrast to the DC PL, the other one PL mode, namely upconversion (UC) PL, describes an anti-Stokes process, in which the material absorbs photons with lower energy and then reemits corresponding photons with some energy gain. As often referred to optical refrigeration and laser cooling, the UC PL phenomenon has been well explored and demonstrated in glass doping with rare-earth elements [1], [2], [3], quantum wells [4], [5], [6], [7] and other semiconductors [8], [9] at cryogenic conditions. Recently, monolayer transition metal dichalcogenides (TMDCs) are found to be direct bandgap semiconductors with visible PL [10], [11], [12], [13], [14], [15], [16] and much higher quantum efficiency than traditional semiconductor materials [17], [18], where solid dipoles of excitons dominate the optical properties due to strong Coulomb binding effect [19], [20], [21], [22], [23], [24], [25]. Benefiting from enhanced photon–exciton [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37] and phonon–exciton interaction strength [38], [39], [40], [41] in a low dimensional scale, as observed in graphene and V–V binary materials [42], [43], TMDCs are viewed as one promising platform for exploring UC PL at the monolayer limit. And there are some research studies reporting the UC PL observed in monolayer TMDCs, for example, two-photon absorption–induced UC PL of B-exciton at 4 K [44] and phonon-mediated doubly resonant UC PL with an energy gain of 30 meV up to 250 K [45] in monolayer WSe2, as well as multiphonon–induced UC PL with an energy gain of 150 meV in monolayer WS2 at room temperature [46]. However, these research studies mainly focus on the excitonic conversion mechanism during the UC PL process, and the underlying dynamical transition process and intrinsic valley properties of monolayer TMDCs are unwittingly less concerned to some extent. Considering the strong excitonic and phonon–exciton interactions in monolayer TMDCs, the relationship between valley depolarization and UC PL process is still blurred. In this way, a deeper study of dynamical valley depolarization mechanism during the UC PL process may bring a new understanding of valleytronics based on TMDCs.

In this work, we investigate both DC PL and UC PL in monolayer WS2. We not only explore the properties of DC PL and UC PL but also focus on the valley properties in these two opposite PL modes. We observe the UC PL, from charged trions to neutral excitons, with energy gain up to 190 meV at room temperature. Valley properties are measured, and different dynamical parameters related to valley depolarization, including initial polarization and exciton lifetime, are analyzed and discussed for both DC PL and UC PL scenarios. Finally, phenomenological valley depolarization processes are modeled and discussed according to the experimental results, which well explain the observation of PL and valley properties in monolayer WS2.

2 Results and discussion

Figure 1a presents the optical image of two WS2 monolayers grown by the chemical vapor deposition method on the Si/SiO2 substrate and marked as S1 and S2. All the results presented here are of S1 sample and those of S2 sample are presented in Supplementary material. The Raman spectrum of monolayer WS2 is shown in Figure 1b, and the Raman interval between out-of-plane A1g mode and in-plane E2g1 mode is around 61.7 cm−1, which is in accordance with previous reports [47], [48]. The schematic of DC PL and UC PL processes in monolayer WS2 is illustrated in Figure 1c. Generally, the hot carriers are firstly generated by the photons with energy above the bandgap and then relax toward the band edge and are finally recombined with radiatively emitting photons, with energy centered at the resonance of A-exciton in DC PL. However, it is found that the A-exciton emission can also occur with excitation energy below the bandgap. In this case, trions, created by incident light with energy on the tail of resonance [45], [46], are somehow converted into A-excitons and then recombine radiatively, which is defined as UC PL. The prototypical PL spectrum excited by 512-nm continuous-wave laser at room temperature is presented in Figure 1d, with trion and exciton emission intensities and peaks fitted by the Lorenz model. During the following PL-related experiments, a short-pass filter and a long-pass filter are used, with the edge at 1.96 and 2.06 eV, respectively. And emission of A-excitons with excitation energy below 1.96 eV (above 2.06 eV) is described as UC PL (DC PL), with corresponding off-resonance energy (Δ) defined as the difference between the excitation energy (Eex) and the peak energy of A-exciton EA = 2.04 eV in monolayer WS2, namely Δ=EexEA.

