Abstract
The electronic nematic phase is an unconventional state of matter that spontaneously breaks the rotational symmetry of electrons. In ironpnictides/chalcogenides and cuprates, the nematic ordering and fluctuations have been suggested to have asyetunconfirmed roles in superconductivity. However, most studies have been conducted in thermal equilibrium, where the dynamical property and excitation can be masked by the coupling with the lattice. Here we use femtosecond optical pulse to perturb the electronic nematic order in FeSe. Through time, energy, momentum and orbitalresolved photoemission spectroscopy, we detect the ultrafast dynamics of electronic nematicity. In the strongexcitation regime, through the observation of Fermi surface anisotropy, we find a quick disappearance of the nematicity followed by a heavilydamped oscillation. This shortlife nematicity oscillation is seemingly related to the imbalance of Fe 3d_{xz} and d_{yz} orbitals. These phenomena show critical behavior as a function of pump fluence. Our realtime observations reveal the nature of the electronic nematic excitation instantly decoupled from the underlying lattice.
Introduction
Ironbased superconductors exhibit attractive properties such as hightransitiontemperature (T_{c}) superconductivity and complex competing phases^{1}. Their electronic structures consist of multiple iron 3d orbitals, thus giving rise to a variety of antiferroic and ferroic ordering phenomena involving spin and orbital profiles^{2,3,4}. Among these mysterious phases, there has been increasing interest in nematic order^{5,6,7,8,9,10,11,12,13}, which spontaneously breaks the rotational symmetry of electrons and triggers a lattice instability^{8}. Recent investigations by electronic Raman scattering^{14,15} and elastoresistivity measurements^{11} unveiled the fluctation of electronic nematicity and its critical behavior commonly in the optimally doped regimes of different material families^{11}.
FeSe exhibits superconductivity (T_{c} = 9 K) and a nematic order accompanied by the tetragonaltoorthorhombic lattice deformation (T_{s} = 90 K) without any magnetic order^{16}. Its electronic structure is given in Fig. 1 (see also Supplementary Note 1). In the tetragonal phase, FeSe exhibits a circular Fermi surface around the Γ point (Fig. 1a). Along k_{x} (k_{y}), the hole band forming the Fermi surface has the yz (xz) orbital component. Note that such momentum (k)dependent orbital characters keep the fourfold (C_{4}) symmetry (Fig. 1b). In the orthorhombic (nematic) phase, the kdependent orbital polarization^{17} modifies the Fermi surface shape into an elliptical one (nematic Fermi surface) as shown in Fig. 1c, resulting in inequivalent Fermi momenta (k_{F}) along k_{x} and k_{y} (k_{Fx} < k_{Fy}). At the same time, the orbital components at the k_{F}’s are mixed, especially along k_{x} as shown in Fig. 1d (Supplementary Note 2). While these characteristics associated with the nematic order have been verified through intensive angleresolved photoemission spectroscopy (ARPES) studies^{17,18,19,20}, the understanding of dynamics and excitations peculiar to this condensed state remain lacking.
Timeresolved ARPES (TARPES) has the potential impact to resolve electron dynamics not only in energy and momentum but also into spin and orbital degrees of freedom. A wide range of materials have been investigated for clarifying their electronic dynamics, such as the recombination of the superconducting quasiparticles^{21,22}, fluctuating charge density waves^{23}, collapse of longrange order^{24,25}, and coupling with optical phonons^{25,26,27}. These results, which are inaccessible from equilibrium state, contributed to the deeper understanding of exotic quantum states, especially those with short lifetimes.
Here, we use TARPES to track the ultrafast dynamics of electronic nematicity in FeSe. By combining detwinned crystals with a linearpolarized probe laser, we can selectively obtain the electrons of xz and yz orbitals (Supplementary Note 3). With this TARPES setup^{28} (Fig. 1e), the ultrafast dynamics of the nematic Fermi surface and the orbitaldependent carrier dynamics can be visualized.
Results
Ultrafast dynamics of nematic Fermi surface
Immediately after photoexcitation (t = 120 fs), the hole bands around the Γ point along k_{x} and k_{y} exhibit remarkable momentum shifts with the opposite signs, and take comparable k_{F} values as indicated by the red and blue arrows in Fig. 2a, b. This observation suggests that the elliptical Fermi surface quickly changes to circular by the photoexcitation, thus indicating the melting of the nematic order. Fig. 2c displays the fluence (F)dependence, where the shift of k_{Fy} (Δk_{F}_{y}) at t = 120 fs gradually increases as a function of F (weakexcitation regime), and saturates at F > F_{c} = ∼200 μJ cm^{−2} where the isotropic Fermi surface is attained (strongexcitation regime).
Here we track the time dependence of Δk_{Fy}(t) for respective F (Fig. 2d). As shown in Fig. 2c, Δk_{Fy}(t) indicates the sudden decrease at t ≈ 120 fs representing the melting of nematicity, followed by the subsequent recovery in ~1 ps. The overall picture of this transient Fermi surface for F > F_{c} is shown in Fig. 2e. We further find that the recovery clearly becomes faster for F > F_{c}, and some modulated feature appears. The time dependences of k_{Fx} and k_{Fy} for 220 μJ cm^{−2}, where the modulation appears most strongly, are presented in Fig. 2f. These data indicate that the C_{2} anisotropy in k_{F} is completely suppressed (k_{Fx} ≈ k_{Fy}) within the time resolution (250 fs), followed by an anomalous hump in the recovery. These behaviors of k_{Fx} and k_{Fy} can be reproduced by the functions including the damped oscillation term in the form of k_{F}(t) = k_{F0} + k_{F1}exp(−t/τ_{1}) + k_{F2}exp(−t/τ_{2}) + k_{F3}exp(−t/τ_{3})cos(2πt/t_{p}) convoluted by the Gaussian of the time resolution, with common values of τ_{1} = 830 ± 50 fs, τ_{2} > 80 ps, τ_{3} = 550 ± 50 fs, and t_{p} = 1.4 ± 0.05 ps. The observed antiphase oscillation of k_{Fx} and k_{Fy} directly represents the Pomeranchuktype oscillation of Fermi surface^{29}, being intensively discussed as the fundamental excitation in the electronic nematic state. The time scale of the oscillatory response (1.4 ps, 3.1 meV) is considerably slow as compared to the coherent A_{1g} optical phonon (190 fs, 22 meV), which is known to strongly couple to the electronic state in this system^{25,26,27}. Their possible interplay is unfortunately hidden in the present TARPES data, possibly due to the duration of the pump pulse (170 fs) comparable to the time period of A_{1g} mode (190 fs) that tends to vanish the coherent oscillation.
Orbitaldependent carrier dynamics
Based on the behavior of transient Fermi surface, we focus on the orbitaldependent carrier dynamics. With ppolarized probe pulse, we obtain the energydistribution curves (EDCs) for xz and yz electrons around the Γ point by integrating k_{y} and k_{x} in 0.00 ± 0.04 Å^{−1}, respectively (see Supplementary Note 3 for experimental settings). The main peak of EDC around −18 meV in Fig. 3a, b, e, f corresponds to the top of the middle (β) hole band sinking below E_{F}, predominantly of yz orbital character (Fig. 1d). In the weakexcitation regime of F = 40 μJ cm^{−2} (Fig. 3a, b), the main peak gets rapidly suppressed, and electrons are excited toward the unoccupied state. Here we track the evolution of the corresponding photoelectron intensities ΔI(t) at E – E_{F} = 7.5 ± 2.5 meV and k = 0.00 ± 0.04 Å^{−1}, i.e. black rectangles in Fig. 1b, d. Figure 3c, d shows that ΔI(t) for xz and yz exhibit the similar exponential decay function with two time constants 850 fs and >80 ps, thus indicating the mostly equivalent relaxation processes of both orbitals. However, we note that the excited tail intensity of EDCs at E > E_{F} is very low for yz, being consistent with the predominantly xz character of the outer (α) hole band top at Γ (Fig. 1d). Substantial spectral weight depletion in the yz states after pumping might be attributed to the photoexcited yz electrons which are partly trapped at the M point. Because of the semimetallic electronic structure, some part of electrons excited by 1.5 eV photons at Γ may quickly gather around the electron bands at M. The momentumdependent signinversion of orbital polarization^{17} realizes the yz dominated electron pocket near E_{F} at M, which may work as the reservoir for photoexcited yz electrons. To fully understand these dynamics, the TARPES covering the whole Brillouin zone is desired.
In the strongexcitation regime, the photoresponse changes drastically. The EDCs in Fig. 3e, f show that the photoexcited states at E > E_{F} also appear in yz, indicating that the C_{4} isotropic state (Fig. 1b) is achieved by the strong photoexcitation (F = 220 μJ cm^{−2}). On the other hand, the excited intensity of xz shows a nonmonotonic relaxation which keeps increasing from t = 120 to 700 fs as indicated by the black arrow in Fig. 3e, being markedly different from yz. As shown in Fig. 3g, h, ΔI(t) of xz exhibits the retarded maximum at t_{ret} = ∼700 fs, whereas the yz electrons show the exponential decay more or less similar to the weakexcitation regime, with the initial maximum at ~250 fs. These contrastive behaviors solely depend on the orbital characters, not on experimental configuration (Supplementary Notes 4 and 5). To discuss the retardation behavior, the F dependence of ΔI(t) for xz is shown in Fig. 3i. In the weakexcitation regime (F < F_{c}), ΔI(t) curves commonly show the simple relaxation with the maximum around 250 fs. With increasing F, the retardation suddenly shows up at F ≈ F_{c}. Its time scale estimated by t_{ret} is 700 fs at F ≈ F_{c} and gradually decreases to 350 fs by increasing F to 430 μJ cm^{−2}.
Fluencedependent dynamics of electronic nematicity
Here we summarize the dynamics of the electronic nematicity in Fig. 4b. By fitting Δk_{Fy}(t) curves in Fig. 2d (Supplementary Note 6), we plot τ_{1} and t_{p}/2 for respective F. τ_{1} is the exponential decay time indicating the quick recovery of nematicity. It shows a constant value (∼800 fs) in the weakexcitation regime and a rapid decrease above F > F_{c}. The time scale of the Fermi surface oscillation indicated by t_{p}/2, which only appears in F > F_{c}, also rapidly decreases from 700 to 300 fs as increasing F. It shows that the oscillation gets more severely damped and hard to observe at high F. We also overlay the time scale of the retarded maximum in xz component t_{ret}. As a result, τ_{1}, t_{p}/2, and t_{ret} similarly show the maximum values at F_{c} = 220 μJ cm^{−2} that monotonically decrease with increasing F, while keeping the common relation τ_{1} ≈ t_{ret} ≈ t_{p}/2. The relation t_{ret} ≈ t_{p}/2 implies that the orbitaldependent carrier dynamics is synchronized with the shortlife nematic Fermi surface oscillation. We note that the transient Fermi surface at t_{p}/2 (≈ t_{ret}) is more elliptical than that expected without the oscillatory response. Such an overshoot of the nematicity in Fermi surface should also appear in the orbitaldependent carrier dynamics. In the process relaxing back from C_{4} isotropic to C_{2} nematic ground state, the electrons at the band top (black rectangle in Fig. 1b, d) change their orbital characters from “(nearly) xz/yz degenerate” to “predominantly xz”. The retarded maximum in I(t) for xz can be thus regarded as an indication of the orbital redistribution from yz to xz (Fig. 4a). The synchronized responses in the Pomenranchuk Fermi surface oscillation and orbitaldependent carrier dynamics thus represent the nematicorbital excitation.
Discussion
Now we discuss the nematicorbital excitation obtained in the present TARPES results by comparing with the nematic dynamics in thermal equilibrium as probed by recent Raman scattering measurements^{15,30}. The electronic Raman spectra of XY symmetry (X and Y are coordinates along the crystal axes of the tetragonal setting) show the characteristic quasielastic peak (QEP) evolving toward T_{s} on cooling the temperature (T), discussed in terms of nematic susceptibility enhancement^{15,30}. The QEP rapidly diminishes at T < T_{s}, on the other hand, and a gap opens in the XY Raman spectra, thus indicating the suppression of lowenergy nematic excitations^{30}. These behaviors are reminiscent of the nematicorbital excitation observed by TARPES, where the peculiar slowing down behavior shows up in F > F_{c}, and the excitation itself suddenly disappears in F < F_{c}. The nematic fluctuation is incoherent in nature, however, by instantaneously triggering the dissolution of the nematic state, it may be appearing as the heavily damped oscillatory response in the time domain.
Further insight of the peculiar F dependence can be obtained by plotting t_{p}^{−1} and τ_{1}^{−1} (Fig. 4c). These values show a more or less Flinear behavior at F > F_{c}, indicating the critical slowing down. At F = F_{c}, t_{p}^{−1} decreases down to 3.1 meV. In F < F_{c}, as already mentioned, the k_{F} oscillation as well as the anomaly in the xz orbital response disappear, and τ_{1}^{−1} becomes constant. In the XY Raman spectrum, the Tlinear behavior was found in the inverse of the QEP intensity above T_{s} (ref. ^{15}), indicative of the Gaussian fluctuation evolving in this regime. Similarly, the elastoresistivity measurement had also revealed the existence of electronic nematic fluctuation at T > T_{s} interpreted as the Curie–Weisslike nematic susceptibility^{30}. Through the analysis of the Tdependent nematic susceptibility in the form of T – T_{0}^{−1}, the authors discuss the meanfield transition temperature T_{0} in terms of the ideal nematic transition purely driven by electrons without any influence of lattice^{15,30}. For FeSe, T_{0} was estimated to be far below T_{s}, i.e. 8, 20 (ref. ^{15}), and 30 K (ref. ^{31}). The Curie–Weisslike behavior of t_{p}^{−1} and τ_{1}^{−1} toward F ≈ 40 ± 20 μJ cm^{−2}, i.e. much smaller than F_{c} = 220 μJ cm^{−2}, may be reflecting that the base temperature of the TARPES measurements (20 K) is close to T_{0}. This scenario is also consistent with the initial photoresponse of Δk_{Fy} with small threshold (<30 μJ cm^{−2}, see Fig. 2c). These results indicate that the electronic nematiciy in the initial ultrafast regime (~120 fs) shows the flexible photoreaction by decoupling from the lattice. Our analysis on the transient electronic temperature (T_{e}) (Supplementary Note 7) indeed shows that T_{e} immediately reaches 88 ± 2 K at 120 fs and then decreases in less than 1 ps (Supplementary Fig. 6). For t > 3 ps, it becomes nearly constant at ~45 K, indicating the realization of quasiequilibrium state where the temperatures of electrons and lattice become equivalent through the electron–lattice coupling^{32}. The maximum lattice temperature is thus much lower than T_{s} (= 90 K), showing that the lattice stays orthorhombic. We also note that the reduction of the lattice orthorhombicity is known to occur in a much slower time scale (e.g. ~30 ps) with a much higher pump fluence (e.g. 3.3 mJ cm^{−2}) for BaFe_{2}As_{2} (ref. ^{33}).
The present results show that the femtosecond photon pulse can perturb the electronic nematic order and instantly decouple it from the lattice. Only in the strongexcitation regime where the nematic state is completely destroyed, there appears the peculiar dynamical process involving the orbital redistribution and shortlife Pomenranchuktype Fermi surface oscillation. This behavior is seemingly related to the critical nematic fluctuation; nevertheless, future theoretical studies on nonequilibrium critical phenomena are highly necessary. The recovery time scale of the nematic Fermi surface is strongly correlated with the shortlife k_{F} oscillation (τ_{1} ≈ t_{p}/2), which also awaits investigations on the dynamics of fluctuation and dissipation in nonequilibrium states. Experimentally, further studies on the nematic dynamics around the quantum critical point in the FeSe_{1−x}S_{x} system^{31} and the coherent nematic resonance mode in the superconducting state is highly desired. Systematic timeresolved diffraction measurements will also help understanding the possible interplay among the nematic excitation and the optical/acoustic phonons^{26,34}. Ultrafast photoexcitation adds to the possibilities for understanding and manipulating the largeamplitude electronic fluctuations associated with phenomena such as unconventional superconductivity, exotic magnetism, thermopower enhancement, and so on.
Methods
Sample preparations
Highquality single crystals of FeSe were grown by the vapor transport method. A mixture of Fe and Se powders was sealed in an evacuated SiO_{2} ampoule together with KCl and AlCl_{3} powders^{16}. The transition temperatures of the single crystals were estimated to be T_{s} = 90 K and T_{c} = 9 K from the electrical resistivity measurements. We showed the data obtained from five single crystals of FeSe which were synthesized less than 2 months before the TARPES measurements.
Time and angleresolved photoemission measurements
The TARPES measurements were done at ISSP, the University of Tokyo^{28}. The laser pulse (1.5 eV and 170 fs duration) delivered from a Ti:Sapphire laser system operating at 250 kHz repetition (Coherent RegA 9000) was split into two branches: one is used as a pump and the other was upconverted into 5.9 eV and used as a probe to generate photoelectrons. The delay origin t = 0 ps and time resolution (250 fs) were determined from the pumpprobe photoemission signal of graphite attached near the sample. The photoelectrons were collected by a VG Scienta R4000 electron analyzer. The E_{F} and the energy resolution (20 meV) were determined by recording the Fermi cutoff of gold in electrical contact to the sample. To detwin the single crystals, we applied an inplane uniaxial tensile strain^{17,19}, which brings the orthorhombic a axis (a > b) along its direction below T_{s}. We chose s and p polarizations to separately observe the xz and yz orbital electrons (see Supplementary Note 3 for the details of experimental geometry and selection rule). Samples were cleaved in situ at room temperature in an ultrahigh vacuum of 5 × 10^{−11} Torr.
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
We thank M. Imada, Y. Yamaji, Y. Gallais and I. Paul for valuable discussions. We acknowledge H. Kontani and Y. Yamakawa for valuable discussions and band calculations. This research was supported by the Photon Frontier Network Program of the MEXT, the CREST project of the JST (Grant Number JPMJCR16F2), GrantinAid for Scientific Research (KAKENHI) (Grant Nos. 15H03687, 15H02106, 15KK0160, 18H01177, 18H05227 and 18H01148) and on Innovative Areas ''Topological Material Science" (No. 15H05852) from Japan Society for the Promotion of Science (JSPS).
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T. Shimojima and K.I. designed the research. T. Shimojima, Y.S., A.N., N.M. and Y.I. performed the TARPES measurements and analyzed the data. S.K., T. Shibauchi, and Y.M. synthesized the single crystals. Y.I. and S.S. set up the TARPES apparatus. T. Shimojima wrote the paper with inputs from S.K., T. Shibauchi, Y.M., Y.I., S.S. and K.I.
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Shimojima, T., Suzuki, Y., Nakamura, A. et al. Ultrafast nematicorbital excitation in FeSe. Nat Commun 10, 1946 (2019). https://doi.org/10.1038/s41467019098695
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DOI: https://doi.org/10.1038/s41467019098695
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