Photoinduced possible superconducting state with long-lived disproportionate band filling in FeSe

Photoexcitation is a very powerful way to instantaneously drive a material into a novel quantum state without any fabrication, and variable ultrafast techniques have been developed to observe how electron, lattice, and spin degrees of freedom change. One of the most spectacular phenomena is photoinduced superconductivity, and it has been suggested in cuprates that the transition temperature Tc can be enhanced from the original Tc with significant lattice modulations. Here, we show a possibility for another photoinduced high-Tc superconducting state in the iron-based superconductor FeSe. The transient electronic state over the entire Brillouin zone is directly observed by time- and angle-resolved photoemission spectroscopy using extreme ultraviolet pulses obtained from high harmonic generation. Our results of dynamical behaviors from 50 fs to 800 ps consistently support the favourable superconducting state after photoexcitation well above Tc. This finding demonstrates that multiband iron-based superconductors emerge as an alternative candidate for photoinduced superconductors. Light-matter interactions can be used to induce a superconducting-like state in some cuprate superconductors at temperatures above the expected transition temperature. Here, the authors provide time and angle resolved spectroscopic evidence to suggest that photo induced superconductivity can also be achieved in Fe-based superconductors

A mong Fe-based superconductors, FeSe has attracted enormous interest owing to the absence of antiferromagnetism, in contrast to other Fe-based superconductors. Moreover, FeSe has potential superiority in exhibiting a higher critical temperature (T c ) of superconductivity under various external applications. Although T c is only~10 K at ambient pressure 1 , a significant increase in T c to~40 K by physical pressure has been achieved [2][3][4] . Regarding fabrications, the intercalation of a spacer layer can increase T c to~40 K 5,6 , and the T c of single-layer FeSe has been reported to be~60 K 7 . The key ingredient for achieving higher T c values lies in the bandstructure design. For example, the dramatic increase in T c for single-layer FeSe is accompanied by the disappearance of the hole Fermi surface (FS) and the increase in the electron FS 7 . In this context, photoexcitation has substantial advantages over other methods because it can instantaneously manipulate a material of interest in situ without any fabrication [8][9][10] . One of the striking phenomena is the photoinduced superconductivity reported in high-T c cuprate superconductors, where the key mechanism is the lattice modulation 11 . Furthermore, it should be emphasized that near-infrared pulses have also been employed for excitation, which initially excite the electronic system, while mid-infrared pulses can resonantly excite the lattice system 12,13 .
Recently, photoexcited phenomena for Fe-based superconductors have been intensively studied. In photoexcited BaFe 2 As 2 , the temporally periodic formation of spin-density waves was observed by terahertz (THz) spectroscopy 14 . The demonstration of chemical potential control 15 and the possibility of photoinduced superconductivity 16 were reported by time-and angle-resolved photoemission spectroscopy (TARPES). The key mechanism is the connection of the electron and spin properties to the lattice motion, and each report is discussed in terms of the clear appearance of coherent phonons 17,18 . In photoexcited FeSe, coherent phonons were also reported by TARPES 19 , and the connection between the dynamical band shift and lattice dynamics was directly measured by combining TARPES and time-resolved X-ray diffraction 20 . However, an important but lacking aspect in photoexcited FeSe is the dynamic properties of the electron pockets located around the Brillouin zone (the M point). By directly observing how the hole and electron pockets change by photoexcitation, we can also gain insight into the response of the lattice degree of freedom in the photoexcited state. Because it is relatively easy to set up, a photon energy of 6 eV is typically employed for TARPES measurements. However, due to the lack of photon energy, TARPES under 6 eV cannot access the M point. This is overcome by using high harmonic generation (HHG) to obtain higher photon energy and capture a larger region of the Brillouin zone 21 .
Here, we investigate the nonequilibrium electronic structure of FeSe by performing TARPES using an extreme ultraviolet (XUV) laser. Oscillations as a result of A 1g coherent phonon excitation are clearly observed for both the hole and electron FSs, and they are found to be in phase with each other, the behavior of which is different from that of BaFe 2 As 2 16 . From long-delay time measurements, we elucidate that the disproportionate band filling between the hole and electron bands persists for longer than 800 ps. Interestingly, this state mimics the electronic structure of a single-layer FeSe. Furthermore, the additional LEM found in both the hole and electron FSs is ascribed to the superconducting gap. By comparing with band-structure calculations, we find that the distance between the neighboring Se and Fe layers increases in the photoexcited metastable state. This result suggests that fairly long-lived nonequilibrium electronic and lattice structures are available by photoexcitation in FeSe, owing to its indirect semimetallic band structure. We propose that a long-lived photoinduced superconducting state could be expected for FeSe.

