The experimental discovery of topological 3D Dirac semimetals (DSMs) provides unprecedented opportunities for investigating intriguing topological phase transition and various exotic quantum states in condensed matter [1–5]. According to the relative magnitude of potential and kinetic energy components of the Hamiltonian of Dirac fermions, the 3D DSMs are classified to type-I and type-II DSMs [6,7]. The noble transition-metal dichalcogenide (TMD) ${\mathrm{PtTe}}_2$ has been identified as a typical type-II DSM with anisotropic and heavily tilted Dirac cones and stands out from other DSM materials due to the topological nontrivial band structure [7,8], ultrahigh electrical conductivity [9,10], and robustness of the remaining semimetal even down to just two triatomic layers [11,12]. Lately, doped ${\mathrm{Pt}}_{1-x}{\mathrm{Ir}}_x{\mathrm{Te}}_2$ has realized the Fermi level tunability and superconductivity, which opens up a new route for the investigation of Dirac physics and topological superconductivity [13,14]. More recently, ${\mathrm{PtTe}}_2$-based broadband photodetectors and image sensors have been fabricated, demonstrating tremendous application value in various photoelectric devices [15–17]. Therefore, the study of ${\mathrm{PtTe}}_2$ cannot only reveal novel condensed-matter physics but also facilitate the versatile development in device physics.

In our previous work, the negative terahertz photoconductivity in ${\mathrm{PtTe}}_2$ was observed and studied using optical pump-terahertz probe spectroscopy, in which the generation of small polarons due to the strong electron–phonon interaction was raised to explicate the anomalous negative terahertz photoconductivity [18]. Terahertz spectroscopy is sensitive to the free carrier but insensitive to the excited electronic states and the coherent phonons. In contrast, optical spectroscopy is a standard tool for investigating the recovery process of carriers at various excited states as well as the generation and dynamical evolution of coherent phonon in solids [19,20]. What is more, so far as we have learned till now, the photoresponse in optical frequency and coherent phonon dynamics in ${\mathrm{PtTe}}_2$ are obscured and urgently need to be unveiled. On the one hand, it is crucial to elucidate the excited-state dynamics for the study of many-body phenomena and light–matter interaction on ultrafast time scales. On the other hand, the exploration for coherent phonons allows significant insight into the microscopic essence of optically driven and controlled lattice or atomic motion.

Herein, the photoexcited carrier and coherent phonon dynamics in type-II DSM ${\mathrm{PtTe}}_2$ films have been investigated systematically at room temperature with ultrafast pump-probe spectroscopy. The cooling of the thermal carriers plays a leading role in the incoherent relaxation processes. The temperature gradient is responsible for the generation of the CAP in the thicker sample. The COP is also observed in ${\mathrm{PtTe}}_2$ films, which has been assigned to the ${\mathrm{A}}_{1\mathrm{g}}$ optical phonon mode. The present study sheds light on the photocarrier and coherent phonon dynamics, which are of paramount importance to explore the applications of ${\mathrm{PtTe}}_2$ in ultrafast optoelectronic and nanoscale devices.

Homogeneous and continuous ${\mathrm{PtTe}}_2$ films with thicknesses of 6.8 and 20 nm were synthesized on fused silica substrate via a novel eutectic solidification method [10]; the lateral size is $10\mathrm{mm}\times 10\mathrm{mm}$. More detailed characterizations about our measured films, including atomic force microscopy, X-ray diffraction, X-ray photoemission spectra, etc., have been shown in our previous work [18].

