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Electronic intraband scattering in a transition-metal dichalcogenide
observed by double-excitation ultrafast electron diffraction
Yui Iwasaki,1,a) Takumi Fukuda,2,a) Godai Noyama,1 Mizuki Akei,1 Hidemi
Shigekawa,3 Paul J. Fons,4 Muneaki Hase,3 Yusuke Arashida,3,b) and Masaki
Hada,3,5,c)
1College of Engineering Sciences, University of Tsukuba, Tsukuba 305-8573, Japan
2

Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan

3

Institute of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan

4

Faculty of Science and Technology, Keio University, Yokohama 223-8522, Japan

5

Tsukuba Research Center for Energy Materials Science (TREMS), University of Tsukuba, Tsukuba 305-8573, JapanThe electronic dynamics in the excited state of transition-metal dichalcogenides (TMDs) has attracted great interest. To
understand the ultrafast intraband scattering process of excited electrons in the conduction band, we demonstrated ultrafast
time-resolved electron diffraction measurements with double-optical-pulse excitation and ultrafast transient reflectivity
measurements of a TMD material, 2H-MoTe2. Due to the saturable absorption (or Pauli blocking) effect present in 2H-MoTe2,
the system does not absorb the second excitation pulse until the excited electrons generated by the first excitation pulse with a
specific fluence are scattered in the conduction band. By exploiting the Pauli blocking effect in ultrafast time-resolved electron
diffraction measurements with double-optical-pulse excitation, we found that the excited electrons were scattered within 100
fs comparable to the excitation optical pulse duration. Furthermore, the excited electrons relaxed to the lowest energy level ofthe conduction band (K- or Σ-valley) within 1–2 ps.

Transition-metal dichalcogenides (TMDs) are two-dimensional layered materials of transition-metal and chalcogen atoms.1–5
The dynamics of the excited electrons in the conduction band of TMDs have particularly attracted attention in optoelectronics
and quantum information since valley-selective electronic excitation can be realized in this class of materials.6–11 The excitedelectrons relax in terms of both momentum and energy to lower energy valleys in the conduction band12,13 under the restrictionof the lattice (phonon), charge, and spin degrees of freedom. The scattering process regarding momentum relaxation occurs
mainly through fast elastic electron–electron interactions. The scattering process in energy relaxation occurs mainly throughinelastic electron–electron and electron–lattice interactions. Time-resolved angle-resolved photoemission spectroscopy (TrARPES) and two-photon photoemission (2PPE) spectroscopy have been used to directly observe the electronic scattering of_____________________________a)Y. Iwasaki and T. Fukuda contributed equally to this work.

b)

Author to whom correspondence should be addressed. Electronic mail: arashida.yusuke.kb@u.tsukuba.ac.jpc)Author to whom correspondence should be addressed. Electronic mail: hada.masaki.fm@u.tsukuba.ac.jp

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excited electrons in the conduction band.14,15 However, observing the electronic scattering of excited electrons in the conduction
band with the other pump-probe methodologies has been quite challenging because, for example, optical pump-optical probe
methods are more sensitive to interband transition between the valence and conduction bands, and these interband phenomenainterfere with the electronic scattering signal within the band.16–18 A complementary method to observe the electronic scatteringof excited electrons is important for further understanding and exploring the excited state dynamics of TMDs.

Here, we propose to observe the ultrafast electronic scattering of excited electrons in the conduction band of a TMD
material, 2H-MoTe2, by using ultrafast time-resolved electron diffraction measurements19,20 with double-optical-pulse
excitation in the Pauli blocking regime. Saturable absorption is a representative third-order nonlinear optical effect in whichlight transmission linearly increases above a certain light intensity via the Pauli blocking effect.21 A nonlinear optical response
is useful not only in the photonics field but also in the material science field. Photoinduced phase transition,22,23 homogeneous
melting,24–26 and laser ablation,27,28 represent nonlinear optical effects used in materials science. Saturable absorption is directly
applied for mode-locked lasers.29–31 In a previous study, we observed saturable absorption effect for a 2H-MoTe2 thin film at
an incident fluence of 4–12 mJ/cm2.32 The critical carrier density for Pauli blocking corresponds to approximately 0.4% ofvalence electrons. This fluence range for saturable absorption is suitable for our ultrafast time-resolved electron diffraction
measurements with double-optical-pulse excitation; therefore, we chose a 2H-MoTe2 thin film for the target material. In thepresent study, we found that the excited electrons were scattered in 2H-MoTe2 within 100 fs and relaxed to the lowest energy
level of the conduction band (K- or Σ-valley) within 1–2 ps by combining ultrafast time-resolved electron diffraction
measurements with double-optical-pulse excitation and ultrafast transient reflectivity measurements.