Figure 1:
Figure 1:

Downconversion (DC) and upconversion (UC) processes in monolayer WS2.

(a) Optical image of monolayer WS2 on Si/SiO2 substrate. (b) Raman spectrum of monolayer WS2. (c) The schematic of DC and UC processes. GS is the ground state. XT, XA and hot represent the trions, A-excitons and hot carriers, respectively. Red and blue lines represent the excitation process by off-resonance energy. Gray lines indicate the emission of A-excitons through DC and UC processes. (d) The PL spectrum of monolayer WS2 excited by 512-nm continuous-wave laser at room temperature. The dash lines show the filter edges.

Citation: Nanophotonics 9, 16; 10.1515/nanoph-2020-0483

2.1 Properties and origins of DC PL and UC PL

For detailed information about DC PL and UC PL, photoluminescence excitation (PLE) experiments are performed. As presented in Figure 2a and c, the intensity of both DC PL and UC PL depends on off-resonance energy, with the shape of the PL spectra and the peaks of the A-exciton nearly unchanged. Surprisingly, the A-exciton emission even remains detectable within 190 meV range of off-resonance energy, exceeding the reported 150 meV energy gain in previous research of monolayer WS2 [46]. To quantitatively analyze the emission properties in DC PL and UC PL, the PL intensity of A-exciton resonance is integrated and normalized in log scale, shown in Figure 2b and d, which obey an evident linear relationship with the off-resonance energy. In this way, the integrated DC PL and UC PL intensity is described as I=A·ek·Δ, where I and Δ are integrated PL intensity and the off-resonance energy, respectively. The fitted parameter k is defined as the fitting slope in Figure 2b and d, representing the decrement of integrated PL intensity with off-resonance excitation. Interestingly, the absolute value of k in UC PL (0.0252/meV) is one order larger than that in DC PL (0.0026/meV) when ignoring the sign. According to this contrast, we believe that the underlying origins of DC PL and UC PL should be different.

Figure 2:
Figure 2:

Photoluminescence excitation (PLE) spectra in downconversion (DC) and upconversion (UC) processes.

(a) DC PL and (c) UC PL spectra under variable excitation energy. Normalized intensity of (b) DC PL and (d) UC PL in log scale, linearly depending on the off-resonance energy.

Citation: Nanophotonics 9, 16; 10.1515/nanoph-2020-0483

In addition to the PLE results, we then also carry out power-dependent PL experiments to explore the underlying origins of DC PL and UC PL. As shown with log–log plot in Figure 3a and b, the DC PL intensity reveals linear dependence on excitation power when the incident power is relatively low (0.1–0.5 μw). With the incident power increasing, the DC PL intensity finally shows obvious sublinear dependence (0.37 and 0.38), which indicates a saturated absorption trend. Similarly, the UC PL intensity also shows linear dependence on low excitation power with log–log plot in Figure 3c and d. However, under high excitation power, the slopes still persist to be 0.81 and 0.9 in UC PL, which are much higher than that in DC PL.

Figure 3:
Figure 3:

Power-dependent photoluminescence (PL) intensity in downconversion (DC) PL and upconversion (UC) PL. (a), (b) The DC PL intensity shows a saturated trend. (c), (d) The slope of UC PL intensity persists under high incident power.

Citation: Nanophotonics 9, 16; 10.1515/nanoph-2020-0483

Though the slopes of DC PL and UC PL intensity similarly change from linear dependence to sublinear dependence, the underlying origins are believed to be totally different according the PLE results in Figure 2 and power-dependent PL intensity behaviors. Apart from the saturated absorption in the DC PL process, the origin of UC PL may be much complex, such as nonlinear two-phonon absorption process and exciton Auger scattering. The linear slopes of UC PL intensity under small incident power exclude the possibility of two-phonon absorption and exciton Auger scattering progress; otherwise, a superlinear trend would be expected [44]. In previous UC PL study of monolayer TMDCs, optical phonons are proved to be necessary to maintain both the momentum and energy conservation in the UC process from trions to A-excitons. With participation of phonons, UC PL intensity starts with linear dependence at small density of trions when phonons are relatively abundant. With the consumption of phonons and the growing density of trions, it shows a slightly sublinear trend, which is different from that in saturated DC PL process. The stable slopes in UC PL here, up to 0.81 and 0.9, represent an efficient excitonic many-body interaction effect even under high excitation power in our experiments.