Ultrafast time-resolved degenerate optical pump-optical probe (OPOP) measurements in transmission configuration were performed with a home-built system. The optical pulses at a central wavelength of 780 nm (1.59 eV) are delivered from a Ti:sapphire regenerative amplifier (Spectra Physics, Spitfire) with single pulse energy of 2 mJ, pulse duration of 120 fs, and repetition rate of 1 kHz. The laser beam was split into the intense pump and weak probe beams, which were focused on the sample, overlapping with the pump spot estimated to be 0.67 mm in diameter, which is roughly twice as large as the probe beam. The fluence of probe light was fixed at about $114{\text{μJ/}\mathrm{cm}}^2$ [21,22]. To further explore the wavelength-dependent photocarrier and coherent phonon dynamics, transient absorption (TA) measurements were implemented, where the commercial TA spectrometer (HELIOS, Ultrafast System) is driven by a Ti:sapphire laser (Coherent, Astrella). The laser output optical pulses centered at 800 nm with a pulse duration of 35 fs and repetition rate of 1 kHz were divided into two beams: one was guided into an optical parametric amplifier to produce 780 nm excitation light; the other was focused on a sapphire slice to generate white light supercontinuum with a pulse duration of 150 fs, which serves as probe beam in the ultrafast system [23–25]. An optical filter was used to remove the redundant fundamental 800 nm beam and NIR parts of the supercontinuum beam. The pump fluence on the samples was fixed at around $1.0{\text{mJ/}\mathrm{cm}}^2$, which was 10 times higher than that of the probe beam. The samples were placed on a holder and moved within a $1\mathrm{mm}\times 1\mathrm{mm}$ plane perpendicular to the probe light propagation direction to avoid thermal accumulation. All the measurements were carried out at room temperature.

The degenerate 780 nm OPOP measurement was first performed to investigate the excited carrier and coherent phonon dynamics of ${\mathrm{PtTe}}_2$ films. The differential transmission response $\mathrm{\Delta }\mathit{T}/{\mathit{T}}_0$ was recorded through varying pump-probe time delay, where ${\mathit{T}}_0$ is the linear optical transmission of probe light without photoexcitation, and the $\mathrm{\Delta }\mathit{T}$ denotes photoinduced transmission change. In Fig. 1, we plot the transient transmission dynamics of 6.8 and 20 nm ${\mathrm{PtTe}}_2$ films with various pump fluences. For 6.8 nm ${\mathrm{PtTe}}_2$, as shown in Fig. 1(a), photoexcitation triggers an immediate rise in transmission, also known as photobleaching (PB), with response time limited by the laser pulse duration, followed by two distinct relaxation processes. The rapid recovery (${\tau }_f$) occurs within a subpicosecond time scale, followed by a slower relaxation (${\tau }_s$) lasting more than a hundred ps. For comparison, the 20 nm ${\mathrm{PtTe}}_2$ film undergoes a rapid recovery, followed by a slight oscillation within the initial 40 ps; further, a slow relaxation is seen to dominate the subsequent signal. Figures 1(c) and 1(d) display the pump-fluence dependent peak value of $\mathrm{\Delta }\mathit{T}/{\mathit{T}}_0$ and the linear fitting, which indicate the transient transmission response does not exhibit saturation in the range of pump fluence that we applied.

We now discuss the underlying physical origins that caused the ultrafast optical response. In general, the differential transmission signal $\mathrm{\Delta }\mathit{T}/{\mathit{T}}_0$ is determined by electronic excitations (excited carriers) and/or lattice excitations (coherent phonons). In a semimetal like ${\mathrm{PtTe}}_2$, the ultrashort optical pump pulses generally excite amounts of photocarriers into a nonequilibrium state characterized by valence band depletion and conduction band filling. Subsequently, the photocarrier thermalization occurs on tens of fs time scale via electron-electron (e-e) scattering, and establishes a hot-carrier distribution with a broadening energy range [26–28]. For the two ${\mathrm{PtTe}}_2$ films, the instantaneous PB signals upon photoexcitation originate from the electrons’ distribution in the conduction band due to the transition of electrons from the valence band into the conduction band by absorbing the pump photons, which block the corresponding interband transitions, i.e., Pauli-blocking or band filling effect [29,30]. Higher pump fluence means the more serious occupation of probing states, resulting in a stronger PB signal, which is coincident with our measurements, as shown in Figs. 1(c) and 1(d). Since the photocarrier thermalization is accomplished in an ultrashort time scale (within 100 fs), which is beyond our temporal resolution, it is a reasonable assignment that the photocarrier thermalization is completed in the ascending process of transient transmission.

