1 Introduction

The interactions among different degrees of freedom in quantum materials, including orbit, spin, charge, and lattice, lead to rich phenomena in condensed matter physics, such as the high-temperature superconductivity, charge density wave (CDW), topological insulating, and so on. Understanding the physical mechanisms behind these novel phenomena is important for the application of those quantum materials. By using femtosecond laser excitation in quantum materials, time-resolved experiments have played important roles in studying the microscopic mechanism of those novel states and controlling the macroscopic phenomena. The time-resolved technology based on the femtosecond laser can realize the time resolution from femtosecond (fs) to picosecond (ps), which is on the time scale of ultrafast dynamic processes in solid materials [1], making it possible that the contribution of different degrees of freedom in quantum materials to their physical properties can be distinguished in the time domain. In addition, by tunning the wavelength of the pump laser to selectively couple with different excitations in quantum materials, it is possible to induce non-equilibrium phenomena, which possess novel physical properties that are difficult to be achieved in the equilibrium state, such as the photoinduced high-temperature superconductivity [2–5], the photoinduced hidden states [6, 7], the coherent manipulation of materials [8–10], metastable states with novel physical properties [11, 12], and so on. Physical mechanisms behind these photoinduced non-equilibrium phenomena are usually the ultrafast change of the free energy or the crystal lattice rather than simple thermal effect caused by the pump laser.

Time- and angle-resolved photoemission spectroscopy (trARPES) is a key experimental method to study the ultrafast electronic dynamics, such as the electronic structures, quasiparticle lifetime, energy gap size, and many-body interactions, in quantum materials after ultrafast photoexcitation, and it has been extensively used in the studies of ultrafast electronic structure dynamics of high-temperature superconductors [13–22], topological insulators [23–28], CDW materials [29–31], and other quantum materials [32–35].

In strongly correlated materials, the macroscopic physical properties are mainly determined by the low energy states, such as the superconducting energy gap, charge density wave energy gap, the renormalized dispersion by electron-phonon coupling, and so on, of which the energy scales are usually on the scale of several meV to tens of meV. The energy resolution in the photoemission experiments should be on the same scale (∼10 meV) to resolve such low energy electronic structure. In trARPES experiments, the energy resolution and time resolution are determined by the bandwidth and the pulse duration of the probe laser pulse respectively. However, for a pulsed laser, the bandwidth and the pulse duration are irreconcilable and their product is determined by the Fourier transform limit, i.e., the cost of reduced time resolution is necessary to get better energy resolution.

Taking the advantage of nonlinear optical crystals, it is possible to generate ultraviolet laser pulses with a narrow bandwidth to serve as the probe beam in the trARPES experiment and realize a high energy resolution of \(10\sim20\text{ meV}\) and the corresponding time resolution of ∼100 fs. In this review, we will focus on the development of a high-resolution trARPES instrument based on nonlinear optical crystals at Shanghai Jiao Tong University and the studies on the ultrafast electronic dynamics in quantum materials on this system. Possible future directions of trARPES are discussed.

2 Time- and angle-resolved photoemission spectroscopy

TrARPES is an experimental tool to study the dynamics of ultrafast electronic structures directly in solid materials after ultrafast laser excitation. It mainly consists of two parts, i.e., the ultrafast laser and the photoemission spectroscopy systems. As schematized in Fig. 1, an infrared pump pulse drives the sample into the non-equilibrium state, and a subsequent probe pulse photoemits electrons out of the sample. These photoelectrons are collected by a hemispherical electron analyzer, in which their emission angles and kinetic energies are resolved. By varying the time delay between the two pulses, the time evolution of the spectra can be recorded. According to different generation mechanisms, the probe laser sources in trARPES are mainly the following three types [36]: (1) the deep ultraviolet (DUV) or vacuum ultraviolet (VUV) pulsed laser based on the frequency conversion in the nonlinear crystals, (2) extreme ultraviolet pulsed laser generated through the high-harmonic generation (HHG) process in the noble gas, (3) the developing X-ray free-electron laser sources. Most of the trARPES groups use nonlinear optical crystals to take the advantages of high stability, high energy resolution, and easy operation [25, 37–50]. At the same time, benefiting from the low photon energy and high energy and momentum resolution in such setups, it is capable to measure low-energy electronic structures near the Fermi level precisely in solid materials, and it has played important roles for studying the ultrafast electronic dynamics of correlated materials, such as the cuprate superconductors, iron-based superconductors, CDW materials, and other quantum materials.