2.2 Valley properties in DC and UC scenarios

After revealing the emission behaviors and origins in DC and UC scenarios, now we turn to their valley properties. As discussed above, excitonic and phonon–exciton interactions are strong in monolayer WS2, which is proved in our efficient UC PL results. In view of the absorption of phonons in the UC scenario, which cannot be regarded as a reverse process of hot carrier cooling in DC process, we assume that the depolarization mechanisms may be different in DC and UC. Moreover, unlike spontaneous DC process driven by carrier energy offset, UC is assisted by one or multiphonons when the off-resonance energy is tuned. In this way, the valley property would be influenced or even modulated by the off-resonance energy.

We perform polarization-resolved PL measurements in both DC and UC scenarios under right circularly polarized lasers with variable excitation energy and calculate the degree of polarization (DOP) as DOP=IσIσ+Iσ+Iσ+, where Iσ and Iσ+ represent the intensity of right and left circularly polarized component signals, respectively. And as illustrated in Figure 4a and b, DOP decreases with the growing absolute value of off-resonance energy in both DC PL and UC PL, which clearly means the valley polarization preserves more efficiently under near-resonance excitation. In addition, the DOP in UC PL is much lower than that in DC PL, and the valley polarization quickly vanishes in UC PL with off-resonance energy from −70 to −130 meV. It is worth noticing that the DOP value can only reflect the resultant distribution of valley polarized excitons in steady states after the depolarization process. Deeper information about the depolarization dynamics cannot be obtained from polarization-resolved PL spectra alone. And as analyzed in previous reports, the resultant valley polarization of A-excitons can be related to dynamical parameters [28], [,], which is described by DOP=P01+τxτv, where the P0, τx and τv denote the initial exciton polarization, exciton lifetime and valley lifetime, respectively. It is clearly seen that the valley properties of A-excitons can be influenced by these three independent parameters, which is complicated for clarification. For discussion, we firstly assume that the variation of τv in the same sample is neglectable at 295 K room temperature since it depends on the intrinsic spin-flip process of A-excitons according to previous report [43], and therefore variations of P0 and τx dominate the DOP behavior in the DC PL and UC PL scenarios. Limited by the experimental instruments, it is difficult to precisely measure the value of initial exciton valley polarization P0. Instead, we lay P0 aside and turn to the exciton lifetime τx by performing pump–probe (transient absorption spectrum) measurements with different off-resonance energies. After analyzing and fitting the dynamical exciton recombination signals (see more details in Supplementary material), we deduce the average exciton lifetime, which is presented with DOP values in Figure 4c. And there are two intriguing observations when taking both the measured DOP value and exciton lifetime into account. Firstly, the average exciton lifetime slightly decreases when pumped with near-resonant excitation in the DC scenario, contributing to the rising DOP in DC PL. But contrastingly, the exciton lifetime in the UC scenario shows a totally opposite trend with excitation from off-resonance to near-resonance energy. Secondly, the DOP value is supposed to intuitively increase based on smaller lifetime in UC PL under the assumption of a constant P0. However, valley polarization gradually vanishes with decreasing exciton lifetime. Additionally, the experimental fact demonstrates that the DOP value of UC PL is obviously smaller than that of DC PL, though the measured lifetimes in both DC and UC scenarios are in the same order. And these changed exciton lifetimes would not result in such evident modulation of DOP alone, considering the small decrement in DC (from 30.7 to 26.9 ps) and anomalous increment in UC (from 15.2 to 28 ps) when pump energy is tuned from off resonance to near resonance. Therefore, we believe that the underlying P0 is variable and can be effectively modulated in both DC and UC processes, which is not well studied but actually dominates and further complicates the unique valley property in monolayer WS2. In this way, variable P0 and exciton lifetime imply different depolarization mechanisms between DC and UC scenarios.

