Ultrafast low-energy electron diffraction traces phase-ordering kinetics of charge density waves

We introduce ultrafast low-energy electron diffraction (ULEED) in backscattering for the study of structural dynamics at surfaces. Using a tip-based source of ultrashort electron pulses, we investigate the optically-driven transition between charge-density wave phases at the surface of 1T-TaS2. Employing spot-profile analysis enabled by the large transfer width of the instrument, we resolve the phase-ordering kinetics in the nascent incommensurate charge-density wave phase. We attribute the observed power-law scaling of the correlation length to the annihilation of topological defects resembling edge-dislocations of the charge-ordered lattice. Our work opens up the study of a wide class of structural transitions at surfaces and in low-dimensional systems. The reduced dimensionality and broken symmetry of a surface endows it with unique physical and chemical properties that drastically differ from the bulk1,2. Prominent surface-specific features involve the electronic, atomic and spin structure, as manifest in modified band structures3,4, surface reconstructions1 or topological states2,5. Many of these phenomena exhibit highly-complex couplings and correlations, which are difficult to disentangle using steady-state analyses of systems in equilibrium. As a result, ultrafast spectroscopy has become an indispensable means to identify the hierarchy and strengths of interactions in the time-domain, by probing the response of materials and surfaces excited strongly out of equilibrium6. Specifically, time-resolved realizations of optical and photoemission spectroscopy yield comprehensive insights into the transient state of the electron and spin systems3,5,7–11. In contrast, access to the structural degrees of freedom with ultimate surface sensitivity and high temporal resolution remains limited, despite notable achievements in time-resolved reflection highenergy electron diffraction (RHEED)12–16. In order to reach a detailed and quantitative understanding of ultrafast structural dynamics at surfaces, a time-resolved implementation of low-energy electron diffraction (LEED) is highly desirable. Although LEED is the most widely used and broadly applicable diffractive technique for surface characterization, an ultrafast realization has proven very challenging17–21. Recently, using the monolayer sensitivity of low-energy electrons, we introduced ultrafast LEED in transmission, studying the dynamics of a polymer superstructure on freestanding graphene20. However, a backscattering geometry promises a greatly expanded range of accessible systems and phenomena, including the dynamics of surface reconstructions, molecular adsorbates, or structural phase transitions. In this work, we present the development of ultrafast low-energy electron diffraction (ULEED) and demonstrate its applicability for the study of structural phase transitions at surfaces. In particular, we investigate the optically-driven transition between two prominent charge-density wave (CDW) phases at the surface of single crystalline 1T-TaS2. We track the formation and nonequilibrium temporal evolution of the incommensurate CDW phase, and identify a coarsening of the CDW texture by analyzing diffraction intensities and spot profiles. Enabled by a compact electron source based on a nanotip photoemitter, ULEED represents a powerful and complementary addition to the toolbox of ultrafast surface science. Fig. 1: ULEED setup and high-resolution diffraction pattern from 1T-TaS2. a, Schematic of the experimental setup for ultrafast low-energy electron diffraction (ULEED). Inset: Electron micrograph of the nanometric photocathode made from an electrochemically etched tungsten tip. b, Miniaturized laser-driven electron source. Inset: Tungsten tip, visible through the hole for laser illumination. c, Electron pulse duration at a kinetic energy of 100 eV, measured using a transient electric field-effect. d, LEED pattern of the NC CDW room temperature phase, recorded with pulsed 100-eV electrons from the miniaturized laser-driven source (logarithmic color scale). A retarding voltage of -20 V is applied at the detector front plate. e, Line profile of the (00) diffraction peak, illustrating high transversal coherence of the source. The fitted spot width of 0.03 Å-1 (FWHM) corresponds to a transfer width of 21 nm. f, Close-up of region marked in (a) showing second-order CDW diffraction spots. g, Line profile of CDW diffraction spots shown in (f), fitted with Lorentzian peak profiles. ULEED is part of a larger family of optical-pump/electron-probe schemes, in which an ultrashort electron pulse samples the momentary state of an optically-excited system by diffraction. In these approaches, the temporal resolution is limited by the electron pulse duration at the specimen position, which is broadened by Coulomb interactions within the electron pulse, velocity dispersion