Results
Displacive excitation of coherent phonons. Figure 1a shows an illustration of our experimental setup for the TARPES measurements. To characterize the cleaved surfaces, we first performed conventional static ARPES using a He discharge lamp (21.2 eV). Figure 1b shows the result of FS mapping, and two FSs are clearly seen around the Γ (0, 0) and M (π, π) points. Figure 1c, d shows the ARPES intensity as a function of energy and momentum taken at around the Γ and M points, respectively. The horizontal momentum axis corresponds to the solid lines in Fig. 1b, while the vertical energy axis corresponds with respect to the Fermi level (E F ). Hole and electron dispersions are observed around the Γ and M points, respectively. The results are consistent with previous reports 22 . All spectra were taken at 15 K in this work. Figure 2a, b shows the momentum-integrated TARPES intensity measured across the hole and electron FSs, with pump fluences of 2.45 and 2.28 mJ cm −2 , respectively, as a function of the pump-probe delays (Δt). All the measurements in this work are performed under the condition in which the space charge effects are minimized. Due to the low efficiency of the HHG process, the energy resolution is set to 250 meV. The integrated range is along the orange-solid and green-solid lines shown in Fig. 1b for the hole and electron FSs, respectively. After intense pulse excitation, electrons are immediately excited above E F , followed by relatively slow relaxation dynamics at both FSs. To see the photoexcited dynamics more clearly, we show in Fig. 2c, d an integrated intensity above E F corresponding to the regions surrounded by green boxes in Fig. 2a, b, respectively. Overall, immediate excitation and overshooting decay at Δt = 0 ps followed by relatively slow recovery dynamics are observed, reflecting the carrier dynamics. In addition, oscillatory behaviors are clearly observed superimposed onto the background carrier dynamics. These oscillatory components are especially evident at the initial time (Δt < 1.5 ps). At later times of approximately Δt = 3 ps, it should be noted that they exhibit a contrasting feature, i.e., the photoemission intensity decreases at the hole FS, while the intensity at the electron FS increases. This behavior is also confirmed in the time-and angle-resolved photoemission spectra shown in Supplementary Fig. 1 as the downward band shifts at the Γ point as well as the increase in electrons in the electron pockets at the M point. These signatures will be discussed later in more detail. To highlight the oscillatory components, we first fit the background carrier dynamics with two-component exponential decay functions convoluted with a Gaussian. They are shown by the black solid lines in Fig. 2c, d and were subtracted from the experimental data. The oscillatory components are displayed in Fig. 2e, f, respectively. These oscillations are in phase with each other and cosine-like, with a frequency of 5.3 THz. From the comparison with Raman spectra 23 , this oscillation frequency is assigned to the A 1g phonon mode, in which two Se layers oscillate symmetrically with respect to the sandwiched Fe layer. The recent results of Raman spectroscopy performed on single-crystal FeSe revealed the frequency of the A 1g phonon mode to be 5.5 THz, which justifies the assignment of the coherent phonon observed in the previous TARPES studies 19,20 . Moreover, the fast Fourier transforms (FFTs) of the oscillatory components are shown in Fig. 2g, and the FFT peak amplitudes for both the hole and electron FSs significantly increase as a function of the pump fluence shown in Fig. 2h. These cosine-like and intensitydependent behaviors confirm that the observed oscillations are attributed to the displacive excitation of coherent phonons (DECP) 24 . According to the DECP mechanism, photoexcitation moves the system to a free-energy curve of excited states with a minimum position at different h from the equilibrium state. As a result, Se atoms simultaneously oscillate with a center at the new stable (metastable) position. Since the oscillatory components of the photoemission intensity above E F reflect the size of FSs 16 , the cosine-like signature indicates that the photoinduced metastable state is toward smaller FSs for the hole and electron pockets.
Long-lived charge disproportionate state. As briefly observed, the photoemission intensity exhibits contrasting features between the hole and electron FSs at a larger delay time (Δt = 3 ps). This feature also persists at a relatively long-delay time, as shown in Supplementary Fig. 2. To investigate this behavior in more detail, we analyzed energy distribution curves (EDCs) for slow dynamics. Figure 3a presents the EDCs before (Δt = −30 ps) and after (Δt = 110 and 810 ps) the arrival of pump pulses for the hole FS, while the result for the electron FS is shown in Fig. 3b. The pump fluences for the hole and electron bands are 2.45 and 2.28 mJ cm −2 , respectively. After photoexcitation, the EDCs for both the hole and electron FSs become significantly broader at Δt = 0.16 ps, yet return soon at Δt = 3.24 ps to almost the same as those at 110 and 810 ps. This indicates that the electronic temperature is well cooled. Regarding the shift of the EDCs, the clear one toward the lower-energy side is noticed at the hole FS. On the other hand, at the electron FS (Fig. 3b), the EDC intensities for Δt = 110 and 810 ps around E -E F = −0.1 eV are reduced, while no clear shift appears. For quantitative insights, we evaluate the shift of the leading-edge midpoint (LEM). Figure 3c shows the temporal LEM shifts. As clearly shown, the LEM shift at the hole FS is negative, while that at the electron FS is negligibly small. In other words, the temporal band filling is disproportionate between the hole and electron bands. Interestingly, the photoexcited electronic structure mimics that of the monolayer FeSe film, in which only electron FSs are observed 7 . Furthermore, this disproportionate band filling persists longer than the measured delay time of 800 ps. This long lifetime of carriers can be ascribed to the indirect semimetallic band structures, where the electron-hole recombination must accompany the assistance of phonons with a large momentum 25,26 . Figure 3d shows the LEM shift as a function of the pump fluence, in which the values and estimated errors are the averages and standard deviations in Δt > 0, respectively. The trend of the disproportionality between the hole and electron bands, as illustrated in Fig. 3e, becomes more evident with increasing pump fluence. However, it should be noted that the negative shift of the LEM for the hole FSs is not equal to the positive shift for the electron FSs, and this signature is more pronounced for higher fluence. of states is similar between the hole and electron FSs, the LEM shift should be the same amount with the opposite sign. Hence, it should be unusual for the LEM shift at the electron FS to be negatively small for a higher fluence. If the overall shift of E F is included in these LEM shifts, one possibility is due to the surface photovoltage (SPV) effect 27 . However, it is not expected to occur in a semimetallic system such as FeSe because the SPV effect is typically induced by the surface band bending of semiconductors. Another possibility is a multiphoton effect due to the strong excitation by a near-infrared pump 28 . Since we confirmed the absence of photoelectron intensities due to a multiphoton effect by measuring no signal with only pump pulses, this explanation can also be unlikely. The Floquet band theory may also explain our results, in which many replica bands appear apart from the original band by the photon energy used for excitation. Although the Floquet band theory significantly changes the band structure, the reported Floquet states have a relatively shorter lifetime around <1 ps [29][30][31] . Because our main focus in this work is LEM shifts at times later than 100 ps, we have concluded that our results are less likely to be explained by the Floquet band theory. After considering all these effects, the overall LEM shifts can be ascribed to a gap originating from some orders.
To identify superconducting signatures more explicitly, we extract the averaged photoinduced superconducting gap, Δ, shown as a black solid line and markers in Fig. 3d, which is given by the following relationship: where m h and m e are the effective masses of the hole and electron pockets, respectively. Their ratio is m h =m e ¼ 4=3 32 . LEM h and LEM e are LEM shifts for the hole and electron pockets, respectively. A detailed description of how to extract the averaged superconducting gap is found in the Supplementary Discussion. Considering that superconductivity coexists with the orbital ordering under equilibrium for FeSe, but the orbital ordering induces no bandgap but a band splitting, the photoinduced superconducting gap is the most plausible origin. The mechanism of the stabilization of the superconducting state due to the displacive excitation is explained in the next section.