Figure 4:
Figure 4:

Polarized photoluminescence (PL) spectra and average lifetime of A-excitons in downconversion (DC) and upconversion (UC) scenarios.

(a) Polarized PL spectra in DC process. (b) Polarized PL spectra in UC process. (c) Degree of polarization (DOP) value and lifetime of A-excitons, presented by circles and squares, respectively.

Citation: Nanophotonics 9, 16; 10.1515/nanoph-2020-0483

2.3 Depolarization-assisted conversion model

According to our experimental results and analysis, we present a phenomenological roadmap to illustrate the observed valley properties during DC and UC scenarios, as shown in Figure 5. It is worth noticing that this roadmap is basically result oriented and only characteristic processes and results are shown, while detailed dynamical parameters of depolarization are not presented. And possible depolarization channels including D’yakonov–Perel mechanism [53], [54], Maialle–Silva–Sham mechanism [55], [56], [57] and Elliot–Yaffet mechanism [58], [59] are discussed in Supplementary material. We firstly consider a universal and basic depolarization model shown in Figure 5a. It starts from the photogenerated trions (hot carriers), created in the −K valley, on set of right circularly polarized UC excitation (DC excitation). Considering the energy and momentum mismatches between the −K and K valleys, we then assume that the trions and hot carriers in −K valley, marked by XTK and XHK, would not directly transfer into the A-excitons in K valley. Under this assumption, only intrinsic and spontaneous depolarization process of A-exciton, from −K (XAK) to K (XAK) valleys, is involved. The whole depolarization in Figure 5a therefore consists of three independent dynamical processes with the following forms:

  1. XHKXAK,

Figure 5:
Figure 5:

The depolarization model in downconversion (DC) and upconversion (UC) scenarios.

(a) Direct conversion channels from trions and hot carriers in −K valley into the A-excitons in K valley are forbidden. (b) With intermediate depolarization of trions and hot carriers, possible conversion occurs from trions and hot carriers in −K valley into the A-excitons in K valley.

Citation: Nanophotonics 9, 16; 10.1515/nanoph-2020-0483

The photogenerated hot carriers are spontaneously downconverted into A-excitons during an ultrafast relaxation process in −K valley.

  1. (2)XTK+i=1NPniXAK,(N=1,2,3),

The photogenerated trions are upconverted into A-excitons with the assistance of one phonon or multiphonons depending on the energy gain in −K valley, where phonon is marked by Pn.

  1. (3)XAKXAK.

Finally, A-excitons converted from both DC and UC process in −K valley partly transfer into A-excitons in K valley with degenerate resonant energy, inducing the valley depolarization.

This model shown in Figure 5a seems to be reliable until theoretical valley polarization behavior is concerned. Since intravalley DC and UC processes would not contribute to the intervalley depolarization of A-excitons, intervalley depolarization only takes effect when XAK is formed and transfered into XAK; the DOP values measured from polarization-resolved DC PL and UC PL should be identical in theory. This is totally different from the observed valley properties that are proved to be effectively modulated by the off-resonance excitation. Additionally, very finite (far below 100%) valley polarization can be observed with near-resonance excitation in DC PL and UC PL spectra out of A-exciton resonance, implying that the intervalley depolarization process is not limited to A-excitons. In this way, the depolarization model is corrected on the basis of Figure 5a, and two intermediates, XHK for hot carriers and XTK for trions in K valley, are added in Figure 5b. Similar to Figure 5a, trions and hot carriers in −K valley are still supposed to obey the conservation of both energy and momentum, so they cannot directly turn into the A-excitons in K valley. However, an indirect transition with the help of intermediates is no longer inaccessible in this roadmap. According to the model in Figure 5b, the dynamical expressions are then corrected as follows which are separately discussed in DC and UC scenarios.