and path length differences upon propagation from the photoelectron source to the sample. In high-energy ultrafast electron diffraction (UED)22–28 and ultrafast transmission electron microscopy (UTEM)29–33, femtosecond temporal resolution is achieved by radio-frequency pulse compression34–36 or reduced propagation distances with tailored gun designs22,32,37. Due to longer electron flight durations, time-resolved experiments with low-energy electron pulses face the challenge of a greatly increased impact of any effect leading to pulse broadening. Moreover, in order to minimize the sample-source distance in the backscattering geometry of LEED, the outer diameter of a pulsed electron gun needs to be reduced accordingly for obtaining diffraction images of sufficient solid angle (cf. Fig. 1a). Addressing these issues, we developed a particularly compact and easily manufactured ultrafast low-energy electron source. It is composed of a sharp tungsten tip (apex radius <25 nm) inserted into an electrostatic lens assembly for acceleration and beam focusing. The nanotip photocathode, suppressor, extractor and gun lens electrodes (aperture radii 200 μm) are contacted and shielded by a flexible printed circuit board (FPCB) (Fig. 1b). Due to its small outer diameter of 2 mm, the FPCB housing allows for operational distances of few millimeters from the sample position, while maintaining the visibility of the diffraction pattern. We generate ultrashort electron pulses via two-photon photoemission (2PPE) by illuminating the tip with 400 nm laser pulses (40 fs duration), as recently demonstrated for low-energy transmission experiments20 and in UTEM32. Beam collimation at the typical operation energies of the gun (40-150 eV) is ensured by optimization of all corresponding electrode voltages. The temporal resolution of the setup is characterized by electron-laser cross-correlation using the transient-electric-field (TEF) effect20,38–40 or the fastest structural responses in backscattering diffraction. For an energy of 100 eV and one to five electrons per pulse, we obtain a temporal resolution down to 16 ps (Fig. 1c), sufficient for investigating a variety of structural evolutions at surfaces. The nanometric photocathode constitutes an electron source with a strongly confined emission area41,42, leading to beams of high transversal coherence length20,32,43. Employing high-dynamic range (16 bit) detection using a phosphor-screen microchannel plate (MCP, Hamamatsu F2226-24P) detector and a cooled CMOS camera, we obtain LEED images of excellent quality, with a momentum resolution = 0.03 Å-1 (cf. Fig. 1e) corresponding to a transfer width of 2 /Δ = 21 nm for a spot size on the sample below 100 μm (full-width-at-half-maximum, FWHM). In a first application of these experimental capabilities, we study the dynamics of a structural phase transition at the surface of 1T-TaS2. This compound exhibits a variety of equilibrium44,45 and metastable46 CDW phases that are coupled to periodic lattice distortions (PLD) and, at low temperatures, are accompanied by electron localization47 or orbital order48. The roomtemperature, so-called “nearly commensurate” (NC) CDW phase, features a particularly interesting structure: It is composed of a close-to-hexagonal arrangement of domain-like commensurate (C) areas separated by discommensurations, which lack complete periodicity49. A LEED pattern of the 1T-TaS2 surface in the NC phase, cleaved in ultrahigh vacuum, is displayed in Fig. 1d (100 eV energy, angle of incidence 6°, logarithmic intensity scale, recorded using nanotip photoelectrons). The image exhibits a multitude of sharp and well-separated diffraction peaks spanning three orders of magnitude in intensity. Specifically, the atomic-lattice Bragg peaks (indexed, for simplicity hereafter called Bragg peaks) are surrounded by six PLD-induced satellite spots each, which are rotated by an angle of ~12° to the lattice44. The large transfer width of the setup and the high signal-to-noise ratio allow us to clearly resolve the closely-spaced higher-order diffraction peaks (Figs. 1f, g), which result from the domain-like structure of the NC phase49. At temperatures above 353 K, 1T-TaS2 exhibits a transition to an incommensurate (IC) CDW phase with wave vectors parallel to those of the atomic lattice44. Hence, this structural phase transition is associated with the appearance of satellite diffraction spots rotated by -12° with respect to the NC satellites (Figs. 2b,c), as recently demonstrated in UED at high electron energies in transmission through a bulk film26,28,50. We now employ ULEED to examine this NC-to-IC transition at the surface. The structural dynamics is triggered by optical pump pulses of 200 fs duration and a center wavelength of 1030 nm. A repetition rate of 25 kHz was selected to ensure structural and thermal relaxation between consecutive pump pulses. To provide a homogeneous sample excitation across the electron beam (100 μm FWHM), the pump beam is focused to a diameter of ~300 μm (FWHM) on the sample, with fluences ranging from 0.56 mJ/cm2 to 5.65 mJ/cm2. The transient state of the sample’s surface structure is subsequently probed by electron pulses with a kinetic energy of 100 eV after a variable delay time Δ . Figure 2b displays the diffraction pattern of the sample after optical excitation to the IC phase (Δ >734 ps), with CDW diffraction peaks in-line with the reciprocal vectors of the atomic lattice. Due to the weak and harmonic PLD, higher-order CDW diffraction peaks are practically absent in the IC phase51. In Fig. 2c, a difference image illustrates the suppression of the NC phase (blue) and the appearance of the rotated IC spots (red), together with an increase of the diffuse background (see also lineout in Fig. 2d). For all time delays, from the raw data, we evaluate the integrated as well as the maximum intensities of both the lattice and CDW diffraction peaks, including background subtraction in a sufficiently large area of interest. The obtained integrated and maximum intensities of the Bragg, NCand IC-CDW diffraction peaks as a function of ∆ are plotted in Fig. 2f, for ten incident optical pump fluences. Figure 2e shows normalized diffraction peak intensities at large delays (Δ =1134 ps). For fluences below 2.83 mJ/cm2, the NC-CDW phase is transiently suppressed by up to about 25% (see blue time curves in Fig. 2f, middle) due to the pump-induced heating of the surface (Debye-Waller effect), recovering on a timescale of several nanoseconds via thermal diffusion into the bulk, consistent with the out-of-plane thermal conductivity of the material52. At a pump fluence of 3.4 mJ/cm2, we observe a sharp threshold behavior, leading to a full suppression of the NC phase. Simultaneously, the IC phase appears, and its diffraction spot intensity saturates for higher fluences (with some indication of a thermal suppression at the highest fluence, cf. Fig. 2e). Interestingly, the time curves of the suppression and emergence of the NC and IC phases, respectively, are markedly different (cf. Fig. 2f): While the NC phase is suppressed within our temporal resolution (see also Refs. 26,28), the IC spot intensity continuously increases over time after an initial fast rise to about half of the signal measured at Δ =1 ns. Notably, the appearing IC signal continuously grows over several hundred picoseconds, an observation which cannot be accounted for by the slower nanosecond thermal relaxation of the newly-created IC phase. Fig. 2: ULEED of the structural phase transition between CDW phases. a, Diffraction pattern of the NC phase recorded at Δ < 0 ps. b, Diffraction pattern of the sample optically-pumped to the IC phase (Δ > 734 ps). Note the CDW satellite spots, which are rotated by -12° with respect to the NC phase in (a). c, Difference image of the pumped and unpumped diffraction patterns (a, blue) and (b, red). d, Line profile of NC and IC CDW diffraction spots marked in (c). e, Fluence dependence of the NC, IC and Bragg diffraction peak intensities at Δ = 1.1 ns, normalized to the NC and Bragg spot intensities , and , at lowest pump fluence and negative times. f, Integrated diffraction spot intensities of the Bragg (top), NC (center) and IC (bottom) diffraction peaks vs. delay time for ten optical pump fluences, normalized to the signal at negative times. Dashed line (ICP panel): Integrated intensity of IC diffraction peaks for highest pump fluence. g, Ratio of integratedto-maximum diffraction spot intensities (normalized to long delays), showing time-dependent narrowing in the ICP spots. Compared to the maximum intensities of the IC diffraction spots (Fig. 2f, bottom), the integrated spot intensity (dashed line, highest fluence) exhibits a somewhat faster rise. This is also evident in the ratio of the integrated to the maximum diffraction signals in Fig. 2g (red line), contrasted with the same evaluation for the Bragg peaks (green line). These observations indicate that the diffraction spot profile or width substantially changes within the first 200 ps after the pump pulse, as directly shown in Figs. 3a, b. In order to quantitatively analyze these spot profiles and associate them with structural correlation lengths in the IC phase, the CDW and lattice diffraction spots are fitted with two-dimensional Lorentzians for all delay times (see Fig. 3a). Figure 3c displays the delay-dependent widths of the IC and lattice diffraction spots as circles and triangles, respectively. We find that the IC diffraction spots initially appear as rather broad peaks that significantly sharpen within 400 ps after the excitation from = 0.06 Å-1 at Δ = 20 ps to < 0.038 Å-1 for ∆ > 400 ps. Here, is the diffraction spot FWHM, taken as the geometric mean of both semi-axes. To analyze the evolution of spot profiles in more detail, we determine a time-dependent peak width that accounts for the finite experimental momentum resolution: