1 Introduction

Electron–phonon coupling in condensed matter physics leads to novel phenomena such as superconductivity, Joule heating, Peierls instability, and magnetoresistance [5,6,7,8]. This interaction, when considered in a strongly coupled regime, provokes local and cooperative lattice distortions, which tend to be rearranged with the generated exciton density. The van der Waals (vdW) layered materials, with a strong Coulomb interaction, provide a large exciton binding energy (0.3–1 eV) in a monolayer [9,10,11], although these values are scaled down to less than 100 meV by charge screening in a thin film. In addition to the large exciton binding energy, excitons are easily localized by defects or impurities [12,13,14,15]. Excitons can be also localized by light illumination, and thus the probability of coupling between localized excitons and phonons is enhanced at a high optical density, eventually inducing an excitonic polaron formation [16, 17]. Such mesoscopic phenomenon is further complicated by the fluence and energy of the laser, let alone the phonon dynamics involving radiative/non-radiative energy dissipations with heat and charge carriers [18].

Coherent phonon spectroscopy via femtosecond pump-probe techniques enables direct measurement of time-resolved lattice vibrations and investigate their interactions with charge, spin, and lattice degrees of freedom in solids [19,20,21]. Transition metal dichalcogenides (TMDs), consisting of a metal layer sandwiched by two chalcogen top and bottom layers, provide an additional degree of freedom in the atomic rearrangement. This permits various types of polymorphs, which are easily engineered by external parameters [1,2,3,4]. Nevertheless, an information on the dynamical behavior of the phase transformation is lacking. In this study, we report picosecond-scale reversible phase transformations in MoTe2 from the 2H to the 1T’ phase using coherent phonon dynamics, induced by the strong electron–phonon coupling through an excitonic polaron formation without a heating effect. All measurements are performed at room temperature.

2 Experiments and discussion

2.1 Time-domain coherent phonon spectroscopy

To generate and detect coherent vibrations of the lattice, the femtosecond pump–probe technique was employed at room temperature. The pump pulse was delivered by a mode-locked Ti:sapphire oscillator with a pulse duration of 60 fs at an excitation energy of 1.57 eV (790 nm) and repetition rate of 400 kHz. In the path of the pump, a scanning shaker (APE Scan Delay, Germany) was installed to mechanically generate the optical time delay. The probe pulse was derived from the same laser, maintaining a weaker intensity of 95% than the pump pulse. The focused spot’s diameter of the pump on the sample was approximately 5 μm, while that of the probe was slightly smaller. The differential transmittance was measured using the probe pulse as a function of the delay time, with respect to the pump pulse, and pump fluence from 24.8 to 918 μJ/cm2.

2.2 Sample preparation and optical characterization

A commercial 2H-MoTe2 purchased from HQ Graphene, Netherlands was exfoliated using a standard taping method. After the exfoliation, a flake of approximately 4–5 layers was transferred onto a quartz substrate, and placed under vacuum during the measurements. The sample was retained without changing the morphology during the pulse laser illumination. After the removal of the laser, the sample was recovered to the 2H phase. The excitons were observed by measuring the absorbance (V-670 UV–VIS-NIR spectrophotometer, JASCO, Germany).

2.3 Change of the total energy

We performed density functional theory calculations using the Quantum Espresso package [27], with the generalized gradient approximation pseudopotentials. The lattice parameters of both 2H and 1T’ phases were set to 3.53 Å, and the structures were fully relaxed. We used k-meshes of 36 × 36 × 1 for the 2H phase and 24 × 24 × 1 for the 2 \(\times\) 2 supercell of the 1T’ phase. We obtained the total energies of the 2H (\({{E}}_{\text{2H}}^{0}\)) and 1T’ (\({{E}}_{{1\text{T}^{\prime}}}^{0}\)) phases in the ground state, i.e., without optical excitations.

The excitation-induced change in the total energy \(\delta{{E}}\) is calculated using:

$$\delta{{E}}^{\text{h,e}}\left({\mu}^{\text{h,e}}\right)={\int }_{0}^{{\mu}^{\text{h,e}}}{\text{d}}\varepsilon\rho(\varepsilon)\varepsilon,$$
(1)

for both holes and electrons with chemical potentials \({\mu}^{\text{h,e}}\) and density of states \(\rho\) of the corresponding phase. The total energy change is then given by \(\delta{\text{E}}\left(n\right)=\delta{\text{E}}^{\text{e}}\left(n\right)+\delta{\text{E}}^{\text{h}}\left(n\right)\), where the number of excited carriers:

$${n}^{\text{h,e}}\left({\mu}^{\text{h,e}}\right) = {\int }_{0}^{{\mu}^{\text{h,e}}}{\text{d}}\varepsilon\rho(\varepsilon),$$
(2)

is required to satisfy \({n}^{\text{h}}={n}^{\text{e}}\).

