Transient gap generation in BaFe2As2 driven by coherent lattice vibrations

Abstract Iron-based superconductors provide a rich platform to investigate the interplay between unconventional superconductivity, nematicity, and magnetism. The electronic structure and the magnetic properties of iron-based superconductors are highly sensitive to the pnictogen height. Coherent excitation of the A1g phonon by femtosecond laser directly modulates the pnictogen height, which has been used to control the physical properties of iron-based superconductors. Previous studies show that the driven A1g phonon resulted in a transient increase of the pnictogen height in BaFe2As2, favoring an enhanced Fe magnetic moment. However, there are no direct observations on either the enhanced Fe magnetic moments or the enhanced spin-density wave (SDW) gap. Here, we use time-resolved broadband terahertz spectroscopy to investigate the dynamics of BaFe2As2 in the A1g phonon-driven state. Below the SDW transition temperature, we observe a transient gap generation at early-time delays. A similar transient feature is observed in the normal state up to room temperature.

Controlling the physical properties of quantum materials along noninvasive and ultrafast pathways is the key for developing next-generation technologies. Dynamical control of materials using ultrashort laser pulses has been successful in a variety of systems to achieve novel phases that are inaccessible at equilibrium (1)(2)(3)(4). The key is to identify tuning parameters which effectively modify the electronic structure of quantum materials.
Quantum materials are remarkably sensitive to structural distortion. In iron pnictides, the iron-arsenic distance (pnictogen height) has a significant impact on superconductivity (5,6), the electronic band structure (7)(8)(9)(10), and the magnetic properties (11,12). The pnictogen height can be periodically modulated by optical excitation of a Raman-active A 1g phonon (Fig. 1A) (13,14). For BaFe 2 As 2 , a displacive excitation towards larger pnictogen height is observed in the transient state (15,16,9), which favors an enhanced Fe magnetic moment. One would expect to see a displacive increase of the spin-density wave (SDW) gap size, but this has not been observed so far due to experimental challenges. In fact, a comprehensive band assignment and gap identification at equilibrium are already challenging (17)(18)(19)(20) due to the multiband nature of iron pnictides: the energy bands close to the Fermi energy come from three orbitals, which experience strong band hybridization and band splitting below the nematic ordering temperature. This situation is further complicated by the twinned domains in as-grown samples (21,22). In the transient state, the A 1g phonon is excited by femtosecond laser pulses in the nearinfrared, the energy scale of which is far above that of the SDW gap. This results in a large contribution from the photoexcited carriers in the phonon-driven state, which may wash out low-energy features such as the SDW gap.
A remarkable result is from a recent time-resolved optical spectroscopy study, reporting a transient feature resembling the SDW gap at a temperature slightly above the SDW transition temperature T SDW (23). This was attributed to the generation of SDW order due to modified iron-arsenic distance in the phonon-driven state. However, it is unclear why the transient SDW order, which is so robust that exists up to room temperature, doesn't exist in the SDW state when driving the same A 1g phonon, as the lattice and band structure modifications are along the same direction for temperatures above and below T SDW (15,16,9). Furthermore, as the transient gap was obtained from the averaged oscillation amplitude of the optical conductivity, it remains unknown whether a corresponding behavior exists in the displacive response to counter the enhanced pnictogen height in the phonon-driven state (15,16).
Here, we report a time-resolved broadband terahertz (THz) spectroscopic probe of BaFe 2 As 2 in the A 1g phonon-driven state. The THz probe covers a spectral range from 8 to 70 meV, which allows the detection of light-induced changes in the itinerant carriers and the low-energy SDW gap. We studied the time and temperature dependence of the transient optical conductivity σ 1 (ω). Below T SDW , we observed a light-induced depletion of the optical conductivity at the equilibrium SDW gap, with a peak forming at higher energies. This is a clear optical signature of gap opening. This feature is observed at early pump-probe time delays, when the photoexcited carriers are accumulating. The transient gap is quickly filled and merges to a free carrier response at later delays. Temperature-dependent pump-probe measurements show that a similar transient gap develops above T SDW and persists up to room temperature. The direct observation of a transient gap from the displacive response at temperatures both below and above T SDW provides new insights into the physics of iron pnictides, and will stimulate promising experiments in the optically induced control of nonequilibrium states of matter.

