# Ultrafast optical melting of trimer superstructure in layered 1T’-TaTe2

Khalid M. Siddiqui1 These authors contributed equally to this work.  Daniel B.
Durham2,3 These authors contributed equally to this work.  Frederick Cropp4,5
Colin Ophus6 Sangeeta Rajpurohit6 Yanglin Zhu7 Johan D. Carlström6 Camille
Stavrakas6 Zhiqiang Mao7 Archana Raja6 Pietro Musumeci4 Liang Z. Tan6 Andrew
M. Minor2,3 Daniele Filippetto5 email<EMAIL_ADDRESS><EMAIL_ADDRESS>Robert A. Kaindl1,8 email<EMAIL_ADDRESS><EMAIL_ADDRESS> 1Materials
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
94720, USA  2National Center for Electron Microscopy, Molecular Foundry,
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
3Department of Materials Science and Engineering, University of California at
Berkeley, Berkeley, California 94720, USA  4Department of Physics and
Astronomy, University of California Los Angeles, Los Angeles, California
90095, USA  5Accelerator Technology and Applied Physics Division, Lawrence
Berkeley National Laboratory, Berkeley, California 94720, USA  6Molecular
Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720,
USA  7Department of Physics, The Pennsylvania State University, University
Park, PA 16802, USA  8Department of Physics, Arizona State University, Tempe,
Arizona 85287, USA

###### Abstract

Quasi-two-dimensional transition metal dichalcogenides (TMDs) are a key
platform for exploring emergent nanoscale phenomena arising from complex
interactions. Access to the underlying degrees of freedom on their natural
time scales motivates the use of advanced ultrafast probes that directly
couple to the self-organised electronic and atomic structural order. Here, we
report the first ultrafast investigation of TaTe2, which exhibits unique
charge and lattice structural order characterised by a transition upon cooling
from stripe-like trimer chains into a $(3\times 3)$ superstructure of trimer
clusters. Utilising MeV-scale ultrafast electron diffraction, the TaTe2
structural dynamics is resolved following intense pulsed laser excitation at
1.2 eV. We observe a rapid $\approx\\!1.4$ ps melting of the low-temperature
ordered state, followed by recovery of the clusters via thermalisation into a
hot superstructure persisting for extended times. Density-functional
calculations indicate that the initial quench is triggered by Ta trimer
bonding to nonbonding transitions that destabilises the clusters, unlike
melting of charge density waves in other TaX2 compounds. Our work paves the
way for further exploration and ultimately directed manipulation of the trimer
superstructure for novel applications.

Harnessing emergent orders in quantum materials has the potential to
revolutionise energy and information technologies 1. Complex interactions
between lattice, electron, and spin degrees-of-freedom in these systems can
give rise to emergent physics such as unconventional superconductivity 2,
topological protection 3; 4, or charge density wave (CDW) order and tailored
interactions in two-dimensional (2D) materials 5. Traditionally, control of
materials has been achieved by adiabatic tuning of external parameters.
Alternatively, ultrashort light pulses can be employed to perturb and
transform states in quantum materials on femtosecond time scales 6; 7. The
quest to probe and control electronic and lattice structural dynamics in
solids has driven the utilisation of advanced ultrafast spectroscopies,
including ultrafast X-ray and electron diffraction 8; 9; 10; 11; 12; 13,
multi-terahertz fields 14; 15; 16, and time-resolved photoemission 17; 18; 19.

Fig. 1: Crystal structure and electron diffraction patterns at thermal
equilibiria. a Layered crystal structure of the low temperature phase of
1T’-TaTe2. The electron beam is incident perpendicular to Ta and Te planes in
the UED experiments. The a, b, and c lattice vectors shown are those of the
monoclinic unit cell. The projection perpendicular to the dashed region is
indicated. Black box: Ta trimer clusters forming along the b-axis in the LT
phase. Representations of LT and HT phases showing enhanced distortions in the
LT phase are presented in the top right. Small black arrows denote the
movement of atoms towards the central Ta atom. b Static electron diffraction
patterns of 1T’-TaTe2 obtained by 0.75 MeV electron pulses at 298 K (HT) and
10 K (LT) along the $[\bar{1}01]$ zone axis. Note the different indices for LT
pattern due to tripling along b-axis. The inset shows the (3x3) PLD satellite
peaks that arise in the LT phase. A few additional peaks are present due to
diffraction from the Si support frame (see Supplementary Note 2 for sample
details). The symmetrised difference pattern between HT and LT phases is shown
below the static patterns, with contributions from the Si frame and Si3N4
membrane removed.

Tantalum dichalcogenides (TaX2, X = S, Se, Te) represent a class of materials
that are well-matched for this pursuit and have gained increasing attention as
quasi-2D systems with enhanced Coulomb and electron-lattice interactions 20;
21; 22. These compounds exhibit rich phase diagrams including semi-metallic,
charge-ordered, and superconducting behaviours. Multiple CDW phases are
observed in 1T-TaS2 which has spawned numerous ultrafast studies to clarify
the formation mechanisms and phase competition 23; 24; 25. Moreover, ultrafast
driving exposed novel metastable phases in these systems, resulting in a new
paradigm of hidden states 26; 27. Members of the
$\text{1T-TaSe}_{2-x}\text{Te}_{x}$ family exhibit varying polytypes, CDW
ground states, as well as superconductivity depending on $x$ 28. Ultrafast
optical melting and switching between CDW phases have so far been demonstrated
in TaSe2 and in $\text{TaSe}_{2-x}\text{Te}_{x}$ alloys, accessing a range of
dynamical pathways and timescales 29; 30; 31.

Curiously eluding ultrafast investigation thus far is TaTe2. This compound
exhibits markedly different properties with respect to the other Ta
dichalcogenides, attributed to weaker electronegativity of Te with respect to
Ta leading to a strong propensity for charge transfer and metal-metal bonding
32; 33; 34. TaTe2 exhibits stronger electron-phonon coupling, higher charge-
order binding energy, and larger lattice distortions than TaS2 and TaSe2 22;
35. The room temperature distorted monoclinic 1T’ crystal structure is
characterised by an intra-layer (${3\times 1}$) linear stripe-like order
composed of double zigzag Ta trimer chains. A structural transition into a
phase with ${(3\times 3)}$ order occurs at a temperature of 170 K, with Ta
atoms forming trimer clusters along the linear chains with commensurate CDW-
like order 33; 36; 37; 38. Unlike other TaX2 CDW systems 39; 40, the low
temperature phase ordering of TaTe2 exhibits metallic behaviour, with enhanced
conductivity and magnetic susceptibility 41. However, the ultrafast response
of this compound to optical driving remains unknown. This motivates the use of
advanced structural probes to follow the evolution of distortions and periodic
order, as a measure of underlying interactions.

We report the first ultrafast study of TaTe2, demonstrating a rapid picosecond
melting of its trimer-cluster lattice superstructure in the low-temperature
phase. Ultrafast electron diffraction (UED) with relativistic electron bunches
is applied using the High Repetition-rate Electron Scattering (HiRES) beamline
42; 43; 44 to probe the time evolution of lattice order after intense near-
infrared (near-IR) excitation. We observe photo-induced melting of the low-
temperature order on a $\approx\\!1.4$ ps time scale, indicative of fast
switching, followed by recovery into a hot ${(3\times 3)}$ trimer phase.
Insight into the nature of trimer cluster melting is obtained via density
functional calculations, which indicate an initial quench driven by charge
transfer transitions from bonding to non-bonding states of the Ta trimer –
suggesting pathways for a photo-induced transition that is unique among the
family of TaX2 materials. This work establishes TaTe2 as a promising material
for optical control, motivating examination of concomitant electronic dynamics
for device applications.

