Photoinduced Dirac semimetal in ZrTe5

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 three-dimensional (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 $\sim$25 meV, consistent with angle-resolved photoemission (ARPES) experiments. However, the gap is closed in the presence of strong spin-orbit 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, $\tau \sim$160 ps, which is two orders of magnitude longer than the conventional phonon-driven structural relaxation. The long relaxation is consistent with the vanishing density of states in Dirac spectrum and slow spin-repolarization of the SOC-controlled 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 WTe2 and MoTe2, 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, ZrTe5 , 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 ZrTe5 is a weak topological insulator, but with a very small band gap (~ 20 meV) at the Γ ( = 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 ZrTe5 crystalline surface 20 . The bandgap of the insulating state closes under pressure and at 6.2 GPa ZrTe5 becomes a (possibly topological) superconductor 21 . Recently, evidence for strain-tuned topological phase transition from weak to strong topological insulator with the Dirac semimetal state at the critical point was reported in ZrTe5 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 ZrTe5 is possible has recently been obtained in surface-sensitive time-resolved (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 sub-picosecond, 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 electron-lattice relaxation 24,25 . Similarly short, few-ps phonon-mediated relaxation times were observed for hot carrier dynamics in ZrTe5 from time-resolved optical reflectivity using similar optical pumping, with even shorter time (~ 0.25 ps) for electron-electron thermalization 26 .
Here, we use bulk-sensitive MeV UED to study the temporal dynamics of the photoinduced structural changes in ZrTe5. We discover a transient metastable atomic structure with a markedly longer thermalization time scale (~ 100-200 ps) consistent with SOC-controlled relaxation 27 and deduce the corresponding electronic band structure as the DSM state using DFT calculations.

Experimental procedure and results
ZrTe5 is a layered material, where each layer is formed by quasi-one-dimensional trigonal prismatic ZrTe3 chains with non-equivalent apical (Te1) and dimer (Te2) tellurium atoms running along the crystalline -axis, which are bound together along the -axis via pairs of Te (Te3) atoms forming zigzag chains [ Fig.   1(a)]. The prismatic chains and the zigzag Te3 chains form two-dimensional sheets of ZrTe5 in the plane, stacking along the -axis via weak van der Waals interaction. Nevertheless, electronically ZrTe5 is a 3D material, with a closed, albeit strongly anisotropic Fermi surface ( F / F ~ F / F ~ 5, where F = � F , F , F � 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 = 3.9943Å, = 14.547 Å, and = 13.749 Å at 300 K and two formula units per unit cell 12,29 for the steady state of ZrTe5. The atomic Wyckoff positions are shown in Supplementary Table 1. In our work, thin single crystals of ZrTe5 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, 〈 2 〉, of the pseudo dielectric function, 〈 〉 = 〈 1 〉 + 〈 2 〉, at 300 K is shown in Supplementary Figure 1; there is weak anisotropy of 〈 2 〉 in this range. The 1.55eV energy is close to the inter-band 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.1(b) and the difference pattern after and before the photoexcitation in Fig.1(c). Here, the diffraction intensity measured at a large time-delay, ≈ 800 ps (averaged within the time window [707, 1000] ps), where the lattice dynamics reach quasi-equilibrium, is subtracted from the intensity at a negative time delay, < 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 (00 ) peaks with systematic increase in intensity for most of the reflections. The intensity of (00 ) Bragg reflections is sensitive to intra-unit-cell atomic displacements, , along the c-axis direction ( indexes atom at position and with atomic scattering factor ). In the frozen-phonon model of a static distortion of the crystal lattice, such displacements lead to an intensity modulation of (00 ) peaks,  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 ZrTe5 and refine Te2 and Te3 positions from the UED patterns before and after photoexcitation using the Bloch-wave 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. 1(d).

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. 2(a). 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 1 ≈ 3 ps, which is consistent with phonon-phonon relaxation and is only slightly slower than the time scale of electron-phonon coupling measured by ARPES 23 . After the initial fast drop, the total Bragg scattering starts increasing, but on a very much slower time scale, 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 time-series, Fig.   2 The two distinct relaxation times, 1 and 2 , obtained by fitting the intensity of Bragg peaks at different wave vectors, , to two-time relaxation dynamics, Fig. 3(a). While the short relaxation time of a few ps, 1 , is consistent with the electronphonon and phonon-phonon scattering mechanisms 24, 25 , the long time, 2 = 160(30) ps, which is roughly two orders of magnitude larger, indicates that conventional electron-phonon 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 ZrTe5 3, 17, 18 . SOC is a relativistic interaction that in atomic systems has a degree of 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 -axis alters the crystal symmetry of ZrTe5 structure, which was not observed in our UED experiment.
The results of the refinement are presented in Figure 3(b), which shows the (00 ) Bragg intensity profiles measured by UED before (top) and after (bottom) the photoexcitation along with the best fits obtained using Bloch-wave ED calculations and varying the Te3 and Te2 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  Table 1). We then keep the sample geometry unchanged and analyze the UED patterns in the photo-excited metastable state at long time delays, ≈ 800 ps. Here, we use an iterative procedure where we first keep Te3 atoms at their steady-state position and vary the Te2 position (green circles in 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 When our manuscript was under review, we became aware of the optical pump-probe work by C.
Vaswani, et al. 44 , which fully corroborates our observations. There, a THz-pump-field induced metastable phase with unique, Raman phonon-assisted topological switching dynamics and with lifetime in excess of 100 ps was observed in ZrTe5. Using first-principles 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 ZrTe5 samples were prepared via a Te-flux method, as described in 3  Structure refinement was carried out by quantitatively comparing the intensities of Bragg reflections before and after photoexcitation with the ones calculated using the Bloch-wave dynamical scattering method. We used to evaluate the goodness of fit, where superscript "exp" refers to experimentally measured intensity and "cal" refers to calculated intensity, the subscript numbers data points in the (0 0 ) scan, and = 430 is the total number of data points. 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][2][3][4][5][6][7][8][9][10] along the incident beam [see Fig. 1(c)]. 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][2][3][4][5][6][7][8][9][10] flake was 51 nm. The minimum 2 obtained in refinement before and after photoexcitation were 1.02 and 1.03, respectively.
The first-principles calculations were performed by using the WIEN2K (version 18.2) implementation 45 of the full potential linearized augmented plane-wave 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 RmtKmax = 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 k-point path to show the opening and closing of the small gap at the Brillouin zone center.

Data Availability statement
The data that supports the findings of this study are available within the article [and its supplementary material].

Acknowledgements
We gratefully acknowledge discussions with Q. Li