Figure 1
figure 1

Schematic of the trARPES. Electrons in the material are excited into the non-equilibrium states by the pump pulse and a subsequent probe pulse photoemits electrons out of the material. Those photoelectrons are then collected by a hemispherical electron analyzer in which their emission angles and kinetic energies are resolved. Time resolution is achieved by varying the time delay between the pump and probe pulses. Ultrafast superconducting gap dynamics in Bi2Sr2CaCu2O8 + δ are shown

Full size image

The trARPES system developed at Shanghai Jiao Tong University is a typical system based on the frequency conversion in nonlinear crystals, as schematized in Fig. 2(a) and shown in Fig. 2(b) [48]. The fundamental laser beam is generated by a commercial Yb-based amplifier with the output wavelength centered at 1028 nm and the pulse duration of 290 fs. The repetition rate is adjustable (500/n kHz, \(n= 1, 2, 3, \ldots\)) with an output power of 15 W at the repetition rate of 500 kHz. The output of the fundamental laser is split into two independent optical parametric amplifiers (OPA1, OPA2) by a ratio of about \(1:1\). The outputs of the two OPAs are tunable between 650 and 900 nm, and the pulse duration of the OPA1 is optimized below 30 fs as the pump and the pulse duration of the OPA2 is optimized at about 55 fs to generate the probe pulse. The polarization of the pump beam can be adjusted by a half-wave plate or a quarter-wave plate. A motorized translation stage with a step resolution of 1 μm is placed in the pump beam path to realize the time resolution.

Figure 2
figure 2

The time-resolved ARPES system at Shanghai Jiao Tong University [48]. (a) Layout of the system, including the ultrafast laser system and the 7 eV laser system. A specially designed repetition rate amplifier is used to increase the repetition rate of the 7 eV laser up to 1.2 GHz and reduce the space charge effect. (b) A photo of the system. (c) The overall time resolution measured at about 1.5 eV above the Fermi energy on a FeSe sample at 4.5 K. (d) The overall energy resolution of the 6.05 eV ultrafast laser measured near the Fermi cut off on a Bi2Se3 sample at 4.5 K. (e) The overall energy resolution of the 7 eV laser measured on a Bi2Se3 sample at 4.5 K

Full size image

Two configurations of nonlinear crystals are used to generate the probe pulses on the trARPES system [48]. A combination of two β-BaB2O4 (BBO) crystals is used to generate probe pulses with a wavelength at 205 nm to realize high time and energy resolution, and an optional combination of a BBO and a KBe2BO3F2 (KBBF) crystal is used to generate probe pulses with a wavelength longer than 185 nm in air to reach higher probe photon energy. In a recent study, the KBBF crystal is used to extend the wavelength of the probe laser pulse to 177 nm in the vacuum chamber [51].

Considering Gaussian shaped pump and probe pulses in time domain, the time resolution in the trARPES experiment is determined by \(\Delta t=\sqrt{\Delta t_{\text{pump}}^{2}+\Delta t_{\text{probe}}^{2}}\), in which \(\Delta t_{\text{pump}}\) and \(\Delta t_{\text{probe}}\) are the pulse duration of the pump and probe pulse respectively. To obtain a better time resolution, it is necessary to optimize both \(\Delta t_{\text{pump}}\) and \(\Delta t_{\text{probe}}\). However, for a Gauss-shaped laser pulse, the product of pulse duration and energy bandwidth has a Fourier transform limit \(\Delta E\cdot \Delta t\ge 4~\hbar \cdot \ln 2\approx 1825\text{ meV} \cdot \text{ fs}\) [52], in which ΔE and Δt are the full-width-at-half-maximum (FWHM) of the energy bandwidth and the pulse duration of a single pulse. To approach the theoretical limit, all spectral components need to have a synchronized phase, i.e., a chirpless pulse with zero group velocity dispersion (GVD). A specially designed four-prism compressor is put in the beam path of the 205 nm probe beam to compensate for the positive GVD introduced by all the optical elements.

