Ultrafast spot-profile LEED of a charge-density wave phase transition

We investigate the optically driven phase transition between two charge-density wave (CDW) states at the surface of tantalum disulﬁde (1 T -TaS 2 ). Speciﬁcally, we employ a recently improved ultrafast low-energy electron diffraction setup to study the transition from the nearly commensurate to the incommensurate (IC) CDW state. The experimental setup allows us to follow transient changes in the diffraction pattern with high momentum resolution and 1-ps electron pulse duration. In particular, we trace the diffraction intensities and spot proﬁles of the crystal lattice, including main and CDW superstructure peaks, as well as the diffuse background. Harnessing the enhanced data quality of the instrumental upgrade, we follow the laser-induced transient disorder in the system and perform a spot-proﬁle analysis that yields a substantial IC-peak broadening for very short time scales followed by a prolonged spot narrowing.

Charge-density waves (CDW) emerge in materials with considerable anisotropy and electron-lattice interaction. 1 As a result, CDW materials undergo a symmetry-breaking phase transition into a new ground state that is characterized by a modulation of the charge density, a periodic distortion of the crystal lattice (PLD), and the formation of an electronic gap.Many studies investigated the interdependence of electronic and lattice degrees of freedom and the characteristic collective modes [2][3][4][5] in the time domain using ultrafast techniques.][26][27] Sensitive structural probes are ideal tools to capture this disorder as they provide access to transient changes of long-range order.
In this work, we study the ultrafast structural dynamics at the surface of 1T-TaS 2 using ultrafast low-energy electron diffraction (ULEED).Specifically, we revisit the phase transition between the NC and IC CDW states, which we investigated previously, 22,23 and provide data from a recently upgraded experimental setup.We employ ULEED to trace the optically induced phase transition and the subsequent relaxation dynamics.High momentum resolution at the 1-ps timescale combined with large scattering efficiency yields clear timedependent traces of peak intensities and spot profiles.This allows us to track the energy relaxation pathways in the presence of transient structural disorder in the system.
The ULEED technique is part of a wider family of stroboscopic pump-probe schemes which provide access to laser-induced nonequilibrium dynamics on surfaces 16,22,28,29 or thin films. 30In our setup, the in situ cleaved sample is optically excited by a fs-laser pulse (wavelength 1030 nm center wavelength, 200 fs duration, 100 kHz repetition rate, 100 lm pump spot diameter) and probed by a low-energy electron pulse (100 eV electron energy, 1 ps duration, 10 lm electron beam size) at a controlled time delay Dt [Fig.1(b)].By sweeping the pump-probe delay, we record a series of diffraction patterns mapping the entire dynamical process (see the supplementary material for a movie file).The time-dependent redistribution of electron diffraction intensity gives a detailed insight into the excitation and relaxation pathways of the structure.In order to achieve ultrafast temporal resolution at such electron energies, the development of a miniaturized photoelectron source, the microgun 16,31  Tantalum disulfide is a van der Waals material that consists of weakly interacting S-Ta-S stacks [Fig.1(d)].In the 1T polytype, the sulfur atoms are octahedrally coordinated around the sulfur atoms 33 [Fig.1(d)].2][43] Multiple temperature-dependent charge-density wave states 34 [Fig.1(c)] emerge at a temperature of below 543 K, each introducing a characteristic superstructure in the system.The orientation and size of the corresponding CDW unit cell change with temperature and lead to CDW phases of different symmetry, namely the incommensurate (IC), nearly commensurate (NC), trigonal and commensurate phase (C) [Fig.1(c)]. 44In this work, we focus on the NC and IC phases whose unit cells are rotated by approximately 12 with respect to each other. 21,22Each CDW phase features a characteristic PLD which is probed via electron diffraction.Moreover, it is important to note that the PLD affects both the displacements of tantalum and sulfur atoms, however, to a different extent concerning the respective directions and magnitudes 32,43 [Fig.1(c)].Commonly the prominent in-plane displacements of tantalum atoms are depicted, leading to clusters of 13 atoms, called "Star of David" formations (NC and C phase). 33For the sulfur atoms, however, the situation is reversed, since the out-of-plane displacements are significantly larger than the in-plane displacements 32,43 [Figs.1(e) and 1(f)].This is important because, at the applied electron energy of 100 eV, ULEED primarily probes the lighter sulfur atoms and is also more sensitive to out-of-plane changes due to diffraction in backscattering. 45n the following, we show the experimental results of the ultrafast structural NC-IC phase transition at the surface of 1T-TaS 2 employing ULEED.The recorded diffraction patterns in both phases exhibit bright main lattice peaks that are each surrounded by six first-order CDW superlattice peaks, labeled by Q NC=IC [Figs.2(a) and 2(b)].In the NC phase, also higher-order spots are visible pointing to a stronger and more anharmonic structural modulation. 46By pumping the room-temperature phase using a fs-laser pulse (2.7 mJ/cm 2 fluence), NC peaks are strongly suppressed within a few picoseconds, while IC spots appear on the line connecting main lattice peaks corresponding to the unit cell rotation of approximately 12 [Figs.2(a  The increase in the main lattice peak intensity indicates the transient loss of CDW order driving the system toward the high-symmetry metallic phase. 12,16,27For longer time delays, the main lattice intensity (black) mirrors the diffuse background curve (gray) which gives insight into the relaxation path of structural modes.Similar observations were made for the laser-induced structural dynamics starting from the IC state and in the absence of a phase transition. 16The main lattice and the diffuse background show a trend reversal after approximately 100 ps indicating Debye-Waller-type suppression and subsequent cooling of the system.In contrast, the IC spot intensity (red) exhibits a continuous increase over the entire delay range of up to 1.5 ns.With the given repetition rate of 100 kHz, the system returns to its initial state within 10 s, the time between two pump cycles.Optically pumping the sample at this repetition rate results in a minor cumulative increase in the sample's base temperature by a few Kelvin.Figures 2(d) and 2(f) show the time-dependent spot profiles and cutouts for several time delays.IC spot analysis (see methods in the supplementary material) yields azimuthal (black) and radial (gray) widths [Fig.2(e)].Normalized to long delay times, the spot widths show a significant increase for early times, pointing to a substantial disorder in the system, followed by a steady narrowing over longer time scales.While this agrees with our previous observations, 22 we additionally find slightly different relaxations for the correlations in radial and azimuthal direction.This potentially points to an intermediate transient hexatic phase in the material which is defined by a specific translational and orientational order of the 2D CDW lattice.In impurity-doped Nb x Ta 1Àx S 2 , a hexatic phase emerges and leads to a significant azimuthal broadening in reciprocal space. 47,48n order to describe the dynamics in the incommensurate phase, we proposed a model 22 based on the kinetics of dislocation-like CDW defects. 25After photoexcitation, a high density of phase singularities of the CDW order parameter leads to strong disorder and substantially broadened diffraction peaks.Incommensurate long-range order emerges over time as pairs of CDW defects annihilate.From pulse-to-pulse, the generation and annihilation process of CDW defects take different realizations precluding an exact microscopic reproducibility.The ensemble dynamics and transient changes of crystalline symmetry, however, are consistent and reversible.In the pump-probe configuration, over many pulses, we form the incoherent sum over many realizations, measuring a pattern with regular diffraction peaks and well-defined widths.
In conclusion, we applied our improved ULEED setup to the surface of 1T-TaS 2 in order to study the ultrafast structural dynamics of the NC-IC CDW phase transition.With high momentum resolution at the 1 ps time regime, diffraction spot analysis yields substantial broadening of IC peaks indicating strong disorder in the system after the phase transition.Referring to our previous study, 22 we attribute this to the kinetics of dislocation-like CDW defects.More generally, ULEED technique facilitates ultrafast structural probing of monolayers and superstructures and, due to the backscattering geometry, is particularly sensitive to out-of-plane displacements.In the future, the approach will allow for the investigation of a wide range of lowdimensional non-equilibrium phenomena, including topological phase transitions, 49 the formation of light-induced metastable phases, 50 and coherently controlled surface transformations. 29e the supplementary material for a methods section and a movie of the measured diffraction images showing the structural phase transition between the NC and IC CDW state and emerging broadening of CDW peaks.
[Fig.1(a), left], was an essential element, providing 1 ps electron pulses at a 150 m working distance in the sample plane [Fig.1(a), right].