Lattice modulation induced by displacive excitations.
To determine whether h becomes higher or lower in the photoinduced metastable state 18 , we performed band-structure calculations based on density functional theory (DFT). The results of the band-structure calculations are found in Supplementary  Fig. 3 29 . Figure 4a-c shows the calculated FSs for the two hole bands (yz/zx(odd) and yz/zx(even)) and the electron band. Because the DFT calculations for FeSe cannot provide quantitative agreement with the measured band dispersions 22,33,34 , banddependent shifts of −0.08 and +0.17 eV, as well as renormalization with factors of 3 and 2, are introduced for the electron and hole bands, respectively. The equilibrium state is shown as the dotted lines, whereas the +5% and -5% changes in h are shown as the solid and dashed lines, respectively. Since the probe pulses are polarized along the detector slit in this work, the contribution to the photoemission intensity around the Γ point has been reported to be mainly from the yz/zx(even) orbital due to the photoemission matrix element 22,34 . In each band, the FS shrinks as h increases. From the comparison between the experiments and calculations, a higher h is interpreted to be realized in the photoinduced metastable state, as illustrated by the yellow arrows in Fig. 4d. This trend agrees with the previous report measuring the band shift at the Γ point by high-energy-resolution TARPES 20 , where the initial dynamics of the downward band shift are revealed to be synchronized with the increase in h. Although a quantitative agreement is difficult to achieve between the DFT calculations and the measured band dispersions, the trend of the band shifts with respect to the change in h should be correct, as reported previously 20 , the authors of which directly measured the dynamics of band dispersions as well as lattice distortions and compared them with DFT + DMFT calculations. Although our method using DFT calculations is less quantitative for reproducing the measured band dispersions than the DFT + DMFT calculations, the fact that both methods predict the same tendency with respect to the change in h strongly suggests that our DFT calculation results should also predict the same tendency.

Discussion
Regarding superconductivity, it has been reported that T c increases with higher h by physical pressure 4 . Photoexcitation can induce the same tendency as the physical pressure and can be another tool for the enhancement of the superconductivity. Successive recent reports on the photoinduced superconductivity in cuprate superconductors have discussed the important role of lattice motions 11,35 . For the excitation employed in most studies, a mid-infrared pulse is used to resonantly excite the lattice degree of freedom (phonons). However, the eventual lattice modulation playing a decisive role in photoinduced superconductivity was found to be the Raman-active A g phonon, which is nonlinearly coupled to the photoexcited infrared-active phonon mode 11 . Thus, it is indicated that the important mechanism relies on how to access the A g lattice modulation that is favorable for the superconductivity. Interestingly, near-infrared pulses are also used for excitation, which initially excite the electronic degree of freedom. Although the precise mechanism is still under debate, it is proposed that the lattice modulation is induced by the change in the distribution of the electronic system 36 , which is very similar to our situation. Along with cuprate superconductors, Fe-based superconductors can be an alternative candidate for photoinduced superconductivity because the pronounced lattice motions are detected by coherent phonons, and interestingly, the present results of higher h in FeSe are favorable for superconductivity. A long-lived aspect of the photoinduced phase owing to the indirect semimetallic band structures is also a characteristic feature for Febased superconductors compared with a short-lived feature for cuprate superconductors due to direct single-band structures.
In summary, we have investigated the photoexcited electron dynamics of the hole and electron FSs in FeSe by TARPES using the HHG technique. We have proposed that the ultrafast optical technique can offer another route to create new long-lived electronic and lattice structures in FeSe as a consequence of its indirect semimetallic band structure.

Method
Time-and angle-resolved photoemission spectroscopy. TARPES is a pump-probe-type measurement, where both pulses are originally generated from a Ti:Sapphire amplification system with a repetition rate of 1 kHz and a pulse   Fig. 3d, the averaged superconducting gap, 〈Δ〉, is shown as black solid lines and markers. Because 〈Δ〉 negatively contributes to the LEM shifts, we plot −〈Δ〉 in Fig. 3d. Error bars in Fig. 3d for LEM h and LEM e are estimated as standard deviations after the arrival of the pump, and that for 〈Δ〉 is obtained via the relationship of Eq. (1). e Illustration of photoinduced LEM shifts for hole (Γ) and electron (M) bands. |G> and |E> represent the ground and photoexcited states, respectively duration of 35 fs. A near-infrared (NIR) pulse (1.55 eV) is used for the pump, while XUV pulses (27.9 eV) are used for the probe. XUV pulses are obtained by selecting the ninth-order harmonic generated from argon gas by using a double-frequency pulse (3.10 eV). The time resolution is measured to be~80 fs from the crosscorrelation measurement between the pump and probe pulses, and the energy resolution is set to 250 meV. Photoemission spectra are measured by using a Scienta R4000 hemispherical electron analyzer.
Sample. High-quality single crystals of FeSe were grown by the chemical vapor transport method by using KCl/AlCl 3 as a transport agent 37 . Clean surfaces were obtained by cleaving in situ.
Band-structure calculations. Band-structure calculations based on density functional theory (DFT) were performed by using a WIEN2k package 38 . a = 3.7707 Å, c = 5.521 Å, and h = 1.4723 Å, where h is the Se height from the Fe layer, were used for the lattice parameters in the equilibrium state 37 .

Data availability
The data supporting the findings of this study are available from the corresponding author upon request.