The overall time resolution for the 6.05 eV ultraviolet pulsed laser generated by the BBO crystals was determined by the pump-probe crosscorrelation at about 1.5 eV above the Fermi energy measured on a FeSe sample (Fig. 2(c)). The obtained FWHM of the spectra is about 113 fs, which is the up limit of the overall time resolution of the system considering the lifetime of the high-energy unoccupied electronic states. The overall energy resolution of the system is characterized by fitting the spectra near the Fermi edge of a metallic sample to an energy resolution convolved Fermi distribution function, giving a resolution of about 16.3 meV (Fig. 2(d)). The product of the time and energy resolution of the trARPES system based on the 6.05 eV ultraviolet laser is about 1842 meV ⋅ fs, which is almost the physical limit for a Gauss-shaped laser pulse. The pulse duration after passing through the nonlinear optical crystals depends on the thickness of the crystal [53]. By adjusting the thickness of the BBO crystal, the time resolution of trARPES system based on nonlinear optical crystals can be better than 50 fs [50]. Tunable time resolution and high energy resolution are very important for studying fine ultrafast electronic dynamics in quantum materials.

The trARPES system in Fig. 2(a) integrates a VUV laser system based on a KBBF crystal with the output wavelength centered at 177 nm (\(h \nu = 7\text{ eV}\)) and a spot size of <30 μm on the sample. The beam spot on the sample of the 7 eV laser can be precisely tuned to coincide with the pump and probe of the ultrafast laser system. In order to improve the energy resolution by reducing the space charge effect, a specially designed repetition rate amplifier is used to reduce the influence of the space charge effect in the photoemission experiment, allowing an output of the 177 nm laser with a repetition rate up to 1.2 GHz and achieving an ultra-high energy resolution of 0.4 meV (Fig. 2(e)). With improved energy resolution, the S-doping dependent superconducting gap in \(\mathrm{FeSe}_{1-x}\mathrm{S}_{x}\) can be precisely tracked [54]. In addition, combined with the ultrafast laser, the photoinduced long-lived metastable states that the lifetime is on the scale of hours, taking the photoinduced hidden phase in the 1T-TaS2 for an example [6], can be precisely detected without time resolution.

Table 1 shows the resolution performance of trARPES systems from different research groups. As discussed above, the product of the energy bandwidth and pulse duration for a Gauss-shaped pulse has a limit of 1825 meV⋅ fs. The resolution performance of a trARPES system can be defined by \({{R}_{\exp}}=\Delta {{t}_{\exp}}\cdot \Delta {{E}_{ \exp}}/1825\text{ meV}\cdot \text{ fs}\), in which \(\Delta {{t}_{\exp}}\) and \(\Delta {{E}_{\exp}}\) are the overall time resolution and energy resolution of the system respectively, and the performance of the probe pulse can be defined by \({{R}_{\text{probe}}}=\Delta {{t}_{\text{probe}}}\cdot \Delta {{E}_{\exp}}/1825\text{ meV}\cdot \text{ fs}\). For a better optimized trARPES system, the \(R_{\exp}\) and \(R_{\text{probe}}\) is closer to 100%. The \(R_{\exp}\) of the trARPES system developed at Shanghai Jiao Tong University reaches a ratio of 101% [48], showing an outstanding resolution performance. The trARPES system from Shen’s group in Stanford possesses a distinguished high time resolution with a relatively reduced energy resolution [53]. Recently, Yang’s Group at Chicago University used a similar setup and also achieved an excellent resolution performance with a ratio of 107% [50].

Table 1 Resolution performance of trARPES systems from different research groups
Full size table

3 Probing the unoccupied electronic states of quantum materials

ARPES is a powerful experimental tool for detecting the momentum-resolved electronic structures in occupied states. However, electrons in the solid obey the Fermi-Dirac distribution, and in the thermal equilibrium state, except for the thermally excited electrons, few electronic states above the Fermi level are occupied. In conventional ARPES experiments, unoccupied electronic states within a finite range above the Fermi level can be obtained by dividing the Fermi-Dirac distribution function. However, this method is no longer applicable to high-energy unoccupied states. TrARPES is a key experimental method to detect unoccupied electronic states in materials nowadays. In the trARPES experiment, the pump laser pulse drives transitions of electrons from occupied states to unoccupied states far above the Fermi level and the subsequent probe pulse detects both the occupied and unoccupied electronic states simultaneously. Many progress has been made in the research of unoccupied electronic states of quantum materials using trARPES, including the CDW materials [29, 55, 56], thermoelectric materials [57], graphene [58], topological insulators [25, 26, 59–61], and so on. These results indicate that trARPES plays an important role in examining unoccupied states in quantum materials.