To quantitatively evaluate the quasiparticle relaxation dynamics, a biexponential decay function convoluted with laser pulse width with the below form [24,31] was utilized to fit the transient profile:$$\frac{\mathrm{\Delta }T}{T_0}(t)=\sum _{i=1,2}{A}_i\cdot \exp (\frac{-t}{{\tau }_i}+\frac{{\omega }^2}{4{\tau }_i^2})\cdot [1-\mathrm{erf}(\frac{-t}{\omega }+\frac{\omega }{2{\tau }_i}\left)\right]+B,$$(1)where $t$ is the pump-probe delay time, ${\tau }_i$ and ${\mathit{A}}_i$ are the correlative relaxation constant and amplitude, respectively, and B is the time-independent offset. The erf represents the error function and $\omega$ is the cross-correlation width. For the 6.8 nm specimen, as shown in Fig. 1(a), one can see that the experimental data can be well reproduced with Eq. (1). By comparison, for the 20 nm ${\mathrm{PtTe}}_2$ film, the transient transmission is seen to consist of two components; i.e., a coherent low-frequency oscillation is superimposed on the incoherent carrier relaxation profile. It is reasonable to ignore the low-frequency oscillation and employ a biexponential function to extract the photocarriers’ lifetime. The fitting time constants ${\tau }_f$ are presented in Figs. 2(a) and 2(b). For the 6.8 nm film, the fast component has a lifetime ${\tau }_f$ of 0.51–0.81 ps with a weight of $\sim 90\%$. While for 20 nm ${\mathrm{PtTe}}_2$, the fast recovery shows a lifetime ${\tau }_f$ of 0.32–0.52 ps with a weight of $\sim 90\%$. The fitted slow relaxation for both films shows an almost identical lifetime of longer than 100 ps with weight of less than 10%. It should be mentioned that the obtained slow lifetime is not accurate due to the limited scanning time window. Here, we ascribe the fast relaxation process of both samples to the cooling of the hot carriers that relax to conduction band edge via electron-optical phonon interaction, which is similar to what has been observed in other semimetal materials [32–35]. Higher pump fluence implies higher electronic temperature; hence, more elastic impact with lattice is needed to release their excess energy, resulting in a longer relaxation time, as shown in Figs. 2(a) and 2(b). One can note that ${\tau }_f$ of 20 nm film is shorter than that of 6.8 nm film, which is owing to the fact that the thicker sample has relatively larger electron–phonon coupling in ${\mathrm{PtTe}}_2$ [18]; thus, the thermal carriers in 20 nm ${\mathrm{PtTe}}_2$ have higher cooling efficiency. The slow component with insignificant weight for both films can be attributed to the interband recombination of electrons in the conduction band bottom and holes in the valence band top with the assist of phonon. Specifically, the type-II DSM ${\mathrm{PtSe}}_2$, an analogue of ${\mathrm{PtTe}}_2$, also shows hundreds of ps lifetimes in carrier recombination [24,29]. Therefore, we can reasonably assign the slow dynamics to electron-hole recombination.

We now focus on the oscillatory response observed in 20 nm ${\mathrm{PtTe}}_2$. Figure 2(c) displays the low-frequency oscillation after subtracting the biexponential relaxation from the total dynamics trace at pump fluence of $994\mathrm{\mu J}/{\mathrm{cm}}^2$. The inset shows the frequency domain of the damped oscillation after fast Fourier transform (FFT) and gives the broader oscillation frequencies of 0–0.2 THz with the central frequency at 21.7 GHz. Further, the central frequencies obtained from FFT under other pump fluences are almost identical. Herein, we assign the low-frequency oscillation to CAP, i.e., the coherent lattice vibration with acoustic-mode gives rise to a modulation of the transmissivity of the probe beam.

