Phonon-assisted electronic states modulation of few-layer PdSe2 at terahertz frequencies

Information technology demands high-speed optoelectronic devices, but going beyond the one terahertz (THz) barrier is challenging due to the difficulties associated with generating, detecting, and processing high-frequency signals. Here, we show that femtosecond-laser-driven phonons can be utilized to coherently manipulate the excitonic properties of semiconductors at THz frequencies. The precise control of the pump and subsequent time-delayed broadband probe pulses enables the simultaneous generation and detection processes of both periodic lattice vibrations and their couplings with electronic states. Combining ultralow frequency Raman spectroscopy with first-principles calculations, we identify the unique phonon mode-selective and probe-energy dependent features of electron-phonon interactions in layered PdSe2. Two distinctive types of coherent phonon excitations could couple preferentially to different types of electronic excitations: the intralayer (4.3 THz) mode to carriers and the interlayer (0.35 THz) mode to excitons. This work provides new insights to understand the excited-state phonon interactions of 2D materials, and to achieve future applications of optoelectronic devices operating at THz frequencies.


INTRODUCTION
Fascinating quantum phenomena in atomically thin 2D materials have attracted tremendous attention from fundamental research to industry owing to their various applications in multiple areas 1 . One of the most interesting features is the reduced screening that leads to enhanced Coulomb interactions compared with their 3D counterparts 2 . For example, tightly bound electronhole pairs, known as excitons, can form in 2D semiconductors with binding energies of hundreds of millielectronvolts (about an order of magnitude larger than those of typical 3D semiconductors) 3 . Phonons are another quasiparticle in condensed matter systems, and their interaction with other phonons, electrons, or photons is of fundamental significance to understand physical properties ranging from mobility to superconductivity. The electron-phonon interaction is typically studied at the electronic ground state using Raman spectroscopy 4 , whereas excitedstate phonon dynamics remains less understood. It is therefore critical to develop a deeper understanding on how different phonon modes interact with other quasiparticle excitations such as excitons.
Optical driving has emerged as a powerful method to generate novel out-of-equilibrium transient phases of quantum matter that are not available at equilibrium. A particularly useful tool to gain knowledge of nature's speediest processes are ultrafast pump-probe experiments, in which the non-equilibrium states are triggered by light pulses and the temporal evolution is subsequently monitored by appropriately-delayed probe pulses. A variety of light-driven excited states have been explored in 2D layered materials, including carrier relaxation dynamics [5][6][7] , superconductivity 8 , the anomalous Hall effect 9 , charge density waves 10 , chiral phonons 11 , and spinvalley dynamics [12][13][14] . In the phonon sector, the impulsive force provided by light pulses can initiate coherent phonon oscillations, in which individual phonon modes are selectively excited and lead to atomic motions that keep pace with their neighbors. For example, vibrational wavepackets for the radial breathing mode and the G mode have been observed in carbon nanotubes 15 and 47.4 THz coherent phonons of in-plane carbon stretching mode have been reported in graphite 16 . In layered quasi-2D materials, these periodic vibrations can induce relative atomic displacements and strains that are associated to either interlayer (shear or breathing) [17][18] or intralayer 19,20 modes. In the electronic sector, the photoexcited free carriers can modify the screening properties of the material, providing an opportunity to shift the conduction band (CB) and valence band (VB) relative to each other [21][22][23][24][25] . This provides an avenue for manipulating the bandgap of the material in an all-optical way without any chemical modification.
Bringing the electronic and phonon sectors together also provides opportunities for applications. Future information technologies call for new devices that can operate at frequencies above 1 THz, or one trillion cycles per second. These high frequencies are particularly useful: they can carry more information (both classical and quantum) than lower frequency signals and can open up new options for applications such as actuators, radars, ultrafast data recording, processing, and communications systems. However, the high-frequency performance of switches or modulators is still a challenge, with a theoretical limitation of the modulation speed to the gigahertz (GHz) regime 26,27 . With the assistance of the strain induced by coherent phonons, one can expect to go beyond the traditional limit and manipulate the transient physical properties (e.g., optical, electronic, and topological properties) that are sensitive to lattice symmetry at frequencies comparable to the terahertz atomic motions. For instance, ultrashort light pulses have been employed to achieve an ultrafast topological switch based on the shear phonon oscillations of fewlayer WTe2 at a frequency of 0.24 THz 28 . Despite these promising developments, the direct demonstration of terahertz-frequency modulation of the electronic bandgap is still missing in current material systems with limited probe energy range.
To address this challenge, we report on an ultrafast modulator of the electronic bandgap of few-layer palladium diselenide operating at terahertz frequencies, taking advantage of electronic (bandgap renormalization) and phonon (field-driven oscillations) effects simultaneously.
Combining broadband pump-probe experiments and first-principles calculations, we reveal the dominant roles of screening in the bandgap renormalization as well as interactions with two types of coherent phonons that preferentially couple to electrons and excitons and operate at 4.3 THz and 0.35 THz, respectively. Overall, the simultaneous interplay of carriers, excitons, and phonons provides a comprehensive view of the non-equilibrium quasiparticle dynamics and many-body interactions in atomically thin 2D materials.

Growth and characterizations of large-area PdSe2
As a transition-metal dichalcogenide (TMD), palladium diselenide (PdSe2) has emerged as a new type of layered material with distinctive physical properties such as remarkable stability in air, high carrier mobility, a negative Poisson's ratio, and pressure-induced superconductivity [29][30][31] .
In addition, PdSe2 is expected to possess abnormally strong interlayer coupling beyond the typical van-der-Waals forces found in layered materials, because its d 2 sp 3 hybridization between the pz band of Se and the d band of Pd is stronger than in other TMDs with d 4 sp hybridization 32 .
Therefore, PdSe2 offers an excellent platform to explore light-driven non-equilibrium many-body interactions that can be harnessed for application in functional devices. In this work, a wafer-scale PdSe2 sample is first synthesized on a quartz substrate using the chemical vapor deposition (CVD) technique with high-purity PdCl2 and Se under vacuum conditions (from SixCarbon Technology, Shenzhen). The top and side view of the crystal structure of PdSe2 is shown in Fig. 1a, exhibiting a puckered pentagonal pattern with an orthorhombic lattice. The high quality of the sample is confirmed by detailed characterizations. The nanoscale surface topographic image is shown in Fig. 1b and the height profile of the sample is shown in Fig. 1c with a measured average thickness of ~2.9 nm. The height corresponds to eight layers with an interlayer distance of ~0.39 nm. According to the AFM images, the height is very uniform over the whole sample, implying uniformity of thickness and further confirming the sample quality. The chemical and stoichiometric characteristics are probed by X-ray photoelectron spectroscopy (XPS). Figure 1d and 1e show the high-resolution XPS spectrum of Se 3d and Pd 3d regions, respectively. The two characteristic peaks at 54.75 and 55.65 eV in Figure 1d are attributed to the 2d5/2 and 2d3/2 doublets of Se 2and the peaks located at 342 eV and 336.75 eV in Fig. 1e are originated from the 3d3/2 and 3d5/2 orbitals of Pd 4+ . The atomic ratio of Pd and Se atoms can be quantitatively estimated to be near stoichiometric. Figure 1f shows the calculated electronic structure of PdSe2 with an indirect bandgap of 1.1 eV using many-body perturbation theory. Figure 1g presents the ground-state absorption spectra of the PdSe2 sample measured by UV-Vis-NIR Spectrophotometer (Agilent Cary 5000). The indirect bandgap is estimated to be 1.1 eV through a linear extrapolation Tauc plot (Supplementary Note 1), in good agreement with the calculated value. The spectrum features a pronounced A-exciton transition resonance near 2.23 eV, corresponding to the strong optical transition between the parallel bands in Fig. 1f. The calculated exciton peak at 2.31 eV is in reasonable agreement with the measurement.

Ultrafast interplay between electronic and lattice excitations
The temporal and spectral evolution of different electronic transitions in PdSe2 is recorded in real time at room temperature by measuring the differential transmission contrast signal ΔT/T using ultrafast transient absorption spectroscopy (See Experimental Section for details). The sample is excited by 35-fs pulses centered at a photon energy of 3.4 eV and with a pump fluence set to 160 μJ/cm -2 . Figure 2a shows the 2D mapping of the ΔT/T signal as the function of pump-probe delay and probe photon energy. Figure 2b shows the ΔT/T spectra near A exciton resonance for the first 10 ps. Interestingly, the variation of the optical response appears immediately after photoexcitation and subsequently the sample exhibits a distinct response at different time delays. A pronounced photobleaching (PB) signal is observed when probing near the A excitonic transition resonance, which can be attributed to population-induced phase-space filling effects arising from Pauli blocking. The absorption can be obtained from the transmission spectrum with the thin-film approximation and the exciton resonance energy is extracted from the absorption spectrum through Lorentz fitting (Supplementary Note 2). Figure 2c shows the exciton energy shift (ΔE) as a function of pump-probe time delay. With increasing time, the exciton resonance energy experiences a dramatic energy shift with a blueshift and redshift crossover as well as pronounced oscillatory components. The large magnitude of this laser-induced energy shift, compared to those in conventional semiconducting quantum well systems or 2D materials 22,[33][34][35][36][37] , is a signature of strong many-body interactions in few-layer PdSe2. Initially, the exciton energy shifts to higher energies, which may be due to the Pauli blocking of the exciton band edge via the Burstein−Moss effect with high carrier density and the dynamic screening of excitons induced by the free carriers.
Afterwards, a pronounced energy redshift occurs at about 1.5 ps. The microscopic mechanism behind the energy shift results from the competition between the quasiparticle bandgap (Eg) shrinkage and the exciton binding energy (Eb) reduction in the presence of strong carrier screening.
Optical excitation above the A exciton resonance generates an abundance of free-charge carriers at the very beginning that precedes A exciton formation. At such high excitation densities, photoexcited carriers strongly screen Coulomb interactions. The carrier-induced screening leads to a bandgap renormalization by reducing both Eg and Eb 23

Phonon dynamics revealed by low-frequency Raman spectroscopy
Having established the importance of two distinct coherent oscillations at THz frequencies, we next proceed to examine their microscopic features. Recent advances in realizing ultra-narrow optical filters have enabled the measurement of ultralow frequency (typically < 60 cm -1 ) Raman modes, offering a highly sensitive probe of interlayer vibrations and couplings in two-dimensional layered materials 4,40,41 . The Raman spectra are obtained in both low-frequency and high-frequency regimes simultaneously with an excitation energy of 2.33 eV, close to the A exciton, as shown in

Electron−phonon coupling from first-principles
To confirm our picture of phonon dynamics in PdSe2, we perform phonon and electron−phonon coupling calculations using the finite difference method 42 . Figure 6a demonstrates In conclusion, our findings provide a pathway for the future development of THz frequency optoelectronic devices that based on layered PdSe2. Furthermore, the observed vibrational phenomena combined with theoretical calculations provide an intuitive picture for exciton-phonon and electron-phonon interactions in 2D layered materials, which is supported by the ultralow frequency Raman spectroscopy with frequencies down to 5 cm -1 .

Sample preparation
High-quality PdSe2 samples are grown on quartz substrate directly by chemical vapor deposition (CVD) method using PdCl2 and Se powder as precursors. Selenium is evaporated at 250°C, PdCl2 is in the middle of a three-zone tube furnace with an intermediate temperature of 500°C, and quartz substrate is in the last high-temperature zone of 600°C. The evaporated Se and PdCl2 are grown on a quartz substrate in a high-temperature zone dragged by 300 standard cubic centimeters per minute (sccm) Ar and 30 sccm H2. The furnace is kept at 600°C for 20 minutes. Then, the temperature is cooled down to room temperature. The single shot G0W0 method is applied on top of the HSE06 hybrid functional 38 . Careful convergence tests are performed using k-point grids of 6×6, 10×10 and 12×12. Consistent with previous work, a 6×6 k-point grid can produce a qualitatively good dielectric function comparable to that of the 14×14 grid 49 , and a 10×10 k-point grid is well-converged. In addition, the G0W0 dielectric functions calculated using 768 and 384 bands show no significant difference. Therefore, we use 384 bands with a 10×10 k-point grid in the calculations. Many body corrections are included in the band structure in Figure 1f in the form of a scissor shift of 0.916 eV.

Lattice dynamics and electron-phonon coupling calculations
We obtain the harmonic interatomic force constants using the finite displacement method in a 2×2 supercell with the PHONOPY code 50 . The full phonon dispersion is shown in Supplementary Fig.   6. We estimate the strength of electron−phonon coupling by calculating the electronic structure along the normal mode uqν 41 : where q and ν are reciprocal space phonon wavevector and branch respectively, Np is the number of primitive cells in the real space supercell, Rp is the position vector of unit cell p, mα is the nuclear mass of atom α, i runs over Cartesian coordinates, hpαi is the displacement coordinate, and wqν;iα is the corresponding eigenvector. We use an amplitude of uqν corresponding to the 1σ of the Gaussian describing the ground state phonon wave function, given by 1/ � 2 , where ωqν is the phonon frequency. We average over negative and positive displacements to calculate the absolute energy change in the presence of the frozen phonons. The electron-phonon coupling strengths for different phonon modes at the Γ point are shown in Supplementary Fig. 5, which can be directly compared with time-and angular-resolved photoelectron spectroscopy (TR-ARPES) 51,52 .

DATA AVAILABILITY
The authors declare that all data supporting the findings of this study are available within the paper and its supplementary information files.