In magnetic topological insulators, the interaction between the magnetic order and nontrivial topological phases can induce novel phenomena, such as quantum anomalous Hall effect, chiral Majorana fermions, and Axion electrodynamics. Intrinsic magnetic topological insulators are expected to promote the observation of topological quantum phenomena, but it is difficult to confirm the existence of magnetic topological surface states in experiments. First principle studies show that EuSn2As2 is an antiferromagnetic topological insulator with a Dirac point lying above the Fermi level [62]. Due to defects introduced in the process of sample growth, the EuSn2As2 sample is usually hole doped, and its Dirac point is far above the Fermi level, which cannot be detected by conventional ARPES. TrARPES has the capability to simultaneously detect electronic structures of occupied and unoccupied states in solid materials, providing an important experimental means for revealing the unoccupied states in topological insulators.

Figure 3 shows a study of unoccupied states of topological insulator EuSn2As2 using trARPES [62]. The panel (a) shows the electronic structure at different pump-probe time delays. The spectra measured at a negative time delay (−0.2 ps) correspond to the equilibrium electronic structure, without Dirac dispersions due to the p-doped sample. After photoexcitation, a Dirac point at the energy of about 0.4 eV above the Fermi level can be clearly resolved. In order to illustrate the topological properties of the surface states, Fig. 3(d) shows the combination of unoccupied and occupied states, which is consistent with the calculation. Constant energy contours of non-equilibrium electronic structures show that the surface state is conical and isotropic (Fig. 3(e)). There is no significant difference between the surface state above the Fermi level in the paramagnetic phase (Fig. 3(b)) and the antiferromagnetic phase (Fig. 3(c)), which may be due to weak coupling between electronic states of the magnetic order and the nontrivial topology, resulting in the energy gap being too small to be detected. These results reveal the relationship between the topological surface states and the magnetic order in EuSn2As2.

Figure 3
figure 3

TrARPES measurements of the magnetic topological insulator EuSn2As2 [62]. (a) The time evolution of the electronic structure. (b) and (c) Curvature intensity maps of photoemission spectra at the delay time of 0.2 ps at 40 K and 4 K, respectively. (d) The combination of unoccupied and occupied electronic structures. (e) Stacked plots of constant energy contours at different binding energies at the delay time of 0.2 ps. The energy of the Dirac point is set to zero

Full size image

The study of the unoccupied electronic states by high time- and energy-resolution trARPES has played important roles in understanding the physics in the quantum materials. In addition to the above study, the long-lived unoccupied Dirac surface state in a p-type Bi2Se3 was detected [25]; by detecting both occupied and unoccupied states, a full CDW gap size of 0.59 eV was directly measured in the CDW material CeTe3 [55]; the strong Coulomb interaction strength was determined in the high-temperature superconductor Bi2Sr2CaCu2O8 by probing the potential unoccupied Hubbard band [63]; the unoccupied small band gap was identified in ZrTe5 to reveal its weak topological phenomenon [64], and so on.

4 Photoinduced ultrafast electronic phase transition

In addition to probing the unoccupied states, trARPES can also detect ultrafast electronic dynamics in solid materials. In the strongly-correlated systems, different degrees of freedom are coupled with each other, and their contributions to the macroscopic physical properties are hard to be distinguished in the equilibrium experiment. Taking the advantage of different recovery or response time scales for different degrees of freedom, it is possible to reveal the roles of different degrees of freedom played in the phase transitions in the time domain from trARPES measurements [16, 20, 30, 65–75]. After the ultrafast photoexcitation, the electronic temperature will sharply increase in an ultrafast time scale while the lattice temperature remains less changed in most materials [76], making it possible to isolate the pure electronic phase transition from the structural transition.