Depolarization of XHKXAK in the DC scenario,

  1. XHKXAK and XHKXHK,

The photogenerated hot carriers in −K valley would experience two different physical processes. In addition to the same intravalley conversion into XAK in Figure 5a, an additional intervalley conversion into hot carriers in K valley would also partly occur in an ultrafast timescale (via long-range exchange effect, carrier–carrier scattering or carrier–phonon scattering effect).

  1. (2)XAKXAK and XHKXAK.

Finally, XAK in the DC scenario is formed, which originates from two physical processes. One is the intervalley depolarization process of XAK, while the other one is an intravalley DC process in K valley.

And similarly, depolarization of XTKXAK in the UC scenario,

  1. XTKXTK,

The photogenerated hot carriers in −K valley would experience two different physical processes. In addition to the same intravalley conversion into XAK in Figure 5a, an additional intervalley conversion into hot carriers in K valley would also partly occurs in an ultrafast timescale (via long-range exchange effect, carrier–carrier scattering or carrier–phonon scattering effect).

  1. (2)XTK+i=1NPniXAK,(N=1,2,3)and XTK+i=1NPniXAK,(N=1,2,3),

Subsequent intravalley UC process occurs in both −K and K valleys, with the assistance of optical phonons to compensate the energy mismatch. Since the energy gain is identical in −K and K valleys, these two UC processes occur with the same conversion rate. One portion of XAK is generated.

  1. (3)XAKXAK.

Finally, A-excitons converted from UC process in −K valley partly transfer into the other one portion of XAK with degenerate resonant energy. As can be seen above, the introduced intermediates XHK and XTK influence valley property in DC and UC scenarios, respectively, which matches well with the experimental fact of contrasting DOP values in Figure 4c.

We then carry out some discussions about these conversion processes referred in Figure 5b to further estimate the depolarization model. Generally, the dynamical rate of each conversion process dominates this result-oriented depolarization model. As reported in previous research studies [49], [50], [57], [60], [61], the intervalley depolarization can quickly take effect (on the order of 1 ps) at room temperature, which means effective intervalley transition spontaneously happens from XHK/XAK/XTK to XHK/XAK/XTK with a very fast rate in Figure 5b. And in Stokes DC scenario, the hot carriers driven by energy offset spontaneously relax to the band edge within several hundred femtoseconds [15]. The dynamical rate of DC process exceeds intervalley transition, verified by the residual 13% DOP value of A-excitons under near-resonance excitation. And with larger off-resonance energy, the intervalley transition between hot carriers is enhanced to some extent, which is in accordance with the weaker valley property as shown in the DC PL scenario of Figure 4c. As for the UC scenario, one phonon or combination of multiphonons is needed, depending on the energy gain. Unlike spontaneous DC process driven by energy offset, the conversion rate (or possibility) from trion to A-excitons in anti-Stokes UC process obeys Fermi’s golden rule, reported by Jones et al. [45]. We follow this calculation method and roughly obtain conversion rates of 0.07, 0.02 and 0.006 ps−1 for off-resonance energy at −70, −100 and −130 meV, respectively. The conversion rate sharply decreases with off-resonance excitation, inducing a higher portion of XTK into XTK. And the valley property of generated A-exciton totally vanishes when off-resonance reaches −130 meV, as illustrated by polarization-resolved UC PL in Figure 4c. Moreover, the conversion rate is theoretically proportional to phonon population (related to energy gain) [45], which follows an averaged thermal distribution as 1/exp(|Δ|kBT1), where |Δ|, kB and T represent energy gain, Boltzmann constant and 295 K room temperature, respectively. We find that this relationship is not identical but pretty similar to the PLE intensity behavior of the UC scenario in Figure 2d. In this way, the depolarization model matches well with our observations in both DC and UC scenarios.