Results
The BaFe 2 As 2 single crystals exhibiting an SDW transition at T SDW = 130 K were grown by self-flux method (see Supplementary   Fig. S1) (24). Near-infrared (800 nm) laser pulses with a 40 fs duration were used to excite the A 1g phonon in BaFe 2 As 2 . The transient optical properties were probed at normal incidence by broadband THz pulses generated by laser-ionized plasma (25). The THz pulses were detected by electrooptical (EO) sampling of the terahertz field in a 100 micron thick GaP and a 300 micron thick GaSe crystal, which cover a detection range from 8 to 28 meV and from 34 to 70 meV, respectively.
The equilibrium optical conductivity σ 1 (ω), above and below T SDW , is shown in Fig. 1B. In the SDW state, several features are seen in σ 1 (ω): a Drude term at low frequencies, representing the free-carrier response; a sharp peak at 32 meV from an E u infrared-active phonon (26, 27); and two peaks at 45 and 110 meV, representing the SDW gaps (26, 18,20). Fig. 1C shows the transient σ 1 (ω) at T = 75 K. At a time delay of 0.5 ps, σ 1 (ω) shows a broadening of the low-frequency Drude component with an enhanced spectral weight. This indicates a higher carrier scattering rate and an increased carrier density, which are from photoexcited carriers since BaFe 2 As 2 is a metal. In the highfrequency region, the transient σ 1 (ω) is suppressed at around 40 meV, and then goes above the equilibrium σ 1 (ω) and peaks at 50 meV. This is an optical fingerprint of gap opening.
In the following, we will focus on the high-frequency region which probes both the transient gap and the tail of the Drude component. The inset of We now focus on the early-time optical response to investigate the temperature dependence of the transient gap. Fig. 2 presents Δσ 1 (ω) from 0 to 1.8 ps at three temperatures. The transient gap formation is seen from below to above T SDW and persists up to room temperature. The transient gap develops at nearly the same energy for all temperatures, with weakened features at higher temperatures. The lifetime of the transient gap remains the same for below and above T SDW (see Supplementary Table S1 and Fig. S4).
The pump fluence dependence of the transient state is shown in Fig. 3A. Using the peak position in σ 1 (ω) to define the gap energy, we obtained the small SDW gap size as 45 meV (Fig. 1B). Similarly, we identified the transient gap size from Fig. 3A using the peak position in Δσ 1 (ω). At 0.5 ps time delay, a transient gap develops near 48 meV with a 0.53 mJ/cm 2 pump fluence. The gap moves to higher energies with increasing fluences. When the pump fluence is approaching 3 mJ/cm 2 , the gap energy saturates (Fig. 3B  upper panel). With the same procedure used for Fig. 1D, we analyzed the time evolution of Δσ 1 (ω) for each pump fluence (see So far we have demonstrated a displacive response of optical conductivity in the phonon-driven state. We now present the oscillatory response. Since the electronic band structure oscillates at the frequency of the driven phonon (9,29), the same oscillation should show up in the spectral weight of optical conductivity, as ωσ 1 (ω) is proportional to the joint density of states (30). However, it is challenging to spectrally resolve the oscillatory response: it is a weak modulation on top of the large background displacive response. In addition, the signal-to-noise and time resolution in the terahertz region are orders of magnitude worse than that in the near-infrared region (23). To minimize the effect from the strong displacive response, fine time delay scans with a 2.5 ps time window were carried out for the low-frequency region, where the signal-to-noise allows a quantitative analysis of the oscillation component. Fig. 4 shows the time evolution of the integrated transient conductivity change, ∫ ω2 ω1 Δσ 1 (ω) dω, with the displacive response subtracted. The spectral weight integral was evaluated with ω 1 = 12 meV and ω 2 = 20 meV. The gray line is an sinusoidal oscillation at 5 THz, serving as a guide to the eye. The oscillation is better resolved at later delays, when the transient gap disappears. Considering the limited time resolution of the low-frequency THz probe (160 fs), the oscillation frequency agrees qualitatively with the A 1g phonon frequency probed by Raman spectroscopy (31,18), and is consistent with the oscillation observed by previous pump-probe studies (32,23,8,9,16,29,33). Similar oscillation is also observed in the high-frequency region where the transient gap develops (see Supplementary Fig. S5). The oscillatory response of optical conductivity verifies that the transient state we studied is a A 1g phonon-driven state.