As a matter of fact, upon ultrafast photoexcitation, the surface layers of material absorb the pump photon, bringing about a transient temperature rise via electron–phonon scattering within the illuminated area. Such sudden temperature elevation sets up localized transient stress, which induces a strain wave, i.e., coherent longitudinal acoustic phonon (CLAP), due to thermal expansion caused by the spatial temperature gradient of material [36–39]. The CLAP propagates away from the surface of the material in the direction of the temperature gradient at sound speed, which modifies the local dielectric constant. When the delayed probe light is incident onto the material overlapped with a pump pulse, the transmissivity of probe light will be modified by the local modulated dielectric function thanks to the launch of CLAP. Therefore, the transmission change characterized by periodic oscillation can be sampled [22,40].

Figure 2(d) visualizes the different thermal responses to ultrafast laser irradiation in the thin and thick films, in which the gradient force is essential in driving the generation of CAP [38]. When the film is thin, as in our case of 6.8 nm, the photo-driven thermalization of the film is homogeneous in the propagation direction of pump pulse, as illustrated on the left drawing in Fig. 2(d). The absence of a temperature gradient signifies that the strain wave cannot be delivered, which is why we did not observe the CAP in 6.8 nm ${\mathrm{PtTe}}_2$. In our 20 nm film, the photoexcitation from the front surface can induce a temperature gradient along the light propagation direction; as a result, the CAP is launched, as illustrated on the right drawing in Fig. 2(d). It should be mentioned that the pump-pulse-induced coherent acoustic vibration of the lattice in 20 nm ${\mathrm{PtTe}}_2$ is not monochromatic but broadband. The sound velocity, $v$, can be determined with $v=4\mathit{d}f$ [36,40], with the $\mathit{d}$ and $f$ denoting the film thickness and CAP frequency. Considering $f=21.7\mathrm{GHz}$ obtained from $\mathit{d}=20\mathrm{nm}$ film the sound velocity in ${\mathrm{PtTe}}_2$ film is obtained to be $v=1.736\text{km/s}$. By using the density of $\rho =9.8\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$ for bulk ${\mathrm{PtTe}}_2$ [41], Young’s modulus (Y) of the film can be evaluated by$$\mathit{Y}=\rho v^2$$(2)from which $\mathit{Y}=29.5\mathrm{GPa}$ is obtained in the 20 nm ${\mathrm{PtTe}}_2$ film according to our CAP measurement. It is close to Young’s modulus of ${\mathrm{PtSe}}_2$ with 28 GPa [39] but less than that in most TMDs with a value around 50 GPa [42], indicating ${\mathrm{PtTe}}_2$ is a softer layered matter. To our knowledge, this is the first time that the sound velocity and Young’s modulus in ${\mathrm{PtTe}}_2$ are determined experimentally.

To gain more insight into probing the wavelength-dependent carrier and coherent phonon dynamics of 6.8 and 20 nm ${\mathrm{PtTe}}_2$, TA measurements were carried out with pumping at 780 nm and probing at 450–760 nm. Figure 3 shows the TA pseudocolor plots and TA spectra, in which $\mathrm{\Delta }\mathit{A}$ denotes the pump-induced absorption change of the probe pulse. It can be seen that the optical response of all probe light shows a negative TA signal, i.e., PB. The CAP is persistently present at all probe wavelengths for 20 nm ${\mathrm{PtTe}}_2$, which is manifested as the appearance of a bottleneck-like color plot around the time window of 1–10 ps as an arrow indicated in Fig. 3(c). In contrast, this phenomenon is absent in the 6.8 nm sample. Unexpectedly, pronounced damping harmonic oscillations were observed at the early probe delays; more detailed color mappings of TA in the first 5 ps are shown in Fig. 5 of Appendix A.