Fig. 2: Ultrafast electron diffraction of TaTe2. a Illustration of the optical
pump, ultrafast electron diffraction (UED) probe experiment.  b Photo-induced
changes in the diffraction patterns, for selected time delays. The patterns
have been symmetrised for visualisation purposes only. c Temporal evolution of
the signals from the main lattice Bragg peaks, separately for the increasing
and decreasing subsets, and of the LT superlattice peaks. Solid lines: fits
with an exponential function convolved with the time resolution of 0.75 ps, up
to 7 ps delay time. The corresponding time constants are
$\tau_{\text{PLD}}=1.44\pm 0.27$ ps, $\tau_{\text{Bragg}\uparrow}=2.44\pm
0.81$ ps and $\tau_{\text{Bragg}\downarrow}=2.25\pm 1.34$ ps. Error bars in
the data indicate standard error calculated using the distribution of laser-
off signals compared to the mean laser-off signal over the course of the
measurement.

## Results

Crystal structure and signatures of structural phase transition. Figure 1a
illustrates the crystal structure of TaTe2 in its low-temperature (LT) phase.
Triple-layer sheets of covalently bonded Ta and Te atoms are separated by
weaker van der Waals forces along the stacking direction. Prominent structural
elements in this material are Ta trimers — sets of three adjacent Ta atoms in
a row that cluster together via enhanced Ta-Ta bonding. Already at room
temperature, Ta atoms are ordered in-plane into trimers assembled into double
zigzag chains along the $b$-axis, which breaks hexagonal symmetry and forms a
three-layer stacking sequence. In the LT phase, additional ordering emerges in
the chains along the $b$-axis in the form of trimer clusters. This ${(3\times
3)}$ lattice superstructure represents a distorted 1T’ polytype with C2/m
space group symmetry and a monoclinic unit cell 45. In this configuration,
each Ta atom in the unit cell is coordinated to six Te atoms in a periodically
distorted octahedral arrangement.

Our DFT calculations of relaxed structures of TaTe2 confirm the distortions
due to an atomic ordering of Ta atoms attributed to metal-metal bonding, in
agreement with the structures previously determined by X-ray diffraction 33.
Moreover, our calculations also reveal enhanced Ta-Ta bonds along the $b$-axis
in the LT phase as highlighted in Fig. 1a, resulting in the tripling of
$b$-axis corresponding to an overall ${(3\times 3)}$ superstructure (cf.
Supplementary Note 1 for additional details).

Fig. 1b shows equilibrium diffraction patterns of a 1T’-TaTe2 flake which we
measured with the 0.75 MeV electron bunches at HiRES, comparing the high-
temperature (HT) phase at 298 K and LT phase at 10 K. As illustrated in Fig.
1a, the electron beam impinges along the $[\bar{1}01]$ zone axis, i.e.
perpendicular to the Ta and Te layers. The measured diffraction patterns
exhibit a large number of Bragg spots reaching up to high momentum transfer,
demonstrating both a high sample crystallinity and a large scattering range
afforded by the relativistic beam energy. More details about the sample and
its preparation are given in the Methods and in Supplementary Note 2.

At 298 K, we observe 2-fold symmetry exemplified, for instance, by differences
of the (020) and (313) Bragg peaks in intensity and their relative distance
from the centre. This is consistent with the (${3\times 1}$) periodicity and
the monoclinic crystal structure.

The pattern at 10 K in Fig. 1b reveals the appearance of new satellite peaks
surrounding the main lattice peaks as a result of the emergent ${(3\times 3)}$
periodic lattice distortion (PLD), in concordance with Ta trimer cluster
formation and the associated unit cell tripling 33; 36; 37; 38. Their
observation also demonstrates that the transverse coherence length of the
electron source is sufficient to track the dynamics of the LT superstructure.
Analogous satellite peaks in the HT phase are $\approx\\!1000$ times weaker
than the main Bragg peaks and are not observed in these measurements (see
Supplementary Note 2).

To determine the signature in the electron diffraction patterns attributed to
the structural phase transition, we calculate the difference between HT and LT
patterns following normalisation by the total electron intensity. The
resulting changes are shown at the bottom of Fig. 1b. While all superlattice
satellites associated with the ${(3\times 3)}$ trimer superstructure are
suppressed, the main Bragg peaks exhibit a mixture of positive and negative
intensity changes. This complex response deviates from observations in TaS2
and TaSe2 where all primary Bragg peaks increased in intensity, opposite to
the suppression of the PLD satellites 23; 46. We attribute this mixed-sign
intensity change signature to the symmetry of the superstructure formation
within the distorted monoclinic unit cell, leading to mixed structure factor
changes for different diffraction orders as supported by our diffraction
simulations (see Supplementary Note 3).47; 48

Ultrafast optical melting of trimer clusters. We utilise the HiRES beamline
for ultrafast electron diffraction. The sample was first cooled into the low-
temperature ordered phase at 10 K, and then photo-excited with near-IR
femtosecond pulses (1030 nm wavelength). Time-delayed electron pulses at 0.75
MeV are used as structural probe, as illustrated in Fig. 2a. Recorded
diffraction patterns with and without excitation provide signatures of photo-
induced changes for each pump-probe time delay.

Difference maps of the diffraction intensity at selected time delays $\Delta
t$ are shown in Fig. 2b for a pump fluence of 2.3 mJ/cm2, indicating
structural changes on a picosecond timescale. For clearer visualisation, these
maps are symmetrised by averaging signals across the vertical and horizontal
mirror plane symmetries (the process is described in Supplementary Note 4). At
early times the signals exhibit a characteristic pattern of changes, including
a decrease of the ${(3\times 3)}$ PLD satellites and a mixture of increased
and decreased intensities of the main lattice Bragg peaks (see diffraction
pattern at $\Delta t=4$ ps in Fig. 2b). This pattern strongly resembles that
of the HT-LT phase transition obtained from the equilibrium data in Fig. 1b.
This indicates that the intense near-IR excitation melts the low-temperature
trimer clusters and induces an ultrafast phase transition to the (${3\times
1}$) ordered HT state in TaTe2.

In order to track the structural kinetics, we fit all peaks for each time-
delayed UED pattern, summing the photo-induced changes of specific subsets for
optimal signal-to-noise (see also Supplementary Note 5). Fig. 2c plots the
dynamics of the set of lattice Bragg peaks exhibiting an intensity increase
(Bragg$\uparrow$) or decrease (Bragg$\downarrow$) in the pattern, as well as
the changes of the superlattice satellites. Normalised to their intensities
before excitation, the PLD satellites undergo $\approx\\!55$% suppression with
a time constant of $\tau_{\text{PLD}}~{}\approx\\!1.4$ ps (details of the
fitting are provided in Supplementary Note 6). This time constant provides a
measure of the (${3\times 3}$) trimer superstructure melting time in TaTe2 in
our experiments.

Alongside the PLD suppression, the primary lattice Bragg peaks also exhibit
strong changes with slower dynamics corresponding to time constants of
${\tau_{\text{Bragg$\uparrow$}}~{}\approx~{}\\!2.4}$ ps and ${\tau_{\text{
Bragg$\downarrow$}}~{}\approx~{}\\!2.3}$ ps. Moreover, oscillations appear in
the Bragg peak traces, with a period of $\approx\\!2$ ps, which may result
from the excitation of coherent phonons. We note that at negative time delays,
a few-percent intensity reduction is observed in both the superlattice and
Bragg$\downarrow$ peaks which we attribute to residual heating accumulated
over several laser pulses.

Fig. 3: Re-formation of superstructure and Debye-Waller dynamics. a
Representative symmetrised difference images for early (centered around
$\approx\\!~{}4$ ps) and late (around $\approx\\!65$ ps) time delays. For
improved signal-to-noise these are calculated by averaging difference patterns
over time ranges, i.e. 3–5 ps for early and 50–80 ps for late time delays. For
the late time delays, all Bragg peaks exhibit a loss of intensity indicative
of a Debye-Waller effect. b Dynamics of the PLD satellite peaks over an
extended time scale. Yellow shading indicates time ranges that were averaged
to generate the difference images. A partial recovery is observed, fit with an
exponential relaxation with offset (red line) with time constant ${\tau=6.6\pm
2.6}$ ps. The long-lived suppression indicates that the lattice system has
thermalised at an elevated temperature.

