Abstract
Novel phases of matter with unique properties that emerge from quantum and topological protection present an important thrust of modern research. Of particular interest is to engineer these phases on demand using ultrafast external stimuli, such as photoexcitation, which offers prospects of their integration into future devices compatible with optical communication and information technology. Here, we use MeV Ultrafast Electron Diffraction (UED) to show how a transient threedimensional (3D) Dirac semimetal state can be induced by a femtosecond laser pulse in a topological insulator ZrTe_{5}. We observe marked changes in Bragg diffraction, which are characteristic of bond distortions in the photoinduced state. Using the atomic positions refined from the UED, we perform density functional theory (DFT) analysis of the electronic band structure. Our results reveal that the equilibrium state of ZrTe_{5} is a topological insulator with a small band gap of ~ 25 meV, consistent with angleresolved photoemission (ARPES) experiments. However, the gap is closed in the presence of strong spinorbit coupling (SOC) in the photoinduced transient state, where massless Dirac fermions emerge in the chiral band structure. The time scale of the relaxation dynamics to the transient Dirac semimetal state is remarkably long, τ ~ 160 ps, which is two orders of magnitude longer than the conventional phonondriven structural relaxation. The long relaxation is consistent with the vanishing density of states in Dirac spectrum and slow spinrepolarization of the SOCcontrolled band structure accompanying the emergence of Dirac fermions.
Introduction
The strong interest in topological Dirac and Weyl semimetals is rooted both in their fundamental attraction as model systems for experimenting with theories of particle physics and in their unique electronic properties, such as the suppressed backscattering, peculiar surface states, chiral and spinpolarized transport, and novel responses to applied electric and magnetic fields controlled by topological invariance, which are promising for technological applications^{1,2,3,4}. Recently, significant attention gained theoretical ideas of how to prepare these phases on demand by photoexcitation and periodic driving by external stimuli (Floquet state engineering)^{5,6,7,8}. Much less explored are the pathways towards experimental realizations of these theoretical proposals. The first strides in this direction are made by the very recent results on WTe_{2} and MoTe_{2}, where metastable crystal symmetry change leading to a topologically distinct phase was induced by THz light pulses^{9,10}. Here, we discover a transition to a topologically distinct electronic phase which does not rely on the change of the macroscopic symmetry of the crystal lattice and therefore can be photoinduced without an accompanying crystallographic phase transition. This discovery is significant because it provides a pathway towards tuning the band structure topology that is decoupled from complexities, domain size limitations, and relaxation phenomena associated with a bulk phase transition between different crystalline phases^{11}.
Zirconium pentatelluride, ZrTe_{5,} is a remarkable topological material. It was theoretically predicted to be at the phase boundary between a weak topological insulator (TI) and a strong topological insulator^{12} and initially was proposed as a rare example of 3D Dirac semimetal (DSM)^{13,14,15}. Recent highresolution ARPES^{16,17,18} and transport^{19} measurements suggest that ZrTe_{5} is a weak topological insulator, but with a very small band gap (~20 meV) at the Γ (q = 0) point and a tiny Fermi surface hosting charge carriers with very small mass^{14,15}. The WTI nature was corroborated by observing the topological edge states at the steps of ZrTe_{5} crystalline surface^{20}. The bandgap of the insulating state closes under pressure and at 6.2 GPa ZrTe_{5} becomes a (possibly topological) superconductor^{21}. Recently, evidence for straintuned topological phase transition from weak to strong topological insulator with the Dirac semimetal state at the critical point was reported in ZrTe_{5}^{22}. Here, we discover that a topological phase transition from TI to DSM can be induced transiently, by ultrafast optical pumping.