We first discuss the relaxation of the electronic system under different probe energy. The general profile of photocarriers’ relaxation of 6.8 and 20 nm films is mostly the same. One prominent feature is that the dynamics of the red and blue sides around 650 nm [as the marks of black dash lines in Figs. 3(a) and 3(c)] are distinct. The relaxation of red side, i.e., 650–760 nm, consists of two components: a subpicosecond fast relaxation followed by a slow process with a lifetime of more than 100 ps, which is similar to the experimental results measured with degenerate 780 nm OPOP. By comparison, the relaxation of the blue side of 650 nm shows an extra slow component except for the fast and slow processes. This slow process has a time constant of a few nanoseconds, which reflects the long-lived electronic states at the higher-lying energy band in ${\mathrm{PtTe}}_2$.

The coherent collective excitations with probe wavelength dependence in ${\mathrm{PtTe}}_2$ are displayed in Figs. 4(a) and 4(c) for 20 and 6.8 nm films, respectively. Apparently, all curves can be treated as the superposition of the nonoscillatory background derived from electronic contribution and high-frequency coherent phonon oscillations; in addition, CAP also contributes to the TA kinetics in the 20 nm ${\mathrm{PtTe}}_2$. Following the aforementioned approach of obtaining CAP oscillation, we have unwrapped the high-frequency damped oscillation component. Figures 4(b) and 4(d), respectively, exemplify the pure time-domain oscillation (green) of 20 and 6.8 nm film at a typical probe wavelength of 525 nm. For the sake of simplification, measuring results of 6.8 nm ${\mathrm{PtTe}}_2$ are dissected thoroughly; more detailed oscillatory signals of 6.8 nm ${\mathrm{PtTe}}_2$ under different probe wavelengths are shown in Fig. 6 of Appendix A. The corresponding frequency domain of the oscillation after FFT is also plotted in the insets of Figs. 4(b) and 4(d), yielding a sharp high-frequency mode of 4.7 THz for 20 nm film and 4.65 THz for 6.8 nm film. Furthermore, a one-component damped oscillation function with the below formula was used to fit the oscillations for further analysis:$$\mathrm{\Delta }A{(t)}_{\mathrm{OSC}}=B·\exp (-\frac{t-t_0}{\tau })·\cos (2\pi ft+\varphi )+C,$$(3)where B, $\tau$, $\mathit{f}$, and $\varphi$ are the oscillatory signal amplitude, damping time, frequency, and initial phase, respectively, which describe the collective excitation dynamics. As displayed in Figs. 4(b) and 4(d), one can see that the experimental data can be reproduced well, and the fitting frequency is 4.70 THz for 20 nm ${\mathrm{PtTe}}_2$ and 4.66 THz for 6.8 nm, which are consistent with FFT results. The dephasing time obtained by fitting is around 2.8 ps and almost independent of the probe wavelength, as shown in Fig. 7 of Appendix A. Figure 4(e) shows the Raman spectrum of 20 nm ${\mathrm{PtTe}}_2$, where two phonon modes, i.e., ${\mathrm{E}}_{\mathrm{g}}$ ($112{\mathrm{cm}}^{-1}$) and ${\mathrm{A}}_{1\mathrm{g}}$ ($156{\mathrm{cm}}^{-1}$, $\sim 4.68\mathrm{THz}$), can be observed clearly. The ${\mathrm{E}}_{\mathrm{g}}$ and ${\mathrm{A}}_{1\mathrm{g}}$ modes originate from the vibration of Te atoms along the in-plane and out-of-plane, respectively. Extracted frequency of periodic oscillations is identical to that of ${\mathrm{A}}_{1\mathrm{g}}$ phonon, which suggests the coherent damping oscillations in ${\mathrm{PtTe}}_2$ under photoexcitation emanated from the ${\mathrm{A}}_{1\mathrm{g}}$ optical phonon, that is, the pump-induced coherent vibration of atoms in each unit cell with ${\mathrm{A}}_{1\mathrm{g}}$ mode modulates periodically the index of absorption.

In general, two mechanisms have been proposed to explicate the generation of COP excited by ultrafast optical pulse: impulsive stimulated Raman scattering (ISRS) and displacive excitation of coherent phonon (DECP) [43–45]. In the ISRS mechanism, an ultrashort laser pulse (pulse duration must be shorter compared with the oscillatory period of lattice), which has a distribution of frequency containing ${\omega }_1$ and ${\omega }_2$, coupled to phonon mode with the energy of $\hslash {\omega }_0$ (${\omega }_0={\omega }_1-{\omega }_2$), exerting an “impulsive” driving force for coherent vibrations of lattice [46–50]. In the DECP model, the excitation of COP is due to a displacement of the ion equilibrium coordinates by electronic excitation [51]. The pump pulse creates excited carriers, leading to electronic redistribution and thus initiating the ion cores to vibration coherently around the new equilibrium positions, which is the refined picture of the DECP model [38,52,53]. Noticeably, the Raman scattering mechanism allows all coherent phonon excitation with Raman-active modes, while the DECP mechanism only favors the excitation of totally symmetric modes (e.g., ${\mathrm{A}}_{1\mathrm{g}}$) [45,51,52]. Consequently, the DECP is responsible for the excitation of the ${\mathrm{A}}_{1\mathrm{g}}$ mode only in our observation. Another conspicuous feature is that the strength of the oscillation is seen to vary significantly with probe wavelength, as shown in Figs. 4(a), 4(c), and Fig. 6 of Appendix A, respectively. Figure 4(f) plots the FFT amplitude of the residual oscillations of 6.8 nm ${\mathrm{PtTe}}_2$ with respect to the probe wavelength. The amplitude of oscillatory signal depends on the probe wavelength, with a maximum around 525 nm; further, no appreciable oscillations above 600 nm were detected in the resolution of our apparatus. We assign the probe wavelength-dependent oscillatory response to the different band modulation induced by the ${\mathrm{A}}_{1\mathrm{g}}$ phonon displacement.

Essentially, ultrafast photoexcitation leads to a displacement of the Te atoms along the outward direction, in turn causing a change in the energy band structure, accompanied by a modulation of optical constants. The coherent vibration of the atoms induced by the ${\mathrm{A}}_{1\mathrm{g}}$ mode around the displaced equilibrium positions leads to the dynamical change of energy bands and the period modulation of the optical absorption, which manifests as the oscillations in the TA kinetics [45,54,55]. The probe wavelength-dependent COP strength is due to the fact that the atomic displacement induced by DECP has different influence on the energy bands at different locations. Thus, it can be deduced that the energy band associated with the electronic transition of 2.4 eV (525 nm), somewhere in the Brillouin zone, is most significantly influenced, while atomic displacement shows negligible effect on the electronic transition below 2.1 eV (600 nm). In-depth analysis of the changed band structures needs more elaborate ab initio calculations [54], which are beyond the scope of this work. In a word, the study herein offers a channel to monitor the dispersion of the variation in optical parameters in a photoexcited nonequilibrium state through tracking the different oscillatory strengths of TA kinetics induced by COP. Moreover, our differential transmission study has also provided a wealth of information on COP modes in the time domain.

In summary, the ultrafast OPOP measurements were conducted to uncover the photocarriers’ relaxation dynamics and the generation mechanisms of coherent phonon in type-II DSM ${\mathrm{PtTe}}_2$ films. The inherent electronic recovery process is predominantly dominated by the cooling of thermal carriers. CAP and COP arise from the inhomogeneous temperature distribution in film and DECP, respectively. Our present study enriches the insight into ${\mathrm{PtTe}}_2$ and will be helpful in predicting the change of electronic bands upon photoexcitation, which paves the way in designing and developing ${\mathrm{PtTe}}_2$-based ultrafast optoelectronics.