Figure 2 (
c) shows in more detail the time traces for spot intensities and the diffuse background.The fast drop of NC spot intensity (blue line) is paralleled by a transient increase in the main lattice peak (black line), and a rapid increase in diffuse background (gray line) and IC spot intensity (red line).

FIG. 1 .
FIG. 1. Experimental setup and materials system.(a) Micrograph of electron microgun (left).The graph (right) shows the derivative of the fastest intensity change [blue curve in Fig. 2(d)] yielding an upper limit for the temporal resolution.(b) Sketch of ULEED setup illustrating the pumpprobe approach.(c) 1T-TaS 2 exhibits several temperature-dependent CDW phases.(d) Layered tantalum disulfide (1T-TaS 2 ) (e) and (f) Illustrations of the in-plane and out-of-plane displacements in the NC and IC phase.The columns correspond to the displacement of tantalum (left column) and sulfur (right column) atoms, respectively.For sulfur, the size of circles indicates the displacement magnitude or direction.The orange rhomb specifies the CDW unit cell, while green areas illustrate electron charge accumulations.Values of NC displacements are obtained from Ref. 32, while, for the IC phase, we assume purely sinusoidal modulation.Displacements are shown exaggerated fivefold for illustration.

FIG. 2 .
FIG. 2. Experimental results.(a) Measured diffraction pattern for NC (negative delay) and IC CDW phase (large positive delay).Five bright main lattice spots and PLD-induced superstructure spots are shown.The dark area corresponds to the electron gun shadow on the detector.The reciprocal vectors Q NC=IC (orange arrows) and Q M (white arrows) indicate the structural change which is realized as a rotation of the superlattice by about 12 .(b) Selected time frames of inset in (a).(c) Normalized time-dependent peak intensities and diffuse background signal are shown (see methods in supplementary material).(d) Line profiles through NC and IC diffraction peak for different time delays.(e) Normalized azimuthal (black) and radial (gray) spot widths vs time.IC spot peak intensity (red) shown for comparison.(f) Snapshots of NC and IC peaks showing substantial broadening after excitation followed by peak narrowing.