Re-formation of lattice superstructure. Following the melting of the trimer
clusters, further structural dynamics ensues that is marked by the recovery of
the ($3\times 3$) superstructure due to lattice thermalisation. Fig. 3a shows
transient difference maps, where the data has been averaged for two
representative time ranges corresponding to early ($\Delta t=3\text{--}5$ ps)
and late (50–80 ps) time delays. The pattern at early times exhibits the clear
signature of the (${3\times 3}$) trimer superstructure melting discussed
above, while at later times such signature disappears and the pattern recovers
the LT superlattice. The broad overall reduction of the peak intensities in
this time range is that expected of a heated state with incoherent thermal
atomic motions via the Debye-Waller effect 46; 49. Between these time ranges,
we note that diffraction peaks on one side of the pattern increase while those
on the other side decrease, indicating mechanical buckling of the sample as it
accommodates the structural phase change and lattice heating50; 51. Difference
images from these time ranges are shown in Supplementary Note 4.

As seen in Fig. 3b – which plots the time evolution of the PLD side peaks over
the entire measurement window – the suppressed satellite peaks recover
$\approx\\!20$% of their original intensity with a $\approx\\!7$ ps time
constant. We note that this timescale may be influenced by simultaneous
contribution from mechanical buckling. The overall suppression of the
diffraction peaks relative to the LT ground state indicates the thermalisation
of the lattice degrees-of-freedom into a “hot” (${3\times 3}$) trimer
superstructure at longer delays. We can estimate the maximum lattice
thermalised temperature due to full thermalisation of the absorbed laser
energy. For the given 2.3 mJ cm-2 fluence this results in a temperature of 177
K, based on the 1T’-TaTe2 heat capacity 33 and the optical constants we
measured of our 60 nm thick flake (see Supplementary Notes 7 and 8). We also
performed experiments on the same sample at 1.75 mJ cm-2 and 1.5 mJ cm-2
fluence. The signature of structural phase transition was reproduced for these
fluences with reduced magnitude (see Supplementary Note 8).

Fig. 4: Proposed stages of the photo-induced dynamics in 1T’-TaTe2. The system
starts in the LT phase with a (${3\times 3}$) superstructure of Ta trimer
clusters (I). Near-IR excitation promotes carriers from bonding to non-bonding
states via a charge-transfer excitation, which results in melting of the
trimer clusters and leaves behind stripe-like trimer chains (II).
Subsequently, the lattice subsystem thermalises, causing the (${3\times 3}$)
superstructure to re-establish and stablise at elevated temperatures (III).
Inset: DFT-calculated density of states projected onto Ta and Te atoms, along
with schematic optically-induced promotion from bonding to non-bonding Ta
orbitals, which lie in the plane. The participating Ta trimer bonding and non-
bonding (with a node in the middle) orbitals are shown.

## Discussion

Fig. 4 illustrates the proposed sequence of phases in the ultrafast dynamics
of TaTe2. Photo-excitation with intense pulses leads to the excitation of
energetic carriers and picosecond melting of the low-temperature (${3\times
3}$) trimer superstructure phase. The transient phase that results corresponds
to a (${3\times 1}$) trimer chain order, as inferred from the close overlap of
the photo-induced change in the diffraction pattern with the fingerprint of
the LT-HT transition. In the subsequent picoseconds, the lattice degrees-of-
freedom thermalise, enhancing Ta-Ta bonds and thereby switching into a hot
(${3\times 3}$) superstructure state. The latter persists for extended times
($\gg 80$ ps) until thermal diffusion transfers heat into the substrate.

Density functional theory (DFT) calculations clarified the electronic states
involved in the photo-excitation. We computed the projected density of states
(DOS) and crystal orbital Hamilton population (COHP) of the relaxed LT and HT
structures of TaTe2, revealing the nature of occupied and unoccupied states,
as shown in Fig. 4 (see Supplementary Note 1 for details). In the LT phase,
the lower-energy region of the valence band (i.e. below -4 eV) consists of Te
$p$-states with a small contribution from Ta $d$-states, whereas the upper
region of the band (i.e. above -2 eV) has mostly Ta character. Negative COHP
values in the upper valence band indicate the bonding nature of Ta trimer
states in this energy region. Trimer formation is enabled by partial charge
transfer from Te to Ta involving $d_{\text{xz}}$ and $d_{\text{xy}}$ states
which leaves uneven charges on Ta sites and enhanced Ta-Ta bonding 36.
Meanwhile, conduction band states near the Fermi level belong to non-bonding
states of Ta trimers, with anti-bonding states lying higher in energy
($\approx\\!4$ eV above $\text{E}_{F}$).

Optical absorption with 1.2 eV photon energy in 1T’-TaTe2 involves dipole-
allowed charge-transfer transitions which depopulate bonding states and
populate non-bonding states of the $b$-axis trimers above the Fermi level.
This weakens the original charge-disproportionation between Ta sites within
these trimers, thus triggering the “melting” of the (${3\times 3}$) order. The
calculations also identified several strongly coupled phonons around 2.7 THz
and 1.8 THz that are expected to be set into motion after optical charge
transfer excitation, including breathing modes of the Te octahedra around the
Ta ions as well as displacement modes of the Ta ions along the trimer axes.
This predicts a cooperative mechanism for photo-induced trimer cluster
dissolution in TaTe2, which can be addressed in future diffraction studies
with higher temporal resolution and time-resolved diffuse scattering to
directly track the phonon modes participating in the transformation.

Our study hence represents the first ultrafast measurement of TaTe2, utilising
short MeV-scale electron bunches to resolve a picosecond atomic-scale melting
of its intriguing trimer clusters and the subsequent thermalisation into a hot
(${3\times 3}$) superstructure phase. In these and other MTe2 systems (where M
= transition metal), changes in the lattice structure are linked to anomalous
changes in conductivity and magnetic susceptibility. The light-driven toggle
and recovery seen here to occur between different lattice symmetries may thus
enable applications, e.g. for ultrafast switching. Moreover, the associated
trimer dynamics in this material opens the possibility for control of the
related electronic modulations in TaTe2 on even faster time scales.

## Methods

Ultrafast Electron Diffraction. The UED experiments were performed at the High
Repetition-rate Electron Scattering (HiRES) beamline at Lawrence Berkeley
National Laboratory (LBNL). The instrument exploits a one-of-a-kind technology
developed at LBNL to provide unique beam properties for ultrafast structural
dynamics studies, coupling relativistic electrons and high repetition rates.
The results reported in the paper validate the technological breakthrough,
which has the potential of broadening the scientific reach of ultrafast tools.
Near-IR laser pulses centred around 1030 nm wavelength and with
$\approx\\!350$ fs duration (full-width at half-maximum, FWHM) were used to
photo-excite the sample. Synchronised electron pulses with 0.75 MeV kinetic
energy (de Broglie wavelength $\lambda=0.011$ Å) were delivered to the sample
for electron diffraction. Experiments were performed at 0.5 kHz repetition
rate, recording 10 frames with the pump beam OFF and 10 frames with the pump
ON for each time delay. Each frame was recorded for an exposure time of 8
seconds. A home-built sample stage interfaced to a closed-cycle cryostat was
used to cryogenically cool the samples down to 10 K. Laser and electron beams
impinged on the TaTe2 sample surface, transmitting through a supporting
silicon nitride window. The electron beam diameter at the sample was
$\approx\\!450~{}\mu$m FWHM, while the pump beam was adjusted to
$\approx\\!750~{}\mu$m FWHM to ensure homogeneous excitation across the probe
volume. The beam charge was $\approx\\!2.5$ fC corresponding to $1.6\times
10^{4}$ electrons/pulse.

