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 reports22. All spectra were taken at 15 K in this work.

Fig. 1 Schematics and conventional angle-resolved photoelectron spectroscopy (ARPES). a Schematics of time- and angle-resolved photoemission spectroscopy (TARPES) for FeSe. An infrared (IR) pulse of 1.55 eV is used for the pump, and an extreme ultraviolet (XUV) pulse of 27.9 eV by high harmonic generation from Ar gas is used for the probe to cover a large area including the M point. b Fermi surface mapping of FeSe. The intensity is mapped onto the in-plane electron momentum (k x , k y ). Orange and green lines represent measured cuts at the Γ and M points for the TARPES measurements, respectively. Black dashed lines indicate the Brillouin zone boundary. c, d Band dispersions at the Γ and M points along the momentums shown in (b). The vertical axes are represented as electron energies (E) with respect to the Fermi levels (E F ). Spectra in b–d were measured by a He-discharge lamp at 21.2 eV Full size image

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 spectra23, 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 studies19,20. 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 intensity-dependent 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 FSs16, the cosine-like signature indicates that the photoinduced metastable state is toward smaller FSs for the hole and electron pockets.

Fig. 2 Time- and angle-resolved photoemission spectra and oscillation behavior. a, b Time-resolved photoemission spectra taken around the Γ and M points, respectively. The vertical axes are represented as electron energies (E) with respect to the Fermi levels (E F ). c, d Integrated photoemission intensity above the Fermi level corresponding to the region surrounded by green boxes in (a) and (b), respectively. e, f Oscillatory components at the Γ and M points. They are obtained by subtracting the carrier dynamics from c and d. Errors bars are estimated as standard deviations of the intensities before the arrival of the pump. Oscillations are in phase between the Γ and M points, as clearly shown by the black dashed lines. g Amplitude of the fast Fourier transformation of (e) and (g). Both of them show peak structures at 5.3 THz. h Fast Fourier transform (FFT) amplitudes at 5.3 THz for the Γ and M points as a function of the pump fluence Full size image

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 observed7. 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 momentum25,26. 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.

Fig. 3 Energy distribution curves and shifts of the leading-edge midpoint. a, b Energy distribution curves (EDCs) for Γ and M points at representative delay times with pump fluences of 2.45 and 2.28 mJ/cm2, respectively. Shifts of the leading-edge midpoint (LEM) as a function of time (c) and pump fluence (d) at hole (Γ) and electron (M) bands. In 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 Full size image

Photoinduced superconductivity

In the single-hole and electron-band picture, photoexcited electrons are relaxed to the electron bands after the relatively fast processes of multiple electron–electron and electron–phonon scatterings. If the density 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) effect27. 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 pump28. 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 ps29,30,31. 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:

$$\Delta = - \frac{{m_{\mathrm{h}}{\mathrm{LEM}}_{\mathrm{h}} + m_{\mathrm{e}}{\mathrm{LEM}}_{\mathrm{e}}}}{{m_{\mathrm{h}} + m_{\mathrm{e}}}},$$ (1)

where m h and m e are the effective masses of the hole and electron pockets, respectively. Their ratio is \(m_{\mathrm{h}}/m_{\mathrm{e}} = 4/3\)32. \({\mathrm{LEM}}_{\mathrm{h}}\) and \({\mathrm{LEM}}_{\mathrm{e}}\) 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 state18, we performed band-structure calculations based on density functional theory (DFT). The results of the band-structure calculations are found in Supplementary Fig. 329. 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 dispersions22,33,34, band-dependent 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 element22,34. 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 TARPES20, 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 previously20, 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.