An indication that ultrafast optical control of the topological electronic band structure in ZrTe_{5} is possible has recently been obtained in surfacesensitive timeresolved (tr)ARPES experiments, suggesting potential for technological applications in ultrafast optoelectronics^{23}. A downshift of the valence energy band was observed following photoexcitation with a subpicosecond, 1.55 eV photon pulse, which was attributed to transient heating after optical perturbation. The corresponding electronic equilibration times in the valence and conduction bands, 1.6 ps and 0.8 ps, respectively, were consistent with the conventional electronlattice relaxation^{24,25}. Similarly short, fewps phononmediated relaxation times were observed for hot carrier dynamics in ZrTe_{5} from timeresolved optical reflectivity using similar optical pumping, with even shorter time (~0.25 ps) for electronelectron thermalization^{26}. Here, we use bulksensitive MeV UED to study the temporal dynamics of the photoinduced structural changes in ZrTe_{5}. We discover a transient metastable atomic structure with a markedly longer thermalization time scale (~100–200 ps) consistent with SOCcontrolled relaxation^{27} and deduce the corresponding electronic band structure as the DSM state using DFT calculations.
Results
Experimental procedure and results
ZrTe_{5} is a layered material, where each layer is formed by quasionedimensional trigonal prismatic ZrTe_{3} chains with nonequivalent apical (Te1) and dimer (Te2) tellurium atoms running along the crystalline aaxis, which are bound together along the caxis via pairs of Te (Te3) atoms forming zigzag chains [Fig. 1a]. The prismatic chains and the zigzag Te3 chains form twodimensional sheets of ZrTe_{5} in the ac plane, stacking along the baxis via weak van der Waals interaction. Nevertheless, electronically ZrTe_{5} is a 3D material, with a closed, albeit strongly anisotropic Fermi surface (\(k_{\mathrm{F}}^c/k_{\mathrm{F}}^a\sim k_{\mathrm{F}}^c/k_{\mathrm{F}}^b\sim 5\), where \(k_{\mathrm{F}} = \left( {k_{\mathrm{F}}^a,k_{\mathrm{F}}^b,k_{\mathrm{F}}^c} \right)\) is Fermi wavevector) and strongly anisotropic dispersion and electron mass^{3,15,16,17,28}. We use the orthorhombic lattice notation [space group Cmcm (#63)] with lattice parameters a = 3.9943 Å, b = 14.547 Å, and c = 13.749 Å at 300 K and two formula units per unit cell^{12,29} for the steady state of ZrTe_{5}. The atomic Wyckoff positions are shown in Supplementary Table 1.
In our work, thin single crystals of ZrTe_{5} exfoliated from high quality bulk crystal samples^{3,28} are excited by 1.55 eV, 60 fs laser pulses with the polarization in the ac crystal plane and probed via diffraction of 100 fs, 4.0 MeV electron pulses. Optical properties of the material in the photon energy region around 1.55 eV are obtained with ellipsometry measurements. The imaginary part, 〈ε_{2}〉, of the pseudo dielectric function, 〈ε〉 = 〈ε_{1}〉 + i〈ε_{2}〉 at 300 K is shown in Supplementary Fig. 1; there is weak anisotropy of 〈ε_{2}〉 in this range. The 1.55 eV energy is close to the interband transition, which is centered around 1.3 eV. Interband transitions can lead^{25} to lattice deformation if the intensity of the excitation is sufficiently high. Experiments were performed at temperatures of 55 K and 27 K, with an incident excitation fluence of 3.5 mJ/cm^{2}. No significant difference in dynamical lattice behavior at these two temperatures was observed.