3 Conclusion

In summary, we have established an in-depth investigation on the emission features and valley properties of monolayer TMDCs in both DC and UC scenarios at room temperature. The PLE measurements are conducted, and two variation slopes with difference of one magnitude in log–log scale are observed, which implies the different underlying emission mechanisms. UC PL is observed with energy gain up to 190 meV. Subsequent power-dependent experiments clarify the origins of DC PL and UC PL, which refer to saturated absorption and phonon-assisted conversion from trions to excitons. Valley properties are measured with polarization-resolved PL spectra, and two contrast valley polarization behaviors are found in DC PL and UC PL scenarios. We deduce different valley depolarization parameters for DC PL and UC PL scenarios. And finally, a phenomenological valley depolarization model is introduced and discussed according to our experimental results. This work can help understand the many-body interactions and valley properties of monolayer TMDCs.

4 Materials and methods

Raman, PL and pump–probe measurements are done by lab-built systems. A 532-nm continuous-wave laser is utilized as excitation during Raman measurement. The integration time is set as 1 (10) second in DC PL (UC PL) measurements. For polarization-resolved PL measurements, a quarter-wave plate and a polarizer with horizonal polarization are set in front of the spectrometer. And in this case, the detected polarization is controlled by rotating the quarter-wave plate. For pump–probe measurements, a Ti:sapphire femtosecond laser is used to provide ultrashort pulses with 800 nm center wavelength. The main portion of the femtosecond laser is sent to an optical parametric amplifier with tunable output energy as pump light. A small power portion is sent through a sapphire crystal to generate a white light continuum as the probe beam. Then, decay signals of A-exciton are analyzed and fitted to obtain dynamical lifetimes. All experiments are carried out at room temperature.

Acknowledgments

The authors are grateful for financial support from the National Natural Science Foundation of China (Grant Nos. 11804387, 11802339, 11805276, 11902358, 61805282 and 61801498), the Scientific Researches Foundation of National University of Defense Technology (Grant Nos. ZK18-03-22, ZK18-01-03 and ZK18-03-36) and the Science Fund for Distinguished Young Scholars of Hunan Province (Grant No. 2020JJ2036).

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

Research funding: The authors are grateful for financial support from the National Natural Science Foundation of China (Grant Nos. 11804387, 11802339, 11805276, 11902358, 61805282 and 61801498), the Scientific Researches Foundation of National University of Defense Technology (Grant Nos. ZK18-03-22, ZK18-01-03 and ZK18-03-36) and the Science Fund for Distinguished Young Scholars of Hunan Province (Grant No. 2020JJ2036).

Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Footnotes

Supplementary Material

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    Downconversion (DC) and upconversion (UC) processes in monolayer WS2.

    (a) Optical image of monolayer WS2 on Si/SiO2 substrate. (b) Raman spectrum of monolayer WS2. (c) The schematic of DC and UC processes. GS is the ground state. XT, XA and hot represent the trions, A-excitons and hot carriers, respectively. Red and blue lines represent the excitation process by off-resonance energy. Gray lines indicate the emission of A-excitons through DC and UC processes. (d) The PL spectrum of monolayer WS2 excited by 512-nm continuous-wave laser at room temperature. The dash lines show the filter edges.

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    Photoluminescence excitation (PLE) spectra in downconversion (DC) and upconversion (UC) processes.

    (a) DC PL and (c) UC PL spectra under variable excitation energy. Normalized intensity of (b) DC PL and (d) UC PL in log scale, linearly depending on the off-resonance energy.

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    Power-dependent photoluminescence (PL) intensity in downconversion (DC) PL and upconversion (UC) PL. (a), (b) The DC PL intensity shows a saturated trend. (c), (d) The slope of UC PL intensity persists under high incident power.

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    Polarized photoluminescence (PL) spectra and average lifetime of A-excitons in downconversion (DC) and upconversion (UC) scenarios.

    (a) Polarized PL spectra in DC process. (b) Polarized PL spectra in UC process. (c) Degree of polarization (DOP) value and lifetime of A-excitons, presented by circles and squares, respectively.

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    The depolarization model in downconversion (DC) and upconversion (UC) scenarios.

    (a) Direct conversion channels from trions and hot carriers in −K valley into the A-excitons in K valley are forbidden. (b) With intermediate depolarization of trions and hot carriers, possible conversion occurs from trions and hot carriers in −K valley into the A-excitons in K valley.