Discussion
We now discuss the possible origin of the light-induced gap at 50 meV. A time-resolved photoemission study of BaFe 2 As 2 reported a displacive downwards shifting of the chemical potential by 50 meV at temperatures both below and above T SDW (9). However, a chemical potential shift will lead to a gap feature only when it creates additional interband transitions. Note that the pump fluence used here is the incident fluence, which is a factor of 2 larger than the corresponding absorbed fluence. Since the chemical potential shift scales linearly with the pump fluence (9), we estimated a 20-meV chemical potential shift with a 0.53 mJ/cm 2 incident fluence. From the band structure of BaFe 2 As 2 (22), a 20-meV chemical potential shift is insufficient to create additional interband transitions. The transient gap is likely from a displacive band reconstruction as a consequence of a transiently increased pnictogen height. Time-resolved X-ray diffraction studies observed a displacive increase of the Fe-As distance in the phonon-driven state. The maximum transient increase of the pnictogen height, considering the sum of the displacive and oscillatory components, is more than 5% of the equilibrium pnictogen height with an absorbed pump fluence of 3.5 mJ/cm 2 (16,15). As the electronic structure and the magnetic properties of iron pnictides are highly sensitive to the pnictogen height (16,11,12), a significant structural modification would visibly affect the SDW order. The lifetimes of both the displaced pnictogen height (15) and the driven A 1g phonon (9) show no systematic variation with pump fluences, which agrees with the fluence independent lifetime of the transient gap. Below T SDW , since the transient gap takes the spectral weight from the equilibrium SDW gap (Fig. 1C), they possibly share the same origin: the transient gap is a blue-shifted SDW gap. This is consistent with the previous observations that an increased pnictogen height favors an enhanced Fe magnetic moment and an enhanced SDW transition temperature (16,15). Kim et al. (23) report a high-energy SDW gap-like feature obtained from the oscillatory response of the optical conductivity at temperatures above T SDW . In fact, with a displacive increase of the Fe-As distance in the phonon-driven state, a lightenhanced SDW is expected in both the oscillatory and displacive responses. In addition, a transient SDW gap robust enough to survive from T SDW up to room temperature is expected to persist for T < T SDW , since the lattice displacement and band modulation induced by the driven phonon were observed for both below and above T SDW (16,15,9). Our result is the first time-resolved optical study focusing on the transient response of the low-frequency SDW gap, which shows persistent gap opening from the displacive response of optical conductivity, and for temperatures both below and above T SDW .
Note that the transient gap develops and decays with different time scales than that of the transient Drude component (Fig. 1C inset and Fig. 1D). This can be understood as the following: the transient Drude comes from the thermalization of photoexcited carriers, which is commonly seen for metals (34). It is a separated process from the transient modification of the lattice structure and band structure (9,15) which lead to the transient gap. Since iron pnictides are multiband materials, the coexistence of photoexcited carriers challenges the detection of the transient gap.
Here, time-resolved optical spectroscopy has advantages in resolving the transient gap from the background of photoexcited carriers thanks to its high-energy resolution (1 meV).

Conclusion
We observed a transient gap generation in BaFe 2 As 2 when the A 1g phonon is excited by laser pulses. The transient gap develops at a higher energy than the equilibrium SDW gap and involves a substantial spectral weight redistribution. The feature appears at early-time delays with a short lifetime. The transient gap formation persists up to room temperature, indicating a robust band structure modification in the phonon-driven state, which is likely from an enhanced SDW order as a direct consequence of a transient increasing in the pnictogen height. These observations provide crucial information for future time-resolved investigations on the nature of this newly discovered transient gap. Our finding also opens up new possibilities to study the impact of lattice distortion on superconductivity and nematic order in iron-based superconductors (35,36) via phonon control of the SDW order.

Materials and methods
Near-infrared (800 nm) laser pulses with a 40 fs duration were used to excite the A 1g phonon in BaFe 2 As 2 . The transient optical properties were probed at normal incidence by broadband THz pulses generated by laser-ionized plasma. The THz pulses were detected by EO sampling of the terahertz field in a 100-micron thick GaP and a 300-micron thick GaSe crystal, which cover a A B  Δσ 1 (ω) dω, with the displacive component subtracted. Here, ω 1 = 12 meV and ω 2 = 20 meV. The data were taken at T = 120 K with a pump fluence of 0.53 mJ/ cm 2 . A sinusoidal function with a 5-THz oscillation frequency is shown as a guide to the eye. detection range from 8 to 28 meV and 34 to 70 meV, respectively. The overall time resolutions are 160 fs for low frequency and 50 fs for high frequency, estimated from the THz pulse width. A longpass filter was used to remove the scattered pump photons. For each pump-probe time delay, the relative delay between the pump and the EO sampling pulses were kept fixed while scanning the terahertz transient. This ensures that each point in the terahertz probe field detects the material at the same pump-probe time delay. The terahertz probe field and the pump-induced change in the probe field were simultaneously recorded using two lock-in amplifiers. The complex reflection coefficient of the photoexcited sample was calculated using a multilayer model, which models the material as a fully photoexcited top layer of a thickness equal to the near-infrared pump penetration depth (27 nm), and an unexcited bottom layer retaining the equilibrium optical response. The probe penetration depth is frequency dependent and in the order of 200 nm.