The excitonic insulating transition is purely electronic origin, and the ground state is analogous to that of the BCS superconductivity. However, strong electron-hole binding induced charge density wave or structural phase transition usually happens at the same critical temperature, making it difficult to distinguish the excitonic insulating phase from those transitions experimentally. Ta2NiSe5 is believed to be an exciton insulator with a second-order electronic and structural phase transition at 326 K. Experimental evidence of the purely electronic phase transition is necessary in isolating the excitonic insulating physics.

The electronic structure of the equilibrium state (Fig. 4(a), left) has a clear “Mexican-hat” shape dispersion at about 0.14 eV below the Fermi level, which is considered to be the characteristic of band mixing between the valence and conduction bands due to strong electron-hole interaction. After being excited to higher electronic temperature by the ultrafast laser pulse with a pump fluence of 0.19 mJ/cm2, the transient electronic structure at 0.3 ps clearly shows the mixed conduction and valence bands with energy gap almost fully closed (Fig. 4(a), right). Figure 4(b) shows the dispersion of valence and conduction bands extracted from Fig. 4(a). With the mean-field theory of the excitonic insulator, the noninteracting bare dispersion of valence and conduction bands can be extracted from experimental data (Fig. 4(b)). With increasing pump fluence, the recovery rate of non-equilibrium electrons in Ta2NiSe5 decreases and saturates above a critical pump fluence of 0.29 mJ/cm2 [66], and the energy gap decreases to 15% of the size at the equilibrium state (Fig. 4(c)). The transient electron temperature under the critical pump fluence is as high as 2000 K, and the system undergoes an ultrafast electronic phase transition from an excitonic insulating to a semimetallic state. Due to the structural phase transition in Ta2NiSe5, phonon modes representing the monoclinic phase appear at low temperature and the characteristic 2.1 THz phonon mode of \(B_{1g}\) symmetry disappears above the transition temperature. It is found that the 2.1 THz phonon mode representing the monoclinic phase still exists above the critical pump fluence of 0.29 mJ/cm2, indicating the crystal structure does not change after pumping, and the photoinduced ultrafast electronic phase transition is purely electronic origin (Figs. 4(d-f)). Ta2NiSe5 undergoes an ultrafast electronic phase transition under femtosecond laser pumping, while its low temperature monoclinic structure remains unchanged. At the same time, based on the effective masses of the bare valance and conduction bands, calculation shows that the gap of 100 meV in Ta2NiSe5 cannot only be a result of electron-hole Columb interaction, which indicates that other many-body effects, such as electron-phonon interaction, must be considered in the electronic phase transition in this system.

Figure 4
figure 4

Photoinduced ultrafast electronic phase transition in the excitonic insulator candidate Ta2NiSe5 [66]. (a) Equilibrium and nonequilibrium electronic structures with a pump fluence of 0.19 mJ/cm2 at the delay time of −0.4 ps and 0.3 ps respectively. (b) The bare conduction and valence bands extracted from the experimental data. (c) The energy gap and the decay rate of non-equilibrium quasiparticles as functions of pump fluence. (d) Time-resolved band shifts at different energies and momentum with pump fluences of 0.1 mJ/cm2 (below \(F_{c}\)) and 0.32 mJ/cm2 (above \(F_{c}\)). (e) Energy shifts after removing the incoherent part shown in panels (d). (f) The corresponding Fourier transform magnitudes of the curves shown in panels (e)

Full size image

FeSe, with a superconducting transition at approximately 9 K, undergoes a tetragonal-to-orthorhombic lattice deformation and a breaking of rotational symmetry of electronic order (nematic phase) at the same temperature of approximately 90 K. However, the extent of the individual contributions of the structural transition and the purely electrical order to the nematic electronic states is still unknown, and it is difficult to differentiate the nematic electronic order from that of the structural transition and determine the contribution to the nematic states from the structural transition from thermal equilibrium measurements. Taking advantage of ultrafast experiments by using strong ultrafast photon pulses to excite only the electronic states, retaining the preserved orthorhombic lattice structure, it is possible to drive only the electronic phase transitions in an ultrafast manner without deforming the crystal lattice.