A typical UED diffraction pattern obtained prior to the photoexcitation is shown in Fig. 1b and the difference pattern after and before the photoexcitation in Fig. 1c. Here, the diffraction intensity measured at a large timedelay, t ≈ 800 ps (averaged within the time window [707, 1000] ps), where the lattice dynamics reach quasiequilibrium, is subtracted from the intensity at a negative time delay, t < 0, before arrival of the pump pulse (averaged within the 160 ps time window). A remarkable change in Bragg reflections is observed, which is most clear for the (00L) peaks with systematic increase in intensity for most of the reflections. The intensity of (00L) Bragg reflections is sensitive to intraunitcell atomic displacements, δz_{v}, along the caxis direction (v indexes atom at position z_{v} and with atomic scattering factor f_{v}). In the frozenphonon model of a static distortion of the crystal lattice, such displacements lead to an intensity modulation of (00L) peaks, ΔI_{00L} ~ ∑_{v}f_{v}(L·δz_{v})\(e^{i(2\pi{L{\cdot}z_v})}\)^{2}^{30}, which is roughly consistent with the observed photoinduced change of the Bragg diffraction pattern. These observations clearly indicate an involvement of the displacements of Te2 and Te3 atoms [Fig. 1a], which reside at lowsymmetry 8f Wyckoff positions in the equilibrium ZrTe_{5} structure^{29} (Supplementary Table 1), with z_{Te2} = 0.151 and z_{Te3} = 0.434, respectively, along the z (caxis) direction. While the above formula for intensity change induced by displacement obtained in kinematic, singlescattering (Born) approximation is very useful for gaining qualitative understanding of atomic displacements, it can rarely (as in ref. ^{9}), if at all, be used for the quantitative analysis of electron diffraction where the interaction of the scattering electrons with the system is strong and multiple scattering effects cannot be neglected. Here, we quantitatively analyze the lattice structure of ZrTe_{5} and refine z_{Te2} and z_{Te3} positions from the UED patterns before and after photoexcitation using the Blochwave dynamical scattering theory, which accurately accounts for multiple scattering effects. The corresponding calculated electron diffraction pattern for the unperturbed equilibrium structure^{29} is shown in Fig. 1d.
Temporal dynamics of scattering
An important further insight is provided by the quantitative analysis of the temporal dynamics of Bragg peak intensities encoding the photoinduced atomic displacements, which is presented in Fig. 2. At the early stage of the photoexcitation, the dynamics is reflected in intensity transfer from Bragg peaks to thermal diffuse scattering (TDS), Fig. 2a. The decrease of Bragg peak intensities is due to the lattice deformation and the increased atomic vibration as a result of energy transfer from the photoexcited electrons to the lattice. The observed time constant that describes these initial dynamics of both TDS and total Bragg scattering is τ_{1} ≈ 3 ps, which is consistent with phononphonon relaxation and is only slightly slower than the time scale of electronphonon coupling measured by ARPES^{23}. After the initial fast drop, the total Bragg scattering starts increasing, but on a very much slower time scale, τ_{2} ≈ 150 ps. This increase is accompanied by a similarly slow further growth of diffuse scattering intensity, which indicates that both signals arise from the same underlying physics.
In our experiment, the intensity of the transmitted central beam is monitored by a separate detector (see “Methods” for details). This allows us to measure total scattering, which provides an important consistency validation. We notice that the intensity of the central beam has a downward trend within the 1 ns window, which becomes very clear after averaging over the multiple measured timeseries, Fig. 2b. The dynamics of the central beam can be described with a single exponent with time constant ≈150 ps, which is consistent with the slow recovery of Bragg peaks and a concomitant increase in thermal diffuse scattering. This indicates that the depletion of the central beam is consequential to the increase of scattering governed by the slow relaxation process.
The individual Bragg peaks also reveal the same twotimescales dynamics, with an initial fast drop governed by the time constant τ_{1} of few ps and a slow recovery within 1 ns window with a much longer relaxation time, τ_{1} ~ 100−200 ps. While the intensity of the majority of Bragg peaks recovers after the initial drop, the level to which it recovers is strongly qdependent [Fig. 2c, d]. Some peaks, notably those having nonzero component along (00L) direction, including (00L) peaks in Fig. 2c, reach higher intensity than in their initial, unperturbed state, which can be explained by the presence of atomic displacements along z (caxis) lattice direction in the transient metastable state. On the other hand, (HH0) peaks show significantly different dynamics, with no recovery at all, Fig. 2d. This indicates the absence of photoinduced atomic displacements in this direction, or a possibility that the relevant displacements are scattered in phase, yielding cancellation of their contributions to the observed Bragg intensity.
