Electronic intraband scattering in a transition-metal dichalcogenide observed by double-excitation ultrafast electron diffraction

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 excited electrons relax in terms of both momentum and energy to lower energy valleys in the conduction band^12,13 under the restriction of 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 through inelastic electron–electron and electron–lattice interactions. Time-resolved angle-resolved photoemission spectroscopy (Tr-ARPES) and two-photon photoemission (2PPE) spectroscopy have been used to directly observe the electronic scattering of 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 phenomena interfere with the electronic scattering signal within the band.^16–18 A complementary method to observe the electronic scattering of 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 measurements^19,20 with double-optical-pulse excitation in the Pauli blocking regime. Saturable absorption is a representative third-order nonlinear optical effect in which light 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 materials 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 a saturable absorption effect for a 2H-MoTe₂ thin film at an incident fluence of 4–12 mJ/cm² (Ref. 32). The critical carrier density for Pauli blocking corresponds to ∼0.4% of valence 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 the present 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 pump pulses 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 ∼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 the supplementary material (Fig. S1).

Ultrafast transient reflectivity measurements were performed on bulk 2H-MoTe₂ with a pump wavelength of 400 nm and a 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 ∼20 μm. The sample used in the reflectivity measurement was a bulk 2H-MoTe₂ sample with a thickness of ∼100 μm.

Figure 2(a) shows the calculated band structure of bulk 2H-MoTe₂. The electronic structure of bulk 2H-MoTe₂ was generated using the plane wave density-functional theory program VASP 6.42.³⁵ Projector augmented waves were used as the basis.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 Monkhorst–Pack 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 of ultrafast time-resolved electron diffraction measurements with double-optical-pulse excitation in the Pauli blocking regime are shown in Figs. 2(b) and 2(c). Figure 2(b) shows the case in which the pulse interval of the two optical pulses (⁠ $t pi$⁠) 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 effect 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 $t pi$ 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 or damage signature in this study, such as that for ablation and tellurium segregation.⁴³ 

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 the intensity changes in the 110 diffraction spots under single-pulse and double-pulse (⁠ $t pi$ = 20 ps) photoexcitation. The intensity changes in the other diffraction spots are provided in Fig. S2. The intensity changes in the diffraction spots under single-pulse photoexcitation show the same behavior as in a previous report.³² The intensity decreases after photoexcitation at ∼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 $t pi$ of 20 ps, as shown in Fig. 2(a). To estimate the time constant of the electronic scattering of excited electrons in the conduction band (τ), we measured the diffraction intensity changes for different pulse intervals of the two optical pulses, as shown in Fig. 3(c). Because the interference pattern of two pulses induces strong instability at $t pi$ = 0 ps, we used single-pulse excitation of 10 mJ/cm² instead of double-pulse excitation of 5 mJ/cm² at $t pi$ = 0 ps. As shown in the figure, the decrease in the intensity for $t pi$ = 0 and 0.1 ps is relatively low compared to those for $t pi$ > 0.2 ps. For $t pi$ > 0.2 ps, the decrease in intensity shows a similar tendency to that for $t pi$ = 20 ps. This suggests that the second pulses with $t pi$ = 0 and 0.1 ps are in the Pauli blocking regime, as shown in Fig. 2(b) and that the electronic scattering of excited electrons in the conduction band has already occurred for $t pi$ > 0.2 ps. The intensity changes in other diffraction spots for $t pi$ values of 0–20 ps are provided in Fig. S3. We can estimate τ using the intensity change as a function of $t pi$⁠, 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 was ∼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 

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 that the scattered electrons relax to the lowest energy valley (K- or Σ-valley) within 1–2 ps. Thermalization of the 2H-MoTe₂ lattice occurs 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 insight into nonlinear optical effects. 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.