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).
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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.