Under higher energy excitation, excitons will have higher initial kinetic energy17. Within a typical exciton radiative lifetime \(\tau_{\text{rad}}\), the exciton reaches an effective exciton temperature (\(T_{\text{exciton}}\)) which is significantly different from the lattice temperature as sketched in Fig.4(a). In Fig.4(b), the effective exciton temperature is retrieved from the fitting of our PL spectra based on our model which incorporates two components: one is the Lorentz function which describes the PL from the exciton inside the light cone; the other is the high-energy tale as elaborated in the SI-Note 6 which describes the acoustic phonon assisted PL (\(T_{\text{exciton}}\) as a fitting parameter) from excitons outside the light cone. The latter contributes more weight as the\(T_{\text{exciton}}\) increases. Our PLE experiments indicate that the effective exciton temperature can be tuned continuously by the excitation energy as shown in the Fig.4(b).
Figure 4 (a) Sketch of the relation between the effective exciton temperature and the excitation energy. The exciton excited by higher energy photon has a higher initial kinetic energy. After a time scale (~\(\tau_{\text{rad}}\)), the excitons reach different effective exciton temperature. (b) The effective exciton temperature as a function of the excitation energy.
In summary, our PL and PLE spectroscopic experiments reveal that the effect of hot excitons and the effective exciton temperature can be remarkably extracted from the PL spectrum of monolayer TMDs. We elaborate the roles of effective exciton temperature and lattice temperature in photoluminescence spectra and the linewidth broadening mechanism. The thermal equilibrium between the excitons and the lattice is not necessarily achieved in linear optical properties of 2D TMDs. The effective exciton temperature could be tuned by excitation energy.
Methods:
Crystal growth
Bulk MoSe2 crystals are grown by the chemical vapor transport (CVT) method. Mo powder (99.9%), slightly excessive Se ingot (99.999%), and a bit of iodine as transport agents are loaded in silica tubes, which are evacuated and sealed. Then, the silicon tubes are put in the reaction zone of 950 ℃ and the growth zone of 900 ℃. After fifteen days, bulk MoSe2 with large size are obtained in the cold zone. The monolayer MoSe2 is mechanically exfoliated onto Si substrate with 285 nm SiO2 film.
Sample preparation:
Monolayer MoSe2 and thin hBN were first exfoliated from bulk MoSe2 crystal onto the different Si/SiO2(300nm) substrates. Afterwards, dry-transfer technique was used to stack them together. Fig.S1 shows the optical image of our hBN encapsulated MoSe2 under bright and dark field.
PLE measurement:
In our PLE measurement, the light source (SuperK EXTREME EXB-3, NKT photonics) is a picosecond laser (80MHz, 5ps) pumped supercontinuum photonic crystal fiber going through a motorized continuous band-pass filter. The PL is collected through long working distance objective (Olympus, 50x) with a spectrometer (Shamrock 193i) and an electron-multiplying charge-couple-device (EMCCD, Andor).
1. Chernikov A, et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS 2. Physical review letters113 , 076802 (2014).
2. Ye Z, et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513 , 214-218 (2014).
3. Ugeda MM, et al. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor.Nature materials 13 , 1091-1095 (2014).
4. Zhu B, Chen X, Cui X. Exciton binding energy of monolayer WS2.Scientific reports 5 , (2015).
5. He K, et al. Tightly bound excitons in monolayer WSe 2.Physical review letters 113 , 026803 (2014).
6. Wang G, et al. Giant enhancement of the optical second-harmonic emission of WSe 2 monolayers by laser excitation at exciton resonances. Physical review letters 114 , 097403 (2015).
7. Mak KF, He K, Shan J, Heinz TF. Control of valley polarization in monolayer MoS2 by optical helicity. Nature nanotechnology7 , 494-498 (2012).
8. Zeng H, Dai J, Yao W, Xiao D, Cui X. Valley polarization in MoS2 monolayers by optical pumping. Nature nanotechnology 7 , 490-493 (2012).
9. Wang Z, et al. Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nature574 , 76-80 (2019).
10. Sidler M, et al. Fermi polaron-polaritons in charge-tunable atomically thin semiconductors. Nature Physics 13 , 255-261 (2017).
11. Zhang Y, et al. Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe 2.Nature nanotechnology 9 , 111-115 (2014).
12. Kormányos A, et al. k·ptheory for two-dimensional transition metal dichalcogenide semiconductors. 2D Materials 2 , (2015).
13. Wellstood F, Urbina C, Clarke J. Hot-electron effects in metals.Physical Review B 49 , 5942 (1994).
14. Chen Y, Li Y, Zhao Y, Zhou H, Zhu H. Highly efficient hot electron harvesting from graphene before electron-hole thermalization.Science advances 5 , eaax9958 (2019).
15. Cortés E, et al. Plasmonic hot electron transport drives nano-localized chemistry. Nature communications 8 , 1-10 (2017).
16. Yan T, Yu H, Xiao K, Yao W, Cui X. Probing the exciton k-space dynamics in monolayer tungsten diselenides. 2D Materials6 , 025035 (2019).
17. Trovatello C, et al. The ultrafast onset of exciton formation in 2D semiconductors. Nature communications 11 , 1-8 (2020).
18. Wallauer R, et al. Momentum-Resolved Observation of Exciton Formation Dynamics in Monolayer WS2. Nano Letters 21 , 5867-5873 (2021).
19. Hägele D, et al. Cooling dynamics of excitons in GaN.Physical Review B 59 , R7797 (1999).
20. Wang L, et al. Slow cooling and efficient extraction of C-exciton hot carriers in MoS2 monolayer. Nature communications8 , 1-8 (2017).
21. Kumar M, et al. Hot exciton cooling and multiple exciton generation in PbSe quantum dots. Physical Chemistry Chemical Physics 18 , 31107-31114 (2016).
22. Hohlfeld J, Wellershoff S-S, Güdde J, Conrad U, Jähnke V, Matthias E. Electron and lattice dynamics following optical excitation of metals.Chemical Physics 251 , 237-258 (2000).
23. Damen T, Leo K, Shah J, Cunningham J. Spin relaxation and thermalization of excitons in GaAs quantum wells. Applied physics letters 58 , 1902-1904 (1991).
24. Ziaja B, Medvedev N, Tkachenko V, Maltezopoulos T, Wurth W. Time-resolved observation of band-gap shrinking and electron-lattice thermalization within X-ray excited gallium arsenide. Scientific reports 5 , 1-7 (2015).
25. Umlauff M, et al. Direct observation of free-exciton thermalization in quantum-well structures. Physical Review B57 , 1390 (1998).
26. Moody G, et al. Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides. Nature communications 6 , 1-6 (2015).
27. Gupta G, Majumdar K. Fundamental exciton linewidth broadening in monolayer transition metal dichalcogenides. Physical Review B99 , 085412 (2019).
28. Shree S, et al. Observation of exciton-phonon coupling in MoSe 2 monolayers. Physical Review B 98 , 035302 (2018).
29. Chow CM, et al. Phonon-assisted oscillatory exciton dynamics in monolayer MoSe 2. npj 2D Materials and Applications1 , 1-6 (2017).
30. Helmrich S, et al. Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in MoSe 2 Bilayers. Physical Review Letters 127 , 157403 (2021).
31. Lorchat E, et al. Filtering the photoluminescence spectra of atomically thin semiconductors with graphene. Nature nanotechnology 15 , 283-288 (2020).
32. Cunningham PD, Hanbicki AT, McCreary KM, Jonker BT. Photoinduced bandgap renormalization and exciton binding energy reduction in WS2.ACS nano 11 , 12601-12608 (2017).
33. Pogna EA, et al. Photo-induced bandgap renormalization governs the ultrafast response of single-layer MoS2. ACS nano10 , 1182-1188 (2016).
34. Liu F, Ziffer ME, Hansen KR, Wang J, Zhu X. Direct determination of band-gap renormalization in the photoexcited monolayer MoS 2.Physical review letters 122 , 246803 (2019).
35. Qiu Z, et al. Giant gate-tunable bandgap renormalization and excitonic effects in a 2D semiconductor. Science advances5 , eaaw2347 (2019).
36. Schaibley JR, et al. Population Pulsation Resonances of Excitons in Monolayer MoSe 2 with Sub-1 μ eV Linewidths. Physical review letters 114 , 137402 (2015).
Acknowledgement:
The work was supported by the Hong Kong University Grants Council/ Research grants council under schemes of (AoE/P-701/20), GRF (17300520) and AoE seed fund of University of Hong Kong and National Key R&D Program of China (2020YFA0309600). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (Grant Number JPMXP0112101001) and JSPS KAKENHI (Grant Numbers 19H05790, 20H00354 and 21H05233). R.D and Z.L. acknowledge support from the Singapore Ministry of Education Tier 3 Programme “Geometrical Quantum Materials” AcRF Tier 3 (MOE2018-T3-1-002), AcRF Tier 2 (MOE2019-T2-2-105). The authors thank Dr. Fengren Fan, Dr. Tengfei Yan, Dr. Bairen Zhu for fruitful discussion.
CONFLICT OF INTEREST:
Wang Yao is a co-author of the manuscript and an editor of Natural Sciences and was not involved at the handling of the peer-review process of this submission.
Author contributions
K. X. performed the experiments and analyzed the data. R. D. and Z. L. provided high quality MoSe2 crystal. K.W. and T.T provided boron nitride crystals. W. Y. provided theoretical support. K.X. performed the simulation. X. C. supervised the project. K. X. and X. C. wrote the manuscript with the aid of all the co-authors.