By comparing with temperature-dependent experiments in the equilibrium state, contributions to the nematic states from lattice and electronic degrees of freedom during the phase transition are determined. The equilibrium electronic structure at Γ point of FeSe consists of a hole-like \(d_{xz}\) band crossing the Fermi level, a hole-like \(d_{yz}\) band with its band top at −20 meV and the \(d_{z^{2}}\) band sitting at −0.2 eV (Fig. 5(a)). Two critical pump fluences of 0.06 mJ/cm2 (\(F_{c1}\)) and 0.2 mJ/cm2 (\(F_{c2}\)) are found in the pump-fluence-dependent energy shift of the \(d_{yz}\) band at 0.2 ps. \(F_{c1}\) corresponds to the critical pump fluence to destroy the nematic phase in FeSe and \(F_{c2}\) corresponds to another high-temperature electronic phase transition. Upon increasing the pump fluence, the \(d_{xz}\) and \(d_{z^{2}}\) bands linearly move to higher binding energy away from the Fermi level (Fig. 5(b)). Compared with temperature-dependent experiments in the equilibrium state (Fig. 5(c)), it is found that the energy shift induced by laser pumping is not an average heating effect. In the temperature-dependent measurements, there are two transition temperatures at 90 K (\(T_{S}\)) and 120 K (\(T_{M}\)). The temperature-dependent energy shift of \(d_{yz}\) band has the same trend as the fluence-dependent energy shift, while the \(d_{xz}\) and \(d_{z^{2}}\) bands move to lower binding energy towards the Fermi level upon increasing temperature. Above \(T_{S}\), the temperature-dependent energy shift of \(d_{xz}\) and \(d_{z^{2}}\) bands are consistent with the energy shift to higher binding energy away from the Fermi level upon increasing pump fluence, which excludes that the upward movement of the \(d_{yz}\) band in the ultrafast measurement is caused by heating effect. By fitting the electronic temperature, it is found that the electronic temperature of \(F_{c1}\) and \(F_{c2}\) at 0.2 ps corresponds to \(T_{S}\) (∼90 K) and \(T_{M}\) (∼120 K) in the equilibrium state, respectively. The absence of \(T_{S}\) in the fluence-dependent energy shift of \(d_{xz}\) and \(d_{z^{2}}\) bands indicates that there is no ultrafast structural phase transition. Due to a longer time scale for structural phase transition in FeSe, it is possible to distinguish between the lattice and electronic degrees of freedom shortly after ultrafast photoexcitation. By comparing time-resolved experiments and temperature-dependent experiments, it is confirmed that the structural transition plays an important role in the nematic phase.

Figure 5
figure 5

Photoinduced ultrafast electronic phase transition in the iron-based superconductor FeSe [68]. (a) Curvature intensity maps of photoemission spectra at equilibrium and at the delay time of 0.2 ps with different pump fluences. (b) Fluence-dependent energy shifts of \(d_{xz}\), \(d_{yz}\) and \(d_{z^{2}}\) bands taken at the delay time of 0.2 ps. (c) Equilibrium-temperature-dependent energy shifts of \(d_{xz}\), \(d_{yz}\), and \(d_{z^{2}}\) bands. The inset shows additional temperature-dependent measurements of the \(d_{yz}\) band on the other two samples with different photon energies and different momentum cuts

Full size image

Such ultrafast photoinduced electronic phase transition is also identified in other materials. The optical driven insulator to metal phase transition is realized in the Mott insulator 1T-TaS2 [65], in which upon optical excitation the electronic temperature is elevated to 1320 K, leading to a collapse of the electronic gap while the lattice temperature remains at 30 K. Destruction of long-range charge order in the CDW material is found in 1T-TiSe2 [30].

5 Photoinduced new states of matter

Using the femtosecond laser to induce new states of matter in solid materials, such as the high-temperature superconducting states [2–5, 77], the spin density wave states [78], the hidden states [6, 7, 79–82], the Floquet electronic states [26, 83, 84], the topological states [9, 85, 86], the semimetallic states [66, 87], and so on, is the frontier of the study in condensed matter physics. Among them, the physical mechanism of light-matter interaction to induce new states is also a major content of exploration. Femtosecond laser pumping can generate coherent phonons in quantum materials [14, 22, 24, 88–93], while with sufficient pump fluence the order parameter of the material can be inversed via strong electron-phonon interactions. Recently, not only the theoretical calculation [94], but also many experimental studies, including the ultrafast X-ray diffraction experiment on the CDW material SmTe3 [95, 96], the ultrafast spectroscopy experiment on TbTe3 [97], and the ultrafast X-ray diffraction experiment on the quasi-one-dimensional CDW material K0.3MoO3 [98], suggest a photoinduced CDW phase inversion, which can be a new way to drive new states of matter out of equilibrium by the ultrafast laser.

If the order parameter inversion could be induced in the top layers or sections of the sample, there are possibly two-dimensional (2D) electronic states in the domain wall, as schematized in Fig. 6(b). Such optically induced 2D electronic states are identified in a three-dimensional (3D) CDW material TiSe2 [31]. In the CDW state, the electronic structure at the center of the Brillouin zone consists of the Γ-Se 4\(p_{x,y}\) band at the Γ point and the A-Se 4\(p_{x,y}\) band and L-Ti 3\(d_{z^{2}}\) band folded from the A point and the L point at the boundary of the Brillouin zone (Fig. 6(c), left). Under high pump fluence, the CDW order in TiSe2 is destroyed. The Γ-Se 4\(p_{x,y}\) band and the L-Ti 3\(d_{z^{2}}\) band are partially recovered at 12 ps. In addition, the femtosecond laser can induce coherent phonon modes related to CDW in TiSe2, and invert the order parameter with sufficient pump fluence. By numerically solving the phenomenological Ginzburg-Landau model, it is found that the macroscopic domain wall between the inverted and the original layer can be placed near the sample surface under a certain pump fluence (Fig. 6(d), top), and can be probed by trARPES which is a surface sensitive experimental tool. By continuously tuning the pump fluence, the photoinduced macroscopic domain wall will appear alternately near the sample surface, which is manifested in the fluence-dependent spectral intensity. Figure 6(d) shows the spectral intensity integrated from the Se 4\(p_{x,y}\) band top to the Fermi level as a function of pump fluence, which changes non-monotonically upon increasing pump fluence. At a fixed pump-probe time delay, the spectral intensity at the Γ point first increases slightly as increasing the pump fluence and then changes dramatically at a critical fluence that destroys the exciton condensation in TiSe2. More interestingly, the spectral intensity reaches a maximum (peak) at a pump fluence of about 0.091 mJ/cm2, and then decreases to a minimum (dip) at a fluence of about 0.116 mJ/cm2. With further increasing the pump fluence, the peak-dip characteristic of the intensity appears alternatively. By comparing the fluence-dependent spectral intensity and the potential energy extracted from numerical simulation, it is found that the dip of intensity and the maximum of the potential energy correspond to the same pump fluence, at which the macroscopic domain wall is placed near the sample surface (Fig. 6(d), up). The spectral linewidth as a function of pump fluence also possesses a peak-dip characteristic. Compared to the electronic structure at the pump fluence of the peaks, the spectral linewidth at the fluence of the dips is reduced. Such a phenomenon can only be induced by a switch of the electronic state from 3D to 2D, which is further evidenced from the comparison between experimental and calculated band energy shifts and the analysis of band folding due to the lattice distortion.

Figure 6
figure 6

Photoinduced two-dimensional (2D) electronic states in TiSe2 [31]. (a) Schematic of the trARPES experimental geometry. (b) Schematic of photoinduced 2D electronic states in TiSe2. (c) Electronic structures with a pump fluence of 0.355 mJ/cm2 and the corresponding second-derivative images at equilibrium and at the delay time of 12 ps. (d) Top: calculated order parameters as a function of depth (z) for different fluences. Bottom: spectral intensity integrated from −0.1 eV (Se-4\(p_{x,y}\) band top) to the Fermi level and Ti-3\(d_{z^{2}}\) band near the Fermi level and the spectral linewidth of the Se-4\(p_{x,y}\) band as a function of pump fluence. Inset shows the energy distribution curves at pump fluences I and I’

Full size image

In addition, at the pump fluence of the dips, the density of states of the Ti 3\(d_{z^{2}}\) band near the Fermi level is enhanced, which is a signature of novel electronic states in the photoinduced 2D states. The peak-dip characteristic in the fluence-dependent intensity persists at 30 K and 80 K, but disappears at 295 K above the CDW transition temperature. By comparing the energy distribution curves (EDCs) of the Ti 3\(d_{z^{2}}\) band near the Fermi level between fluences at the peaks and dips, an energy gap of about 2 meV is identified at the domain wall (Fig. 6(d), inset). It has shown that doping Cu [99] or applying pressure [100, 101] will suppress the CDW in TiSe2 and induce superconductivity, and the enhancement of density of states near the Fermi level at domain walls is believed to be responsible for the superconductivity in TiSe2. The photoinduced 2D electronic state has similar characteristics of the enhanced density of states near the Fermi level and the gap opening, suggesting that there might be the photoinduced superconductivity in the photoinduced 2D domain wall. The energy gap in the photoinduced 2D state still exists at 30 K, which is much higher than the superconducting transition temperature of about 4.5 K in CuxTiSe2. A recent research on K3C60 shows that a transient superconducting gap with a size comparable to that in its equilibrium state is induced by an ultrashort far-infrared laser pulse at 100 K [2], which is much higher than the equilibrium superconducting transition temperature of 20 K. Despite different microscopic origins, the energy gap opening in TiSe2 and K3C60 under femtosecond laser pumping may share the same non-equilibrium physics that photoinduced energy gaps can exist in the non-equilibrium state even at an electronic temperature higher than the superconducting transition temperature in the equilibrium state. In addition, the photoinduced coherent conductivity observed in cuprates, which possess CDW phase at high temperatures, might also be a result of photoinduced macroscopic domain walls [4]. Such a quasi-2D electronic state with novel properties through photoinduced order parameter inversion provides a new platform for studying exotic low-dimensional physics in solid materials.

There are only a few success in the study of photoinduced novel or hidden electronic states in quantum materials by trARPES. Besides the above study, the novel Floquet-Bloch state, which is a result of electron motion in both of periodic lattice structure in real space and the periodic potential in time domain, is experimentally realized in the topological insulator Bi2Se3 by mid-infrared pump in 6 eV trARPES [26].

6 Summary and outlook

TrARPES has become a powerful experimental tool in condensed matter physics for its capability of directly detecting ultrafast electronic dynamics in solid materials such as the nonequilibrium quasiparticle recovery time, unoccupied states, many-body effects, ultrafast electronic phase transitions, and so on, and has achieved remarkable results in a variety of systems.

In the future development of trARPES, to directly control CDW and other materials with large energy gaps, it is necessary to develop mid-infrared pump lasers and to directly couple with the lattice degrees of freedom or other excitations at low energies in quantum materials, it is necessary to develop pump laser sources in the terahertz range with a high repetition rate. A laser source with a large-scale tunable wavelength may provide a more effective way to manipulate the macroscopic properties of quantum materials through laser pumping.

In addition, the current probe light source in this review is only limited at the deep ultraviolet range, making it hard to detect the ultrafast electronic dynamics away from the Brillouin zone center. The application of high repetition rate ultrafast deep ultraviolet light source by the high-harmonic generation process in the noble gases will extend such high-resolution ultrafast study to large momentum in the Brillouin zone. Moreover, most of the current trARPES systems use ultraviolet probes with isolated wavelengths or wavelength tunable in a small range, leading to the relevant research limited on some momentum areas in the Brillouin zone of the quantum materials. The development of femtosecond probe light sources with tunable photon energy is crucial to the study of ultrafast electronic dynamics in 3D quantum materials. It is expected to achieve a breakthrough by developing high-repetition rate deep ultraviolet or vacuum ultraviolet free electron lasers.

The effective combination of various ultrafast experimental technologies, such as the ultrafast electron diffraction, time-resolved X-ray diffraction, ultrafast optical spectroscopy, and so on, can provide a complete physical picture of the ultrafast process in quantum materials from the ultrafast electronic structure and the ultrafast lattice dynamics.

Finally, due to the complexity of the interaction between laser and matter, it is also important to establish the relevant ultrafast theory and appropriate theoretical model in the study of the quantum materials manipulated by ultrafast light sources.