TaTe2 samples. Single crystals of 1T’-TaTe2 were grown by the chemical vapour
transport technique 52 at $750-850^{\text{\lx@text@degree}}$C for 14 days
using iodine as a transport agent. The crystals were repeatedly mechanically
exfoliated with Scotch tape until optically transparent and then dry
transferred onto 20-nm thick Si3N4 windows using polydimethylsiloxane (PDMS)
stamps 53. The thickness of the TaTe2 flake was determined to be
$\approx\\!60$ nm using atomic force microscopy (AFM) (see Supplementary Note
2).

Simulations and image analysis. Details of DFT calculations, electron
diffraction simulations, and diffraction image analysis methods are provided
in Supplementary Notes 1, 3, and 5, respectively.

## Acknowledgements

We gratefully acknowledge Nord Andresen for developing the cryogenic sample
stage and other excellent engineering efforts at HiRES, as well as Germán
Sciaini for stimulating discussions. K.M.S., D.F., and R.A.K. acknowledge
support for ultrafast materials UED studies by the Laboratory Directed
Research and Development (LDRD) Program of Lawrence Berkeley National Lab
under U.S. Department of Energy (DOE) Contract DE-AC02-05CH11231. Development
and operation of the HiRES instrument (D.F., F.C) was supported by DOE under
the same Contract No. Funding for D.B.D. was provided by STROBE: A National
Science Foundation Science and Technology Center under Grant No. DMR 1548924.
Work at the Molecular Foundry was supported by the DOE Office of Basic Energy
Sciences under Contract No. DE-AC02-05CH11231. C.O. acknowledges support from
the DOE Early Career Research Award program. A.R. gratefully acknowledges
support through the Early Career LDRD Program of Lawrence Berkeley National
Laboratory under DOE Contract No. DE-AC02-05CH11231. S.R. was supported
through the Center for Non-Perturbative Studies of Functional Materials funded
by the Computational Materials Sciences Program of DOE Office of Basic Energy
Sciences, Materials Sciences and Engineering Division. This research used
resources of the National Energy Research Scientific Computing Center, a DOE
Office of Science User Facility supported by the DOE Office of Science under
Contract No. DE-AC02-05CH11231. The financial support for sample preparation
was provided by the National Science Foundation through the Penn State 2D
Crystal Consortium-Materials Innovation Platform (2DCC-MIP) under NSF
cooperative agreement DMR-1539916.