Coherent phonons (or in-phase phonons) are generated by irradiating a pulsed laser to the sample with an input pump-pulse duration shorter than the phonon period [22, 23]. We used a semiconducting 2H-MoTe2 thin film (4–5 layers) to generate coherent phonons using a pump–probe technique with a pump pulse (duration of 60 fs, central wavelength of 780 nm, and repetition rate of 400 kHz; see also Methods and Extended Data Fig. 1) for two different pump fluencies of 24.9 μJ·cm−2 and 918 μJ·cm−2 (Fig. 1). The differential transmittance change ΔT/T (Fig. 1a) abruptly peaks at zero time delay and exponentially decreases in the subsequent time delay, which is attributed to the change of the photoexcited carrier density. The increasing maximum of ΔT/T with the fluence is attributed to the increase of the excited carrier density (see also Extended Data Fig. 2). In addition to this large electronic contribution, a weakly decaying oscillatory signal originating from the coherent phonons is clearly visible owing to the large amplitude of oscillation of ~ 10–3 near zero delay. This change is still visible but less apparent at a low pump fluence. By subtracting the exponential decay component, we can clearly visualize such oscillatory behaviors of coherent phonons even at a low pump fluence (Fig. 1b).

Fig. 1
figure 1

Differential transmittance change for 5-layer 2H-MoTe2 film at 780 nm. a Differential transmittance at 24.87 and 918 μJ/cm2 fluences. b Coherent phonon oscillation data in time domain, extracted from (a) by removing the exponential decay component. c Fast Fourier transform (FFT) spectra. At higher excitation fluence (top), three frequencies deconvoluted, whereas a single peak appeared at lower fluence (bottom). The peak at ~ 5.22 THz (173 cm−1) corresponds to A1g mode in the semiconducting 2H phase, while the two peaks at 4.99 THz (166 cm−1) and 4.83 THz (163 cm−1) correspond to Bg and Ag modes in the metallic 1T’-phase, respectively

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At a higher fluence, the oscillatory signal clearly reveals a beating pattern with a large amplitude, indicating that the coherent lattice vibrations consist of different vibrating frequencies. By performing a fast Fourier transform of the time-domain coherent lattice vibrations, we obtain various phonon modes, as shown in Fig. 1c. Three peaks at 5.22, 4.99, and 4.83 THz (173, 166, and 163 cm−1) are well matched with the A1g mode of the semiconducting 2H-MoTe2, and Bg and Ag modes of the metallic 1T’-MoTe2, respectively [24] (see also Extended Data Fig. 3a). At a lower fluence, a long-lived oscillation is exclusively observed in Fig. 1b, corresponding to the coherent A1g mode (173 cm−1) of 2H-MoTe2. This strongly indicates that, at a high fluence, the structural transformation evolves with time from a semiconducting 2H to a new metallic 1T’ phase.

Excitons are simultaneously generated with the coherent phonons by the pump pulse, which is confirmed by the absorbance spectrum at room temperature of the 2H-MoTe2 phase (see Extended Data Fig. 3b). At a high pump fluence, the exciton density is high and starts interacting with the coherent phonons, leading to a formation of polarons [17]. This disturbs the coherent phonons, dephases the coherency of the phonons, and consequently induces new coherent phonons at different phases. A metallic 1T’-MoTe2 film is stable at a high carrier density [1]. Therefore, the structural evolution from a semiconducting 2H phase to a metallic 1T’ phase at a high fluence appears to occur naturally. This will be further discussed in the following section.

To systematically investigate the phase transformation, the pump fluence was varied from 24.9 to 918 μJ·cm−2, and subsequently reduced to 24.9 μJ·cm−2. When the pump fluence exceeds approximately 100 μJ·cm−2, the single peak of the A1g phonon mode of 2H-MoTe2 (5.22 THz) at a low pump fluence is no longer stable and slightly softened (Fig. 2a and b). In addition, new peaks near the Ag and Bg modes emerge, representing the characteristics of the metallic 1T’-MoTe2. These peaks remain stable until the highest fluence used in this experiment. The single peak of the A1g phonon mode of the original 2H-MoTe2 is fully recovered at a low fluence. A similar trend was observed in the amplitude variance (Fig. 2c). Notably, the new phase emerges when the excited carrier density exceeds approximately 4 × 1014 cm−2. This photoexcited carrier density is similar with an externally injected carrier density to induce a phase transition [4].

Fig. 2
figure 2

Evolution of phonon modes during the photo-induced phase transformation. a FFT spectra with the increase and decrease of the pump fluence. b Variation of the phonon frequencies with the pump fluence. c FFT amplitude as a function of the pump fluence. At the high-power regime, two phases (2H and 1T’) emerge. With the decrease of the power, the 2H phase is fully recovered

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Furthermore, the thermal effect owing to the laser illumination is negligible in this experiment. The phonon softening of the 2H phase at a high pump fluence of 918 μJ·cm−2 is 1.3 cm−1 (Fig. 2b), which is a negligible temperature increment determined by the temperature coefficient of 0.8 meV/K [25]. Stable phonons of the 1T’ phase (Bg: 166 cm−1 and Ag: 163 cm−1) are obtained at a fluence of 918 μJ cm−2, whose positions are equal to those observed at room temperature, thus confirming the negligible thermal effect in our case [26]. The thermal effect is further evaluated at a higher repetition rate (80 MHz) of the pump pulse. In this case, the heat is accumulated in the sample, eventually burning the sample at a significantly lower fluence (see Extended Data Fig. 4 and Supplementary Note).

Wavelet transform (WT) can be employed to analyze amplitudes and frequencies of lattice vibrations and visualize their temporal evolution. The Gaussian function is used as the basic window function:

$$f\left(t\right)=\frac{1}{\omega \sqrt{2\pi }}{e}^{-{(t-{t}_{i})}^{2}/(2{\omega }^{2})},$$

where \({t}_{i}\) and \(\omega\) are the position and width of the Gaussian function in the time domain (\(\omega\)= 1 ps in this study), respectively. The Gaussian function multiplied by the oscillatory signal in Fig. 1b is further Fourier-transformed to obtain the WT mapping, as shown in Fig. 3a and b. The obtained phonon frequencies correspond to the Fourier transform data, shown in the top panels, except the broader spectral width. At the high-fluence regime, transient frequencies and amplitudes apparently emerged, compared to a monotonic frequency at the low-fluence regime. Distinct two-phonon modes at the semiconducting A1g (5.22 THz) and metallic Ag (4.83 THz) were apparent at a later time delay (~ 5 ps), although two-phonon modes at an early time delay (~ 2 ps) were dubious with a broad spectral width (Fig. 3b). After ~ 5 ps, these two-phonon modes decay, and the metallic Bg (4.99 THz) evolves with a further delay (see Extended Data Fig. 5). This assures that the structural transformation from the semiconducting to the metallic phase occurs in an ultrafast picosecond time-scale.

Fig. 3
figure 3

Time–frequency analysis with pump fluence. a and b WT chronograms of Fig. 1a and b, respectively. The top panels represent the normal Fourier transform spectra. c Dephasing time as a function of the pump fluence for the coherent A1g phonon mode in the 2H phase, and d a similar plot for the two coherent Bg and Ag phonon modes in the 1T’ phase

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A coherent phonon oscillation at a low pump fluence is persistent without a considerable decay even with a long delay time, while the large amplitude of the coherent phonons at a high pump fluence rapidly decays with the delay time (Fig. 1b). To obtain dynamic quantities of the coherent phonons, i.e., dephasing time, each oscillation with different fluences is fitted to a sum of damped oscillations:

$$y = {A}_{n} \times \mathrm{sin }\,\left({\Omega }_{n}\left({t}_{n}-{\varphi }_{n}\right)\right)\times {e}^{-t/{\tau }_{n}},$$

where n denotes the number of phonon modes depending on the fluence, A represents the amplitude, Ω represents the phonon frequency, t represents time, φ represents phase, and τ represents the dephasing time. The extracted dephasing time τ is plotted as a function of the fluence for each phonon mode (Fig. 3c and d). At a low fluence, the 2H phase is dominant with a dephasing time of 20 \(\pm\) 5 ps. When the fluence exceeds approximately 100 μJ cm−2, the dephasing time decreases and reaches the value of approximately 2.5 ps at the highest fluence. Moreover, the newly emerging coherent phonons of the Bg and Ag modes in the 1T’-phase reveal faster dephasing times (~ 2 \(\pm\) 0.5 ps and ~ 0.5 ps, respectively) in the high‑fluence regime, independent of the fluence. This suggests that the coherency of lattice vibrations is perturbed by the photoexcited electron–hole pairs at a high density within a picosecond time-scale.

An emergence of polarons is expected when the photoexcited electron–hole pairs moving in a crystal are coupled to phonons [17]. At a low pump fluence, the phonon intensity associated with the 2H-MoTe2 phase is linearly proportional to the excited carrier density up to 4 × 1014 cm−2 (Fig. 4a). In this regime (blue box), the phonon density of the 2H phase increases linearly with the exciton density; however, the exciton density would not be sufficient to dephase the motion of the coherent phonons, thus still preserving the stable 2H-MoTe2 phase. In the intermediate regime (white box), the photoexcited carrier density exceeds 4 × 1014 cm−2, leading to a strong exciton–phonon coupling to form exciton polarons. This strong exciton–phonon coupling disturbs and dephases the coherent phonons of the 2H phase with a delay time. The dephased phonons subsequently create new coherent phonons of the 1T’ phase, which are stable at a high carrier density. Consequently, the 2H and 1T’ phases initially coexist, as already demonstrated in Fig. 2b. The coherent phonons corresponding to the 1T’ phase become stable and dominant (Fig. 2c) when the exciton density exceeds 9 × 1014 cm−2. The 1T’ phonon density is represented by another linear slope (Fig. 4a).

Fig. 4
figure 4

Evolution of the lattice distortion through a polaron formation. a FFT intensity of the time-domain oscillation signal as a function of the excited carrier density. b Composition variation from the semiconducting 2H phase to the metallic 1T’-phase with the excited carrier density. c Total energy per Mo atom depending on the density of photoexcited electrons and holes for the 2H and 1T’ phases, with respect to the energy E2H,0 of the 2H phase in the absence of any photoexcited carriers. All values are given per one MoTe2 layer

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The slope of the phonon density in the intermediate regime can be expressed as a sum of the slopes of the 2H and 1T’ phases: Sint = (1 − \(x\)) S2H + \(x\) S1T’, where Sα represents the slope of the α phase and \(x\) represents the composition of the 1T’ phase expressed in percentages. For known slopes at each point, we obtain x as a function of the exciton density (Fig. 4b). Our analysis clearly demonstrates the phase transformation from the 2H to the 1T’ structure with coexistence in the intermediate region. In addition, the change in the total energy is calculated as a function of the photogenerated carrier density (see Methods section). We estimate the total energy difference between the 2H and 1T’ phases, as shown in Fig. 4c. The 2H phase is preferred at a low optical carrier density, while the 1T’ phase becomes more stable at a carrier density above approximately 1014 cm−2 of the MoTe2 monolayer. This carrier density is in agreement with the experimentally observed onset of the transition between the two phases in 4–5 layers of a MoTe2 film (Fig. 2b). The control of the exciton–phonon coupling amplitude accompanying lattice distortions is the key to induce the dephasing of coherent vibrations. The dephasing time is ultrashort with a time-scale of a few picoseconds. The phase transition is fully reversible within several picoseconds by simply removing the laser illumination, thus recovering the semiconducting 2H phase from the metallic 1T’ phase. This paves the way for applications of van der Waals layered materials for ultrafast light-induced switching/memory devices and optical data processing in optoelectronics.

3 Conclusion

We investigated ultrafast reversible structural transformations in MoTe2 thin films at room temperature. By employing a femtosecond pump–probe technique, we have successfully demonstrated that high photon density can induce a rapid transition from the semiconducting 2H phase to the metallic 1T’ phase in MoTe2. This transition is attributed to the strong exciton-phonon coupling that leads to polaron formation, significantly altering the lattice structure without thermal effects. We reveal that the structural transformation is fully reversible within a few picoseconds by simply turning the laser on or off, highlighting the role of polarons in facilitating this rapid phase change. We provide crucial insights into the temporal evolution of phase transitions in transition metal dichalcogenides (TMDs), which are vital for developing future optoelectronic devices. The ability to reversibly and rapidly change the structural phase of MoTe2 paves the way for the creation of ultrafast light-induced switching/memory devices and offers new avenues for optical data processing in optoelectronics. This results not only advance the understanding of the fundamental structural properties of TMDs but also open up possibilities for their application in high-speed, low-energy consumption electronic and photonic devices.