The two distinct relaxation times, τ_{1} and τ_{2}, obtained by fitting the intensity of Bragg peaks at different wave vectors, q, to twotime relaxation dynamics, ΔI = A(1 − \(e^{t/{\tau_1}}\)) + B(1 − \({e^{t  {\tau _2}}}\)), are presented in Fig. 3a. While the short relaxation time of a few ps, τ_{1}, is consistent with the electronphonon and phononphonon scattering mechanisms^{24,25}, the long time, τ_{2} = 160(30) ps, which is roughly two orders of magnitude larger, indicates that conventional electronphonon scattering is suppressed and implicates a different mechanism, involving much weaker interactions compared to the Coulomb forces that govern electron and phonon scattering. This is entirely consistent with the involvement of SOC, which is broadly recognized to be important for determining the electronic properties of ZrTe_{5}^{3,17,18}. SOC is a relativistic interaction that in atomic systems has a degree of smallness described by the fine structure constant, α ≈ 1/137, i. e. is typically two orders of magnitude weaker compared to Coulomb interactions. SOCcontrolled electronic spin relaxation times of the order of hundreds of picoseconds to few nanoseconds are indeed observed in semiconductor quantum wells^{27,31,32} and in bulk Ge^{33} and graphene^{34}. The long relaxation times result from the weakness of SOC compared to the Coulomb interaction that governs conventional charge relaxation, combined with the small density of conduction electrons. In the case of Dirac electrons in graphene, as well as in the present case of ZrTe_{5}, the latter is a consequence of the vanishing density of states near the Dirac point^{35}.
Blochwave dynamical scattering structure refinement
In order to quantitatively analyze the photoinduced changes of ZrTe_{5} crystalline lattice and determine the positions of Te atoms in the transient metastable photoexcited state, we conducted a structural refinement by comparing the experimental electron diffraction patterns with the ones calculated using the Blochwave dynamical scattering method. We focus on the (00L) reflections, of which sufficient number (up to L = 20) are present in our data and which show clear and systematic changes in the difference pattern [Fig. 1c]. As discussed above, this allows us to refine the positions, z_{Te3} and z_{Te2}, of Te3 and Te2 atoms at the lowsymmetry crystallographic 8f Wyckoff site and DebyeWaller (DW) factor, which quantifies the degree of crystallographic disorder and reflects the strength of TDS. We note that displacement of Te1 and Zr atoms along the caxis alters the crystal symmetry of ZrTe_{5} structure, which was not observed in our UED experiment.
The results of the refinement are presented in Fig. 3b, which shows the (00L) Bragg intensity profiles measured by UED before (top) and after (bottom) the photoexcitation along with the best fits obtained using Blochwave ED calculations and varying the z_{Te3} and z_{Te3} atomic positions and DW factor. We used χ^{2} analysis (see “Methods”) to evaluate the goodness of the fit. We first refine the diffraction pattern measured at the steady state, before the photoexcitation. In addition to the Te3 and Te2 atomic positions, in this refinement we also determine the sample geometry, including sample thickness and minor crystal tilt and bending, and DW factor, B = 0.46. The values of the atomic positions obtained in this refinement, z_{Te2} = 0.151 and z_{Te3} = 0.434, are in agreement with the results of ref. ^{29} (Supplementary Table 1). We then keep the sample geometry unchanged and analyze the UED patterns in the photoexcited metastable state at longtime delays, t ≈ 800 ps. Here, we use an iterative procedure where we first keep Te3 atoms at their steadystate position and vary the Te2 position (green circles in Fig. 3c) to obtain z_{Te2} = 0.151(1) for the minimum χ^{2} ≈ 1.24. We then vary the position of Te3 at this fixed position of Te2 [black circles in Fig. 3c] to determine z_{Te3} = 0.432(1) and B = 0.52, with significantly improved goodness of fit (χ^{2} ≈ 1.03; for 430 free parameters in the fit, the 5% test of statistical significance corresponds to χ^{2} ≈ 1.11). The increased value of DW factor is in agreement with the observed increase of TDS in the photoexcited state [Fig. 3a, b]. We then again vary the Te2 atom position using the newly obtained z_{Te3} = 0.432 [red circles in Fig. 3c] to verify that the global minimum is achieved. We thus conclude that the observed marked changes of the Bragg reflection pattern in the transient photoexcited state induced by a femtosecond laser pulse result from a small but clearly identifiable displacement of the Te3 atoms and a much smaller, barely identifiable displacement of the Te2 atoms, which we were able to refine in our analysis.
Discussion
In order to understand the physics underlying the observed transient structural change, its relation to the electronic properties of ZrTe_{5} and the role of SOC, we performed the first principles DFT calculations of the electronic band structure, which are presented in Fig. 4. The photoinduced structural modification in ZrTe_{5} is characterized by the displacement of Te3 atoms in the 8f Wyckoff positions along the caxis direction, from z_{Te3} = 0.434 to z_{Te3} = 0.432, which corresponds to an elongation of the Te3–Te3 bond by ~1% [Fig. 1a and inset of Fig. 3a]. Such a selective response of Te3 atoms to the laser pump agrees well with the electronic density of states (DOS) where the dominant contribution to the DOS at and above the Fermi level is provided by a large peak derived from 5p orbitals of the Te3 atoms [Fig. 4a]. The 1.55 eV incident photons excite electrons from the valence bands to the conduction bands, preferentially populating the Te3 derived states contributing to this peak. The resulting increased Coulomb repulsion pushes Te3 atoms apart, thus weakening the Te3–Te3 bond. Since the DOS at the Fermi level is predominantly contributed by the Te3 atoms’ 5p orbitals, the seemingly small change in the structural parameters could affect the lowenergy electronic structure significantly.
To explore the evolution of photoexcitation modified band structure of ZrTe_{5}, we performed a series of the firstprinciples calculations for z_{Te3} = 0.430−0.437 (see Supplementary Discussion and Supplementary Figs. 2–5 for details). The total energy minimum occurs at z_{Te3} = 0.434 (Supplementary Fig. 2), in good agreement with the experiment. The corresponding calculated band structure reveals that the equilibrium state of ZrTe_{5} has a small direct gap of ≈25 meV at the Γpoint and a smaller indirect gap between Γ and M points [Fig. 4c], also in good agreement with the ARPES results. In sharp contrast, at z_{Te3} = 0.432 both gaps are closed and Dirac point emerges at the Brillouin zone center (Γ point), manifesting a photoinduced Lifshitztype phase transition from topological insulator to Dirac semimetal [Fig. 4(d),(e)]. Wannier functional analysis of the electronic structure reveals a charge transfer of ~0.6% from Te1 to Te3 atoms accompanying this displacement (such displacement corresponds to the 15–19 meV A_{g} Ramanactive modes of lattice vibrations^{21}). This is consistent with the picture that the 1.55 eV laser illumination weakens the Te3–Te3 bond by selectively moving Te3 atoms apart. The calculated total energy per formula unit for the transient photoexcited state at t ≈ 800 ps (z_{Te3} = 0.432) is only 12 meV higher than of the equilibrium structure at time zero (z_{Te3} = 0.434). Remarkably, band structure calculations in the absence of SOC show that the gap is not closed, and the Dirac semimetal state is not formed neither at time zero, nor in the photoexcited structure at t ≈ 800 ps [Supplementary Fig. 4]. Hence, it is the strong SOC in the ZrTe_{5} crystal that locks electronic spins and momenta, imparting electronic charge quasiparticles with chiral nature^{3,36} that is fully responsible for the formation of the transient photoinduced DSM state.
Strong SOC in ZrTe_{5} has wideranging experimental consequences. In magnetotransport, SOC is manifested in a very large Lande factor, g ≈ 15.4−24.3, observed from Zeeman splitting^{13,14,37}. A circular dichroic (CD)ARPES directly reveals the SOCcontrolled chiral band structure, where electronic states near the Fermi level are spinpolarized^{36}. This is consistent with the chiral magnetic effect observed in longitudinal magnetotransport^{3}. Chirality protection can also explain the exceptional quasiparticle coherence, which is revealed by recordnarrow ARPES spectra^{17} and remarkably robust quantum transport underpinning a number of unusual and fascinating novel phenomena, such as vanishing quantum oscillations (zerospin effect)^{19}, 3D quantum Hall effect^{28}, the anomalous Hall effect^{38}, and twoparticle resonant states^{39}. The exceptionally long, 160 ± 30 ps equilibration time of the photoexcited transient state in ZrTe_{5}, which DFT calculations show to be DSM observed in our present work, is very naturally explained by a spinrelaxation time of the SOCgoverned chiral electronic structure. As we show in Supplementary Figs. 4 and 5, the closure of Dirac gap in ZrTe_{5} band structure is governed by SOC. Hence, the newly emergent electronic Dirac quasiparticles are chiral (helical)^{40}, with spinmomentum locking that is distinct from that in the static TI phase. The electronic spin reequilibration that is invariably required for the formation of the transient Dirac state relies on weak magnetic interactions and therefore must involve a correspondingly long SOC controlled spin relaxation time, such as observed in semiconductor quantum wells^{27,31,32}, bulk Ge^{33}, and graphene^{34}, and as we observe here. The electronphonon relaxation mechanisms, on the other hand, are suppressed due to the vanishing density of states in the Dirac electronic spectrum^{35}.
In conclusion, the simultaneously acquired temporal evolution of Bragg intensity of many reflections enables us to observe the subtle changes in atomic structure of complex electronic materials after pulsed laser excitation^{11,41,42}. Here, we report a photoinduced deformation of the local structure in ZrTe_{5}, which selectively weakens specific TeTe bond and underlies electronic topological phase transition to a Dirac semimetal. The optical excitation with a femtosecond laser pulse induces metastable transient state whose energy is only slightly above the ground state. The change in atomic positions in the photoinduced state is quantitatively determined from the Bragg intensities of UED through structural refinement using Blochwave dynamical scattering theory. The DFT band structure calculations show that in the presence of spinorbit coupling this photoinduced metastable state features chiral Dirac quasiparticles, which emerge at the Γpoint. The equilibration time to the transient Dirac semimetal observed in this work is about two orders of magnitude longer than phononmediated thermalization times, consistent with the vanishing density of states in Dirac spectrum and slow spin repolarization of SOCgoverned chiral electronic state. We note that similar considerations might apply to equally long relaxation times of the photoexcited coherent atomic displacements observed in Bi, another wellknown topological material with strong SOC^{43}. Our results open exciting new opportunities for photoninduced band engineering of topological DSM states and call for a number of followup studies. Further support to our findings can be obtained by timeresolved CDARPES experiments^{23,36}, which can directly probe the relaxation times of the chiral band structure. The coherent atomic displacements observed in our work indicate connection to a particular optic phonon mode, thus suggesting a possibility of energyselective tuning of the band structure in ZrTe_{5} by populating this mode using THz excitation.
When our manuscript was under review, we became aware of the optical pumpprobe work by Vaswani et al.^{44}, which fully corroborates our observations. There, a THzpumpfield induced metastable phase with unique, Raman phononassisted topological switching dynamics and with lifetime in excess of 100 ps was observed in ZrTe_{5}. Using firstprinciples modeling similar to ours, the authors identify a modeselective Raman coupling driving the system from strong to weak topological insulator with a Dirac semimetal phase established at a critical atomic displacement. In their case, the topological transition is controlled by the phonon coherent pumping, as suggested above.
Methods
Single crystalline samples
Single crystalline ZrTe_{5} samples were prepared via a Teflux method, as described in^{3}. High purity Zr and Te elemental mixture Zr_{0.0025}Te_{0.9975} were sealed under vacuum in a doublewalled quartz ampule and first melted at 900 °C in a box furnace and fully rocked to achieve homogeneity for 72 h. The melt was followed by slow cooling and rapid heating treatment between 445 °C and 505 °C for 21 days, in order to remelt crystals with small sizes. The resultant single crystals were typically ~0.1 × 0.3 × 20 mm^{3}. Crystals were chemically and structurally analyzed by powder Xray diffraction, scanning electron microscopy with energy dispersive Xray spectroscopy, and transmission electron microscopy. The samples for UED measurements were exfoliated using Scotch tape, yielding typical lateral crystal size around 50–100 um. The flakes have an average thickness around 100 nm as determined with electron energy loss spectroscopy.