## References

  * (1) Tokura, Y., Kawasaki, M. & Nagaosa, N.  Emergent functions of quantum materials.  _Nat. Phys._ 13, 1056–1068 (2017).
  * (2) Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J.  From quantum matter to high-temperature superconductivity in copper oxides.  _Nature_ 518, 179–86 (2015).
  * (3) Hasan, M. Z. & Kane, C. L.  Colloquium: Topological insulators.  _Rev. Mod. Phys._ 82, 3045 (2010).
  * (4) Armitage, N. P., Mele, E. J. & Vishwanath, A.  Weyl and Dirac semimetals in three-dimensional solids.  _Rev. Mod. Phys._ 90, 015001 (2018).
  * (5) Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H.  2D materials and van der Waals heterostructures.  _Science_ 353, aac9439 (2016).
  * (6) Zhang, J. & Averitt, R.  Dynamics and control in complex transition metal oxides.  _Ann. Rev. Mat. Res._ 44, 19–43 (2014).
  * (7) Basov, D. N., Averitt, R. D. & Hsieh, D.  Towards properties on demand in quantum materials.  _Nat. Mater._ 16, 1077 (2017).
  * (8) Cavalleri, A. _et al._ Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition.  _Phys. Rev. Lett._ 87, 237401 (2001).
  * (9) Lee, W. S. _et al._ Phase fluctuations and the absence of topological defects in a photo-excited charge-ordered nickelate.  _Nature Commun._ 3, 838 (2012).
  * (10) Trigo, M. _et al._ Fourier-transform inelastic x-ray scattering from time- and momentum-dependent phonon–phonon correlations.  _Nat. Phys._ 9, 790–794 (2013).
  * (11) Otto, M. R. _et al._ How optical excitation controls the structure and properties of vanadium dioxide.  _Proc. Natl. Acad. Sci._ 116, 450–455 (2018).
  * (12) Sie, E. J. _et al._ An ultrafast symmetry switch in a Weyl semimetal.  _Nature_ 565, 61–66 (2019).
  * (13) Zong, A. _et al._ Evidence for topological defects in a photoinduced phase transition.  _Nat. Phys._ 15, 27–31 (2019).
  * (14) Rini, M. _et al._ Control of the electronic phase of a manganite by mode-selective vibrational excitation.  _Nature_ 449, 72–74 (2007).
  * (15) Porer, M. _et al._ Non-thermal separation of electronic and structural orders in a persisting charge density wave.  _Nat. Mater._ 13, 857–861 (2014).
  * (16) Coslovich, G. _et al._ Ultrafast dynamics of vibrational symmetry breaking in a charge-ordered nickelate.  _Sci. Adv._ 3, 1600735 (2017).
  * (17) Perfetti, L. _et al._ Time evolution of the electronic structure of 1T-TaS2 through the insulator-metal transition.  _Phys. Rev. Lett._ 97, 067402 (2006).
  * (18) Rohwer, T. _et al._ Collapse of long-range charge order tracked by time-resolved photoemission at high momenta.  _Nature_ 471, 490–493 (2011).
  * (19) Sobota, J. A., He, Y. & Shen, Z.-X.  Electronic structure of quantum materials studied by angle-resolved photoemission spectroscopy Preprint at {https://arxiv.org/abs/2008.02378} (2020).
  * (20) Sipos, B. _et al._ From Mott state to superconductivity in 1T-TaS2.  _Nat. Mater._ 7, 960–5 (2008).
  * (21) Cho, D. _et al._ Nanoscale manipulation of the Mott insulating state coupled to charge order in 1T-TaS2.  _Nat. Commun._ 7, 10453 (2016).
  * (22) Miller, D. C., Mahanti, S. D. & Duxbury, P. M.  Charge density wave states in tantalum dichalcogenides.  _Phys. Rev. B_ 97, 045133 (2018).
  * (23) Eichberger, M. _et al._ Snapshots of cooperative atomic motions in the optical suppression of charge density waves.  _Nature_ 468, 799–802 (2010).
  * (24) Haupt, K. _et al._ Ultrafast metamorphosis of a complex charge-density wave.  _Phys. Rev. Lett._ 116, 016402 (2016).
  * (25) Vogelgesang, S. _et al._ Phase ordering of charge density waves traced by ultrafast low-energy electron diffraction.  _Nat. Phys._ 14, 184–190 (2017).
  * (26) Stojchevska, L. _et al._ Ultrafast switching to a stable hidden quantum state in an electronic crystal.  _Science_ 344, 177 (2014).
  * (27) Han, T.-R. T. _et al._ Exploration of metastability and hidden phases in correlated electron crystals visualized by femtosecond optical doping and electron crystallography.  _Sci. Adv._ 1, e1400173 (2015).
  * (28) Luo, H. _et al._ Polytypism, polymorphism, and superconductivity in TaSe2-xTex.  _Proc. Natl. Acad. Sci._ 112, E1174–E1180 (2015).
  * (29) Sun, S. _et al._ Direct observation of an optically induced charge density wave transition in 1T-TaSe2.  _Phys. Rev. B_ 92, 224303 (2015).
  * (30) Wei, L. _et al._ Dynamic diffraction effects and coherent breathing oscillations in ultrafast electron diffraction in layered 1T-TaSeTe.  _Struct. Dyn._ 4, 044012 (2017).
  * (31) Li, J. _et al._ Ultrafast decoupling of atomic sublattices in a charge-density-wave material Preprint at https://arxiv.org/abs/1903.09911 (2019).
  * (32) Wilson, J. & Yoffe, A.  The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties.  _Adv. Phys._ 18, 193–335 (1969).
  * (33) Sörgel, T., Nuss, J., Wedig, U., Kremer, R. & Jansen, M.  A new low temperature modification of TaTe2—comparison to the room temperature and the hypothetical 1T-TaTe2 modification.  _Mater. Res. Bull._ 41, 987 – 1000 (2006).
  * (34) Doublet, M.-L., Remy, S. & Lemoigno, F.  Density functional theory analysis of the local chemical bonds in the periodic tantalum dichalcogenides TaX2 (X = S, Se, Te).  _J. Chem. Phys._ 113, 5879–5890 (2000).
  * (35) Gao, J. J. _et al._ Origin of the structural phase transition in single-crystal TaTe2.  _Phys. Rev. B_ 98, 224104 (2018).
  * (36) Chen, C. _et al._ Trimer bonding states on the surface of the transition-metal dichalcogenide TaTe2.  _Phys. Rev. B_ 98 (2018).
  * (37) El Baggari, I., Stiehl, G. M., Waelder, J., Ralph, D. C. & Kourkoutis, L. F.  Atomic-resolution cryo-STEM imaging of a structural phase transition in TaTe2.  _Microsc. Microanal._ 24, 86–87 (2018).
  * (38) Wang, H. _et al._ Charge density wave and atomic trimerization in layered transition-metal dichalcogenides 1T-MX2 materials.  _EPL_ 130 (2020).
  * (39) Svetin, D., Vaskivskyi, I., Brazovskii, S. & Mihailovic, D.  Three-dimensional resistivity and switching between correlated electronic states in 1T-TaS2.  _Sci. Rep._ 7 (2017).
  * (40) LeBlanc, A. & Nader, A.  Resistivity anisotropy and charge density wave in 2H-NbSe2 and 2H-TaSe2.  _Solid State Commun._ 150, 1346–1349 (2010).
  * (41) Chen, H., Li, Z., Guo, L. & Chen, X.  Anisotropic magneto-transport and magnetic properties of low-temperature phase of TaTe2.  _EPL_ 117, 27009 (2017).
  * (42) Filippetto, D. & Qian, H.  Design of a high-flux instrument for ultrafast electron diffraction and microscopy.  _J. Phys. B_ 49, 104003 (2016).
  * (43) Ji, F. _et al._ Ultrafast relativistic electron nanoprobes.  _Commun. Phys._ 2 (2019).
  * (44) Siddiqui, K. _et al._ Ultrafast structural dynamics of materials captured by relativistic electron bunches.  _Proc. SPIE 11497, Ultrafast Nonlinear Imaging and Spectroscopy VIII, 114970J_ (2020).
  * (45) Vernes, A., Ebert, H., Bensch, W., Heid, W. & Näther, C.  Crystal structure, electrical properties and electronic band structure of tantalum ditelluride.  _J. Condens. Matter Phys._ 10, 761–774 (1998).
  * (46) Erasmus, N. _et al._ Ultrafast dynamics of charge density waves in 4Hb-TaSe2 probed by femtosecond electron diffraction.  _Phys. Rev. Lett._ 109, 167402 (2012).
  * (47) Kirkland, E. J.  _Advanced Computing in Electron Microscopy_ (Springer US, 2010).
  * (48) Ophus, C.  A fast image simulation algorithm for scanning transmission electron microscopy.  _Advanced Structural and Chemical Imaging_ 3 (2017).
  * (49) Storeck, G. _et al._ Structural dynamics of incommensurate charge-density waves tracked by ultrafast low-energy electron diffraction.  _Struct. Dyn._ 7, 034304 (2020).
  * (50) Kwon, O.-H., Barwick, B., Park, H. S., Baskin, J. S. & Zewail, A. H.  Nanoscale mechanical drumming visualized by 4D electron microscopy.  _Nano Lett._ 8, 3557–3562 (2008).
  * (51) Mannebach, E. M. _et al._ Dynamic structural response and deformations of monolayer MoS2 visualized by femtosecond electron diffraction.  _Nano Lett._ 15, 6889–6895 (2015).
  * (52) Ubaldini, A., Jacimovic, J., Ubrig, N. & Giannini, E.  Chloride-driven chemical vapor transport method for crystal growth of transition metal dichalcogenides.  _Cryst. Growth Des._ 13, 4453–4459 (2013).
  * (53) Castellanos-Gomez, A. _et al._ Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping.  _2D Mater._ 1, 011002 (2014).
  * (54) Blöchl, P. E.  Projector augmented-wave method.  _Phys. Rev. B_ 50, 17953–17979 (1994).
  * (55) Kresse, G. & Furthmüller, J.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set.  _Phys. Rev. B_ 54, 11169–11186 (1996).
  * (56) Kresse, G. & Joubert, D.  From ultrasoft pseudopotentials to the projector augmented-wave method.  _Phys. Rev. B_ 59, 1758–1775 (1999).
  * (57) Giustino, F.  Electron-phonon interactions from first principles.  _Rev. Mod. Phys._ 89, 015003 (2017).
  * (58) Giannozzi, P. _et al._ QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials.  _J. Phys. Condens. Matter_ 21, 395502 (2009).
  * (59) Wei, L.-L. _et al._ Charge density wave states and structural transition in layered chalcogenide TaSe2-xTex.  _Chin. Phys. Lett._ 34, 086101 (2017).
  * (60) Wang, H. _et al._ Charge density wave and atomic trimerization in layered transition-metal dichalcogenides 1T-MX2 materials.  _EPL_ 130, 47001 (2020).
  * (61) Palmer, D. C.  Visualization and analysis of crystal structures using crystalmaker software.  _Z. Kristallogr. Cryst. Mater._ 230, 559–572 (2015).
  * (62) Byrnes, S. J.  Multilayer optical calculations Preprint at https://arxiv.org/abs/1603.02720 (2016).
  * (63) Luke, K., Okawachi, Y., Lamont, M. R., Gaeta, A. L. & Lipson, M.  Broadband mid-infrared frequency comb generation in a Si3N4 microresonator.  _Opt. Lett._ 40, 4823–4826 (2015).
  * (64) Schinke, C. _et al._ Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon.  _AIP Adv._ 5, 067168 (2015).
  * (65) Rodríguez-de Marcos, L. V., Larruquert, J. I., Méndez, J. A. & Aznárez, J. A.  Self-consistent optical constants of SiO2 and Ta2O5 films.  _Opt. Mater. Express_ 6, 3622–3637 (2016).
  * (66) Durham, D. B., Ogletree, D. F. & Barnard, E. S.  Scanning Auger spectromicroscopy using the ScopeFoundry software platform.  _Surf. Interface Anal._ 50, 1174–1179 (2018).
  * (67) Barnard, E. S.  ScopeFoundry: A python platform for controlling custom laboratory experiments and visualizing scientific data.  http://www.scopefoundry.org/.

Supplementary Information

Ultrafast optical melting of trimer superstructure in layered 1T’-TaTe2

Khalid M. Siddiqui, Daniel B. Durham, Frederick Cropp, Colin Ophus, Sangeeta
Rajpurohit, Yanglin Zhu, Johan D. Carlström, Camille Stavrakas, Zhiqiang Mao,
Archana Raja, Pietro Musumeci, Liang Z. Tan, Andrew M. Minor, Daniele
Filippetto, and Robert A. Kaindl

## Supplementary Note 1: Density functional theory

Supplementary Figure 1: a, b DFT relaxed atomic structures of HT and LT phase
viewed within a single layer. Two inequivalent Ta ions in HT are indexed as
Ta1 and Ta2. The Te ions within the layer around Ta1 ions are indexed as Te1,
the respective Te ions around Ta2 are indexed as Te2. The four inequivalent Ta
ions in LT are indexed as 1A, 1B, 2A, and 2B. The Te ions in the layer around
1A and 1B Ta ions are labelled as Te1. For 2A and 2B Ta ions, the same Te ions
are labelled as Te2.