The experimental setup for ultrafast time-resolved electron diffraction is shown in Fig. 1. Ultrafast time-resolved electron
diffraction measurements were performed on an ultrathin 2H-MoTe2 film with a pump wavelength of 400 nm under vacuum
conditions. A femtosecond laser with a central wavelength of 800 nm, a repetition rate of 1 kHz, and a pulse duration of ~100
fs was used for ultrafast time-resolved electron diffraction.33,34 An optical pump pulse with a wavelength of 400 nm was
generated by second harmonic generation (SHG) from a beta barium borate (BBO) crystal. The optical pump pulse was doubled
by a Mach–Zehnder interferometer (indicated by a dotted red square in Fig. 1). The pulse interval between the optical pumppulses was adjusted by the optical stage. The optical pump pulses were focused onto the sample with a diameter of 360 μm.
The pulse duration of an optical pump pulses was approximately 100 fs and the incident fluence was 5 mJ/cm2. The acceleration
voltage of the electron probe pulse (~1 ps) was 75 kV and the diameter of the electron beam was 100 μm. The sample
preparation method is shown in supplementary material (Fig. S1).

2

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FIG. 1. Experimental setup for double pulse excitation ultrafast time-resolved electron diffraction. BS and CCD are beam splitter and charge
coupled device, respectively. A dashed red box represents a Mach–Zehnder interferometer to generate double-excitation pulse.

Ultrafast transient reflectivity measurements were performed on bulk 2H-MoTe2 with a pump wavelength of 400 nm anda probe wavelength of 400 nm under ambient conditions. The ultrafast transient reflectivity measurement was conducted using
a femtosecond-pulsed laser source with a central wavelength of 800 nm, a repetition rate of 100 kHz, and a pulse duration of~45 fs. A 400-nm pump pulse was generated by SHG from a β-BBO crystal. The spot diameter of the pump and probe light
were approximately 20 µm. The sample used in the reflectivity measurement was a bulk 2H-MoTe2 sample with a thickness ofapproximately 100 µm.

Figure 2(a) shows the calculated band structure of bulk 2H-MoTe2. The electronic structure of bulk 2H-MoTe2 wasgenerated using the plane-wave density-functional theory program VASP 6.42.35 Projector augmented waves were used as thebasis.36 The generalized gradient approximation (GGA) in the form of PBESol (PBE) was used.37 A value of 520 eV was used
for the energy cutoff based on a convergence study that yielded a tolerance of 1 meV in total energy. An 8×8×2 MonkhorstPack grid was used for Brillouin zone integration. Spin-orbit coupling was enabled. According to the band structure, the 400
nm (3.1 eV) excitation photons can excite electrons at almost all momenta in the band structure. Schematic illustrations ofultrafast time-resolved electron diffraction measurements with double-optical-pulse excitation in the Pauli blocking regime areshown in Figs. 2(b) and 2(c). Figure 2(b) shows the case in which the pulse interval of the two optical pulses (𝑡pi ) is longer

than the time constant of the electronic scattering of excited electrons in the conduction band (τ). In this condition, the first
optical pulse excites an electron from the valence band to the conduction band, and the photoexcitation level is sufficient to
induce the saturable absorption effect. Electronic scattering occurs in the conduction band on the timescale of τ. Subsequently,
the second optical pulse again excites an electron from the valence band to the conduction band, where the Pauli blocking effect3

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does not occur since the previously excited electron is no longer in the same state. The electron probe pulse observes the thermal
effects induced by the absorbed light through the Debye–Waller factor. Ultrafast time-resolved electron diffraction
measurements have been widely used for this class of materials.38–42 In contrast, when 𝑡pi is shorter than τ, as shown in Fig.
2(c), the system does not absorb the second pulse due to the Pauli blocking effect. For this experiment, the time resolution of

the system is not determined by the duration of the electron probe pulse but by the duration of the two excitation optical pulses.
Note that the incident fluence used for this study is below the damage threshold, and we find no structural phase transition ordamage signature in this study, such as that for ablation and tellurium segregation.43

FIG. 2. (a) Calculated band structure of 2H-MoTe2. The blue arrow shows a representative electron transition of 400-nm (3.1 eV) excitation.
Schematic illustrations of ultrafast time-resolved electron diffraction measurements with double-optical-pulse excitation in the Pauli block
regime. The cases of 𝒕pi > 𝝉 (b) and 𝒕pi < 𝝉 (c).

Figure 3(a) shows the electron diffraction pattern from a 40-nm-thick 2H-MoTe2 single crystal. The electron diffraction
shows a sixfold symmetric pattern with diffraction spots from the {100}, {110}, and {200} planes. Figure 3(b) shows theintensity changes of the 110 diffraction spots under single-pulse and double-pulse (𝑡pi = 20 ps) photoexcitation. The intensitychanges of the other diffraction spots are provided in Fig. S2. The intensity changes of the diffraction spots under single-pulse
photoexcitation show the same behavior as in a previous report.32 The intensity decreases after photoexcitation at approximately
10 ps due to the thermal (Debye–Waller) effect. As shown in the figure, the intensity under double-pulse photoexcitation
decreases by twofold compared to that under single-pulse photoexcitation, which suggests that the second pulse was absorbed
in the sample without the Pauli blocking effect at a 𝑡pi of 20 ps, as shown in Fig. 2(a). To estimate the time constant of theelectronic scattering of excited electrons in the conduction band (τ), we measured the diffraction intensity changes for different

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pulse intervals of the two optical pulses, as shown in Fig. 3(c). Because the interference pattern of two pulses induces strong
instability at 𝑡pi = 0 ps, we used single-pulse excitation of 10 mJ/cm2 instead of double-pulse excitation of 5 mJ/cm2 at 𝑡pi = 0

ps. As shown in the figure, the intensity decreases for 𝑡pi = 0 and 0.1 ps are relatively low compared to those for 𝑡pi > 0.2 ps.
For 𝑡pi > 0.2 ps, the intensity decreases show a similar tendency to that for 𝑡pi = 20 ps. This suggests that the second pulses
with 𝑡pi = 0 and 0.1 ps are in the Pauli blocking regime, as shown in Fig. 2(b), and that the electronic scattering of excitedelectrons in the conduction band has already occurred for 𝑡pi > 0.2 ps. The intensity changes of other diffraction spots for 𝑡pi

values of 0–20 ps are provided in Fig. S3. We can estimate τ using the intensity change as a function of 𝑡pi , as shown in Fig.
3(d). An exponential fit to the data in Fig. 3(d) yield a value of τ ≈ 100 fs. Since the pulse duration of the excitation pulse wasapproximately 100 fs, we can conclude that the time constant of the electronic scattering of excited electrons in the conduction
band should be less than 100 fs. This result corresponds well to the previously reported time constants obtained by Tr-ARPES
and 2PPE spectroscopy.44–46

FIG. 3. Ultrafast time-resolved electron diffraction measurements of 2H-MoTe2 with two-pulse excitation. (a) Electron diffraction patternfrom a single-crystalline 2H-MoTe2 thin film. (b) Intensity changes of the 110 diffraction spots under single-pulse and double-pulse (𝒕pi =20 ps) photoexcitation. The black and red arrows show the excitation time points. (c) Intensity changes of the 110 diffraction spots for various
pulse intervals of the two optical pulses. (d) Intensity change of the 110 diffraction spot as a function of 𝒕pi .