Pumpprobe diffraction experiments
Pumpprobe diffraction experiments were performed at SLAC using the 4.0 MeVUED facility with 3.5 mJ/cm^{2} excitation fluence (1.55 eV pump) at 55 K and 27 K. The exposure time of a single shot for excitation and probing were 60 fs and 100 fs, respectively; 900 singleshot images were integrated at each time step. The time interval between measured points varied from 0.25 ps in the region of fast dynamics to 26 ps is the region of slow dynamics, as reflected by the density of points in Fig. 2. In the experimental setup the center beam was monitored by a separate detector. For quantitative intensity analysis and minimizing the effect of longterm electron count fluctuation due to the possible beam drifts intensities of the diffraction patterns in all the analysis were normalized by the corresponding value of the central beam intensity.
Structure refinement
Structure refinement was carried out by quantitatively comparing the intensities of Bragg reflections before and after photoexcitation with the ones calculated using the Blochwave dynamical scattering method. We used \(\chi^{2} = \frac{1}{N}{\sum \nolimits_i} {\left( {\frac{{{\boldsymbol{I}}_i^{{\mathrm{exp}}}  a  b{\boldsymbol{I}}_i^{{\mathrm{cal}}}}}{{\sigma _i}}} \right)^2}\) to evaluate the goodness of fit, where superscript “exp” refers to experimentally measured intensity and “cal” refers to calculated intensity, the subscript i numbers data points in the (00L) scan, and N = 430 is the total number of data points. σ_{i} are the standard deviations, which were obtained as mean square deviations from the average for the set of diffraction patterns collected within the respective time window and a and b are fitting parameters corresponding to the background and intensity scaling constant. The calculated intensity accounts for diffraction from a single crystal flake with its plane horizontal and [010] parallel to the incident electron beam and a smaller twisted flake with [1–10] along the incident beam [see Fig. 1c]. The refinement of the diffraction patterns before photoexcitation was used to determine the sample geometry, which included sample thickness, small sample tilt, and bending. From the fitting, the thickness of the [010] single crystal flake was determined to be 80 nm and the thickness of the smaller [1–10] flake was 51 nm. The minimum χ^{2} obtained in refinement before and after photoexcitation were 1.02 and 1.03, respectively.
Firstprinciples calculations
The firstprinciples calculations were performed by using the WIEN2K (version 18.2) implementation^{45} of the full potential linearized augmented planewave method in the generalized gradient approximation^{46} of density functional theory with the SOC treated within the second variational method. The basis size was determined by R_{mt}K_{max} = 7 and the primitive Brillouin zone was sampled with a regular 24 × 24 × 6 mesh containing 628 irreducible k points to achieve energy convergence of 1 meV. The band structure was plotted in a dense 721 kpoint path to show the opening and closing of the small gap at the Brillouin zone center.
Data availability
The data that supports the findings of this study are available within the article [and its Supplementary Material].
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Acknowledgements
We gratefully acknowledge discussions with Q. Li and J. Tranquada and help of T.N. Stanislavchuk with ellipsometry measurements. This work at Brookhaven National Laboratory was supported by Office of Basic Energy Sciences (BES), Division of Materials Sciences and Engineering, U.S. Department of Energy (DOE), under contract DESC0012704. We also acknowledge the use of Ellipsomentry facility at the Center for Functional Nanomaterials, a DOE user facility at BNL sponsored by the DOE BES Scientific User Facilities Division under the same contract. The SLAC MeVUED is supported by the DOE BES Scientific User Facilities Division Accelerator and Detector R&D program under contract No. DEAC0276SF00515.
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Y.Z. conceived and directed the project. Y.Z. and T.K. coordinated the UED experiment with X.J.W. T.K. conducted the UED experiment with the assistance from J.Y. and J.T. G.G. provided the samples. T.K., L.W., and I.Z. analyzed the data and prepared the figures with input from Y.Z. L.W. carried out structure refinement using the Blochwave method. WG.Y. performed the ab initio DFT calculations. I.Z. and WG.Y. proposed the interpretation of the results. I.Z. and T.K. wrote the paper with input from Y.Z. and all authors.
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Konstantinova, T., Wu, L., Yin, WG. et al. Photoinduced Dirac semimetal in ZrTe_{5}. npj Quantum Mater. 5, 80 (2020). https://doi.org/10.1038/s41535020002808
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