To understand the melting of lattice distortions in TaTe2, we investigated the
nature of electronic states involved in the charge-transfer transitions during
photo-excitation. We performed DFT calculations with the Vienna ab initio
Simulation Package (VASP) using projected-augmented wave basis set 54; 55; 56
and experimental lattice parameters 33. We choose a plane wave cut-off energy
of 350 eV. A k-grid of size ($8\times 8\times 8$) and ($4\times 4\times 4$) is
used for the LT and HT ionic relaxation, respectively. For the ionic
relaxation, we use the Perdew-Burke-Ernzerhof generalised gradient
approximation (GGA) with a force convergence criterion of 1meV/Å.

The HT and LT relaxed structures, shown in Supplementary Figure 1, are
consistent with the experimental atomic structure with (3x1) and (3x3)
superstructures, respectively. The HT structure has two inequivalent Ta ions
which forms the centre (Ta1) and edges (Ta2) of the trimers in the double zig-
zag chain. The LT phase has four inequivalent Ta ions (1A, 1B, 2A and 2B).
Every Ta ion is surrounded by an octahedron of Te ions.

Supplementary Figure 2: a, c Density of states of TaTe2 structure projected on
Ta d-states (red) and Te s-states (yellow) and p-states (blue) for HT and LT
relaxed structures. The Fermi-level is shown by horizontal dashed line. b, d
COHP for HT and LT relaxed structures. For LT, corresponding bond lengths of
the selected bonds are listed in the legend (in Angstroms).

To investigate the energy-resolved bonding nature between ions, we performed a
crystal orbital Hamilton population (COHP) analysis with the local orbital
basis suite towards electronic structure reconstruction (LOBSTER) code. The
Ta-Te COHP for the HT phase in Supplementary Figure 2 is the averaged over all
Ta-Te pairs. For the Ta-Te COHP in the LT phase, we categorise Ta-Te pairs
into two groups with inter-atomic distance in the range 2.50-2.75 Å and
2.75-2.95 Å.

The projected density of states and COHP of the relaxed HT and LT structures
are shown in Supplementary Figure 2. Both structures are metallic with
overlapping bands at the Fermi level. However compared to HT, the LT structure
has larger density of states at the Fermi level. The lower energy region of
the valence band of both structure consists of Te p-states with a small
weightage from Ta d-states. In addition, the negative COHP between Ta1(Ta2)
and Te1(Te2) states confirms the bonding nature of these states. The
corresponding anti-bonding states, with positive COHP, with largely Ta
contribution form the conduction band.

Supplementary Table 1: Integrated COHP (ICOHP) between Ta atoms at the Fermi level calculated for LT and HT phase. ICOHP values in bracket are for opposite spin direction. Phase | Bond type | Distance (Å) | ICOHP
---|---|---|---
LT | Ta(1A)-Ta(2A) | 3.256 | -0.957(-0.952)
Ta(1B)-Ta(2A) | 3.160 | -1.281(1.282)
Ta(1B)-Ta(2B) | 3.445 | -0.622(-0.625)
Ta(1B)-Ta(1A) | 3.331 | -0.989(-1.012)
Ta(2A)-Ta(2A) | 3.517 | -0.693(-0.686)
Ta(2B)-Ta(2B) | 3.684 | -0.363(-0.366)
Ta(1B)-Ta(1B) | 4.220 | -0.020(-0.029)
HT | Ta1-Ta2 | 3.282 | -0.491(-0.491)
Ta1-Ta1/Ta2-Ta2 | 3.637 | -0.209(-0.209)

The upper region of the valence band has mostly Ta contribution. The negative
COHP between Ta1 and Ta2 reveals the bonding nature of the states. We
attribute the upper region of the valence band to the bonding states of Ta
trimers, as suggested by previous studies 36. The respective non-bonding and
anti-bonding states of the trimers lie high in energy forming the conduction
band. The integrated COHP (ICOHP) between Ta atoms at Fermi level is
summarised in Supplementary Table 1. The average Ta-Ta COHP along trimer axis
in LT phase has greater magnitude compared to HT phase. This indicates the Ta-
Ta bonding is stronger in LT phase. ICOHP suggests the Ta-Ta bonding along b
direction in HT phase is very small or negligible. However, the LT phase has a
significantly stronger Ta-Ta bonding, confirmed by higher ICOHP, along $b$
direction.

Supplementary Figure 3: Three optical phonon modes found to be most strongly
coupled to 1.2 eV photoexcitation using excited-state DFT calculations, with
green arrows indicating relative displacement vectors. a in-plane in-phase Ta
mode and $B_{u}$ symmetry. b in-plane out-of-phase Ta mode and $B_{u}$
symmetry. c in-plane Ta with out-of-plane Te displacements and $A_{g}$
symmetry. Ta atoms are in blue, Te are in purple.

The optical absorption in 1T’-TaTe2 involves mainly two kinds of dipole-
allowed charge-transfer transitions: between Te p-states to Ta states
(type-I); and from bonding states to the non-bonding states of the Ta trimers
(type-II). The antibonding Ta states, involved in type-I transitions, in the
conduction band are strongly coupled to the breathing modes of Te octahedra
around Ta ions. On the other hand, the non-bonding d-states of Ta trimers,
involved in type-II transitions, are coupled to the displacements of the Ta
ions, along the trimer axes. Type-I transitions redistribute electrons from Te
to Ta and do not affect the original PLD of TaTe2 which is attributed to the
unequal charges on Ta ions. We ascribe the melting of PLD to the type-II
transitions. The charge-transfer type-II transitions weaken the original
charge-disproportion between Ta sites within trimers.

Electron-phonon couplings were calculated within Density Functional
Perturbation Theory 57, as implemented within the Quantum Espresso software
package 58. We solve for phonon modes at the $\Gamma$-point, and calculate
electron-phonon coupling matrix elements for bands within 1.2 eV of the Fermi
level. For 1.2 eV excitation, we identify three strongly-coupled phonon modes,
shown in Supplementary Figure 3. The first and second mode have in-plane in-
phase and out-of-phase Ta displacements, respectively, at 1.8 THz. The third
mode is in-plane out-of-phase Ta displacements with out-of-plane Te
displacements at 2.7 THz.

## Supplementary Note 2: Sample preparation and pre-characterisation

A single crystal of TaTe2 was synthesised through the chemical vapour
transport (CVT) method52; 41. The Ta, Te powder, and 20 mg I2 were mixed with
a stoichiometric ratio and loaded into a quartz tube (10 cm inside diameter,
18 cm length), then sealed under vacuum. The quartz tube was heated up by a
double-zone furnace, where the hot end and the cold end were set at
$850{\text{\lx@text@degree}}$C and $750{\text{\lx@text@degree}}$C,
respectively. The temperature gradient was kept for 14 days. Then the furnace
was shut down, and the quartz tube was naturally cooled down to room
temperature. The black plate-like crystals were found at the cold end of the
quartz tube.

Supplementary Figure 4: Composition characterisation of CVT-grown TaTe2
crystal using EDS in a scanning electron microscope. a SEM micrograph of the
crystal, highlighting two regions from which EDS spectra are obtained. b-c
Average EDS spectra obtained while rastering the electron beam over the
regions indicated in the micrograph.

The composition of the synthesised crystals was confirmed to be close to TaTe2
using energy-dispersive x-ray spectroscopy (EDS), shown in Supplementary
Figure 4. The composition in two regions separated by nearly a millimeter is
found to be the same, suggesting uniform composition across the sample.

Supplementary Figure 5: a White light microscope image of TaTe2 flake on 20 nm
silicon nitride window using reflected light. b AFM topography map of TaTe2
flake.

The exfoliated flake for UED experiments was mounted on a Si3N4 membrane
suspended across a 30 $\mu$m x 30 $\mu$m square window in a Si support chip
produced by Norcada. A white light microscope image is shown in Supplementary
Figure 5. The reflectance contrast differs between the Si-supported region of
the flake and the region only supported by the Si3N4 membrane, suggesting the
sample is thin enough to permit some optical transmission. Optical properties
in the red to NIR region (700-1100 nm) are characterised in more detail in
Supplementary Note 7.