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Comparing the results of the ultrafast time-resolved electron diffraction measurements with those of ultrafast transientreflectivity measurements is worthwhile. We discuss the 400-nm optical pump and single 400-nm optical probe measurements
at an incident fluence of 5 mJ/cm2, as shown in Fig. 4. In the 400-nm-pump and 400-nm-probe measurements, the transientreflectivity can trace the electronic dynamics accompanying the interband transition, scattering, and relaxation at all momenta
in the band structure of 2H-MoTe2. As shown in the figure, a sharp decrease, relaxation, and a long-lived component are
observed. We performed time-domain fit using a decreasing function (step-like error function: θ(𝑡; τ𝑠1 ) = [erf(𝑡/τ𝑠1 ) + 1]/2),
a damping (exponential decay) function, and a rising long-lived component with a step-like error function [θ(𝑡; τ𝑠2 )]:𝑦(𝑡) = 𝜃(𝑡, 𝜏𝑠1 ) ∙ 𝜉1 ∙ exp(−𝑡/𝜏1 ) + 𝜃(𝑡, 𝜏𝑠2 ) ∙ 𝜉2 ,(1)

where 𝜏s1 and 𝜏s2 are the decay and rise time constants of the step-like error functions, 𝜉1 and 𝜉2 are their amplitudes, and 𝜏1
is the decay constant (lifetime) of the decreasing component. The transient reflectivity at a probe wavelength of 400 nm

decreases with a 𝜏s1 of 0.28 ps after photoexcitation and recovers within 1–2 ps. An immediate decrease in the reflectivity is

expected to be due to the state-filling effect occurring immediately after photoexcitation by the pump light leading to a decreasein the number of electrons transitioning from the valence band to the conduction band. The recovery occurs through relaxationof the excited electrons to the lowest energy level of the conduction band: the K- or Σ-valleys.47–50 This behavior is very similar
to that in a previous report.51 The rise time constant of the step-like error function for the long-lived component, 𝜏s2 can be

fitted with any value between 0 and 2 ps. Because many linear and nonlinear contributions are involved in the long-lived
component and the rise time cannot be precisely determined, we cannot connect this long-lived component to the ultrafast
electronic scattering of excited electrons in the conduction band. Importantly, observing the time constant of the electronic
scattering of excited electrons in the conduction band by simple transient reflectivity measurements is challenging because thesignal is buried in complex linear and nonlinear contributions.

FIG. 4. Transient reflectivity at a probe light wavelength of 400 nm and an incident fluence of 5 mJ/cm2.

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This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
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In summary, we demonstrated ultrafast time-resolved electron diffraction measurements with double-optical-pulse
excitation and ultrafast transient reflectivity measurements of 2H-MoTe2 to understand the dynamics of excited electrons in
the conduction band. By exploiting the Pauli blocking effect (saturable absorption), we observed electronic scattering in the
conduction band using ultrafast time-resolved electron diffraction measurements with double-optical-pulse excitation. The
excited electrons are scattered in terms of momentum within 100 fs. Ultrafast transient reflectivity measurements showed thatthe scattered electrons relax to the lowest energy valley (K- or Σ-valley) within 1–2 ps. Thermalization of the 2H-MoTe2 latticeoccurs more slowly through electron–lattice coupling within ~10 ps. Thus, the double pulse excitation in the Pauli blocking
regime will be critical to understanding the electronic dynamics in the excited state, which gives insights into nonlinear opticaleffects. Note that one may access faster phase relaxation time constants by using faster excitation optical pulses (<35 fs), 52
which is essential for coherent control of electron systems in materials.

SUPPLEMENTARY MATERIAL
See supplementary material for sample preparation, intensity changes of the 100 and 200 diffraction spots with single- anddouble-pulse excitation, and intensity changes of the 100 and 200 diffraction spots with 𝑡pi values of 0–20 ps.

ACKNOWLEDGMENTS
This work was supported by the Japan Society for the Promotion of Science (JSPS) Research Fellowships for Young Scientists,
JSPS Kakenhi Grants-in-Aid (Nos. JP22KK0225, JP22KJ0352, and JP23H01101). This work was also supported by the Japan
Science Technology Agent (JST) FOREST Program (No. JPMJFR211V) and CREST program (No. JPMJCR1875). Part ofthis work was carried out with the support of the National Institute for Materials Science (NIMS) Electron Microscopy Analysis
Station, Nanostructural Characterization Group through the NIMS Open Facility (No. 22NM8222). We thank Ms. Koda at the
Nanostructural Characterization Group for preparing the samples.

AUTHOR DECLARATIONSConflict of Interest

The authors have no conflicts to disclose.

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DATA AVAILABILITY

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

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This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0170153

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