We used tapping-mode atomic force microscopy to map the topography of the
sample (Supplementary Figure 5). The thickness of the sample was determined to
be 61.5 nm. Some rippling of the sample was observed on micrometer length
scales, with a standard deviation of 5.8 nm. The influence of this rippling on
the diffraction patterns is discussed in Supplementary Note 3.

Supplementary Figure 6: Selected area diffraction pattern from the TaTe2 flake
measured in a 300 kV TEM at room temperature. Weak satellite peaks are
observed between the primary diffraction peaks, including the two highlighted
by the white arrows.

The crystallinity of the TaTe2 flake was characterised before UED measurements
using selected area diffraction (SAED) in TEM using a 300 keV electron beam at
room temperature, including the diffraction pattern shown in Supplementary
Figure 6. In addition to the intense peaks corresponding to the main lattice
Bragg spots observed with the beam at HiRES (750 keV), we observe satellite
peaks at room temperature with about 1000 times lower intensity than adjacent
primary diffraction peaks. These peaks appear perpendicular to the b axis,
along the a* direction indicated in Fig. 1, with a q vector of 1/3 (111). Such
peaks have been observed in prior TEM studies of TaTe259; 60. They are not
predicted to appear in kinematical simulations: instead, their presence has
been attributed to limited coherence length of the PLD along the stacking
direction59 and may involve contribution from random thermal atomic motion and
multiple scattering.

## Supplementary Note 3: Electron diffraction simulations of contributions to
diffraction peak dynamics

Supplementary Figure 7: Comparison of kinematical and dynamical diffraction
methods to the measured UED pattern at 300 K. a Symmetrised measured UED
pattern. b Kinematical diffraction pattern for HT phase. c,d Dynamical
diffraction pattern computed using multislice method considering a flat sample
and a sample with gaussian distribution of tilt angles with $\sigma_{\theta}$
= 30 mrad. All simulated patterns show the square root of the intensity.

Kinematical diffraction simulations that consider the limit that each electron
undergoes no more than one scattering event were carried out. In this case,
the diffraction peak intensities for a single crystal are largely determined
by the kinematical structure factors, with modifications due to factors such
as sample thickness and incident electron energy. We use the SingleCrystal
commercial software tool to compute kinematical electron diffraction
patterns61. A computed pattern for the HT phase is shown in Supplementary
Figure 7b.

Because of the high atomic numbers of the constituent Ta (Z = 73) and Te (Z =
52) atoms as well as the 60 nm thickness, electrons are likely to undergo
multiple scattering events as they pass through this sample. To investigate
the influence of multiple scattering, we used the multislice approach to
compute dynamical electron diffraction patterns. In this approach, the
electron beam interaction with the sample is modeled as sequential interaction
with and propagation through slices of projected electrostatic potential of
the atoms. The envelope of the electron wave function passing through the
material can be obtained from the Schrödinger equation for fast electrons
as47:

$\frac{\partial{\psi(\mathbf{r})}}{\partial{z}}=\bigg{[}\frac{i\lambda}{4\pi}\nabla_{xy}^{2}+i\sigma
V(\mathbf{r})\bigg{]}\psi(\mathbf{r})$ (S3.1)

Here, $\psi$ is the electron wave function, $\lambda$ is the electron de
Broglie wavelength, $\sigma$ is the interaction parameter, and V is the
electrostatic potential of the material. The two terms on the right-hand side
correspond to propagation (left term) and interaction (right term). Within a
finite slice, these two terms can be applied separately as operators48. First,
an interaction operator is applied in real space:

$\psi_{p+1}(\mathbf{r})=\psi_{p}(\mathbf{r})e^{i\sigma
V_{p}^{2D}(\mathbf{r})}$ (S3.2)

where $V_{p}^{2D}(\mathbf{r})$ is the projected electrostatic potential within
the slice. We use the parameterised projected potentials for Ta and Te atoms
as determined by Kirkland 47. Second, a propagation operator is applied in
reciprocal space:

$\psi_{p+1}(\mathbf{q})=\psi_{p}(\mathbf{q})e^{-i\pi\lambda|\mathbf{q}|^{2}t}$
(S3.3)

We start with a plane wave beam (spatially uniform envelope) and advance the
beam through each slice by applying the interaction and propagation operator
until it reaches the end of the material. The diffraction is then obtained
from the Fourier transform of the exiting envelope:

$I(\mathbf{q})=|\mathcal{F}(\psi(\mathbf{r}))|^{2}=|\psi(\mathbf{q})|^{2}$
(S3.4)

For the simulations shown here, we use a simulation box that is 1.92 nm long
along the b axis and 1.09 nm along the a* axis (axes defined in Fig. 1), with
the thickness of the crystal divided into 0.223 nm slices.

A computed pattern using the multislice method for a 60 nm thick film of the
HT phase is shown in Supplementary Figure 7c. Strong dynamical effects are
observed, leading to asymmetry in the pattern and dramatically different
diffraction peak intensities than obtained via kinematical simulation.

However, this calculation assumes a plane wave incident beam incident on a
perfectly flat sample. As the AFM measurement in Supplementary Note 2
demonstrates, rippling is present across the film, leading to an angular
distribution of the order of several to tens of mrad. Because the electron
probe is 100s of micrometers in size, the entire range of tilt angles is
sampled simultaneously. We find the peak intensity distribution is sensitive
to sub-mrad changes in the sample tilt in these simulations due to strong
interference effects between the scattered beams. To achieve more realistic
behaviour, we must average the diffraction over the distribution of tilt
angles present in the sample.

To account for these effects, we perform dynamical simulations for many tilt
angles and perform a Gaussian-weighted average of the intensities from these
tilts. For a 60 nm thick film, we find that a distribution of tilt angles with
$\sigma_{\theta}=30$ mrad provides the best agreement with the measured
diffraction patterns (shown in Supplementary Figure 7d). This is larger than
the $\sigma_{\theta}=6.5$ mrad we calculate from the AFM topography map:
however, this value is an underestimate as nanoscale topographic features are
smoothed out in this large area scan (pixel size = 118 nm). By averaging over
many tilt angles, the distribution of peak intensities is smoothed out and
symmetrised across the pattern. Patterns simulated in this way show better
agreement with the measured patterns than either single-tilt plane-wave
simulations or kinematical diffraction simulations. Quantitative agreement
could be further improved, for instance, by knowledge of the atomic
displacement parameters and the exact distribution of tilt angles.

Supplementary Figure 8: Simulated difference patterns for the LT to HT
transition. a-c Kinematical simulations for both Ta and Te atom motions, Ta
motions only, and Te motions only. d-f Multislice simulations with
$\sigma_{\theta}$ = 30 mrad for both Ta and Te atom motions, Ta motions only,
and Te motions only. The dashed circles at the centre of each difference image
indicate the central part of the beamstop for ease of comparison with measured
difference patterns.

We employ both kinematical and dynamical diffraction simulations to
investigate the contribution of atomic motions to changes in diffraction
patterns of TaTe2. The structural phase transition in TaTe2 involves multiple
3D atomic motions, including weakening of Ta-Ta bonds and reorganisation of
the Te chalcogens. In principle, one could separate the contributions of these
motions and determine their timescales to understand whether they occur
cooperatively or sequentially. For example, in $\mathrm{TaSe_{2-x}Te_{x}}$ it
was found that Ta and chalcogen in-plane motions could be readily separated;
Ta motions caused all primary diffraction peaks to rise, while Te motions
caused some to rise and others to fall31.

Difference images between simulated diffraction patterns for the LT and HT
phase, as well as hypothetical structures where only the Ta or Te atoms move
from LT to HT positions, are shown in Supplementary Figure 8. We observe that
the diffraction peak changes upon transformation from LT to HT phase
(Supplementary Figure 8a,d) are mostly accounted for by the Ta atom motions
(Supplementary Figure 8b,e), and that this motion alone causes a mixture of
positive and negative changes in the primary diffraction peaks much like that
observed in our UED experiment. On the other hand, changes due to Te atoms
(Supplementary Figure 8c,f) are smaller and somewhat different from those
found for the Ta atoms. These simulations show that the overall symmetry
change of the trimer superstructure within the highly distorted, monoclinic
crystal structure causes the mixture of positive and negative diffraction peak
changes observed in our experiment. Dynamical scattering modifies the
magnitude and, for a few reflections, the sign of the changes, but is not the
root cause of the mixed signs.

Supplementary Figure 9: Illustration of the effect of lattice heating on the
electron diffraction pattern. a,b Model of the low-temperature TaTe2 unit cell
before thermalization (LT) and after thermalization (LT*). Thermal ellipsoids
correspond to magnitude of incoherent atomic motions. c Difference image
between LT and LT* diffraction patterns calculated using kinematical
diffraction simulations. The square root of the difference is shown to more
clearly observe the changes in the superlattice peaks.

To qualitatively illustrate thermal reduction of diffraction peak intensities,
to which we attribute behavior in our UED patterns at longer time delays, we
performed kinematical diffraction simulations including a “thermal ellipsoid.”
This ellipsoid represents the magnitude of random atomic displacements in the
material. The difference image between diffraction patterns simulated with
small and large thermal ellipsoids is shown in Supplementary Figure 9. The
small thermal ellipsoids are those obtained from x-ray diffraction
measurements of the LT phase33 whereas the larger ellipsoids are chosen to be
twice as large for simplicity. Indeed, all diffraction peaks decrease upon
heating, providing a qualitative explanation for the largely negative peak
changes observed from 50 to 80 ps in the UED experiment. We note that for
accurate quantitative modeling of the influence of thermalisation on the
diffraction pattern, a good model of the atomic displacement magnitudes and
accounting for dynamical scattering is needed.

## Supplementary Note 4: Difference images for selected time ranges

Supplementary Figure 10: Photo-induced changes in the raw, unsymmetrised
diffraction pattern at selected time ranges. For improved signal-to-noise
these are calculated by averaging difference patterns over the time ranges
listed above the patterns.

The photo-induced changes in the diffraction pattern at early (t
$\approx\\!~{}1.75$ ps and 4 ps), intermediate (t $\approx\\!~{}10$ ps and
38.5 ps), and late (t $\approx\\!~{}65$ ps) time delays are shown in
Supplementary Figure 10. After several picoseconds, significant asymmetry in
the changes is observed, with diffraction signals mainly increasing in the
upper half of the pattern and mainly decreasing in the lower half. Intrinsic
changes in the material would typically affect peaks on opposite sides
equally, as their intensities are related by Friedel’s law. These asymmetric
changes, on the other hand, we attribute to mechanical buckling of the sample,
causing the sample to tilt relative to the electron beam. Such an induced tilt
misalignment would reduce the deviation from the Bragg condition of
reflections on one side of the pattern relative to the other, consistent with
the observed behaviour.

This buckling could be caused by a combination of structural phase transition
of the TaTe2 flake and lattice heating, both of which cause volumetric
expansion that would strain the flake. The asymmetric changes subside at the
50–80 ps time range, suggesting local equilibrium is then re-established.

This asymmetric behaviour occurs simultaneously with the initial stages of PLD
recovery, complicating isolation of the recovery timescale. Such an effect
could be reduced in future studies if thinner flakes can be achieved, for
which the diffraction peak intensities are less sensitive to sample tilt and
photo-induced strain would likely be reduced. Nonetheless, these observations
motivate further development of dynamical diffraction analysis techniques to
account for contributions such as tilt misalignment, multiple scattering, and
sample heating in UED experiments of strongly scattering samples.

Supplementary Figure 11: Difference map symmetrisation process for clearer
visualization of changes. a Average of raw difference patterns acquired from
3–5 ps. The two mirror planes expected for this structure are superimposed. b
Symmetrised difference map obtained by averaging signals across the mirror
planes.

To more clearly visualise the diffraction changes, we symmetrise the
difference maps displayed in the article (Figs. 1, 2, and 3) by averaging
signals across the two mirror plane symmetries. An example of this process for
the difference map averaged from 3–5 ps (Fig. 3a) is shown in Supplementary
Figure 11. This process not only enhances signal-to-noise, but also averages
out some of the asymmetric changes introduced by the apparent sample buckling
discussed above, making contributions from intrinsic structural change more
clearly visible. We note that this process is not used to calculate
quantitative signals; instead, whole pattern fitting is performed on the non-
symmetrised diffraction patterns as discussed in Supplementary Note 5 and
groups of peak intensities are tracked as a function of time.

## Supplementary Note 5: Quantifying diffraction peak changes using whole
pattern fitting

Supplementary Figure 12: Whole pattern fitting of the mean pump off image. a
Measured mean pump off image. b Whole pattern fit function. c Spline
background function with knot points indicated as white dots. All images show
the square root of the intensity.

To quantify diffraction peak intensities in the patterns, we performed whole
pattern fitting (WPF) in which entire non-symmetrised diffraction patterns are
fit with a background function and peak functions simultaneously. Compared to
fitting peaks individually, WPF further constrains the fit by enforcing common
features between the diffraction peaks, such as shape and positioning on a
reciprocal lattice. In this case, the components include the background, the
Si diffraction, the TaTe2 primary diffraction, and the TaTe2 superlattice
diffraction. Within each of the three diffraction peak groups, peak positions
are defined using reciprocal lattice vectors for that group and all peaks
within the group are constrained to have the same shape (though varying
intensities). All diffraction groups share the same pattern centre.

To capture effectively the peak tails, the peaks are fit with generalised
Gaussian functions of the form:

$I(r)=Ae^{-(r/(\sqrt{2}\alpha))^{\beta/2}}$ (S5.1)

Here, r is the radial distance from the peak center, I is the intensity, A is
the amplitude, $\beta$ is the shape parameter (normal distribution for
$\beta$=2, stronger tails for decreasing $\beta$), and $\alpha$ is the width
parameter (equivalent to the rms width when $\beta$=2).

The background fit function is a 2D spline comprised of 4th order B-splines,
or basis splines, generated on a polar grid with knot points as shown in
Supplementary Figure 12c. Such a spline has continuous 1st and 2nd derivatives
everywhere on the grid, including at the knot points. The spline is fit to the
data by fitting the magnitudes of the B-spline components.

The UED patterns undergo significant preprocessing. First, the dark background
reference is obtained by computing the median image of the acquired dark
background frames. Then, for each time point, the dark background is
subtracted, x-ray spikes are removed, frames are normalised by the total
signal and aligned to 0.1 pixel precision using masked cross-correlation and
Fourier shift, and then finally averaged to obtain background subtracted and
processed pump ON and pump OFF images.

To extract the time-resolved peak intensities, WPF is performed on the entire
series of diffraction patterns. First, WPF is performed on the mean pump OFF
image allowing all background and diffraction peak group parameters to vary.
This is shown as an example in Supplementary Figure 12. Then, WPF is performed
on the individual frames with added constraints: the overall background
intensity, individual B-spline components, and the peak $\beta$ factor are
fixed, whereas the individual peak intensities and peak group $\alpha$ vary.

## Supplementary Note 6: Transient data fitting

The transient data were fit using the following model function assuming
exponential kinetics:

$F(t)=H(t-t_{0})\cdot[c1\cdot(1-\exp(-\frac{t-t_{0}}{\tau}))]+C$ (S6.1)

where $H(t-t_{0})$ is the Heaviside step function, $\tau$ is the time
constant, $t_{0}$ is time zero, $c_{1}$ and C are amplitude and constant
offset, respectively. The fit function, F(t) was numerically convolved with a
Gaussian function to account for the instrument time-resolution of
$\sigma_{IRF}=0.75$ ps. Individual fits of the data are provided in
Supplementary Figure 13 and the recovered values of the fit constants are
collated in Supplementary Table 2 .

Supplementary Figure 13: Transient fits of the data using the exponential kinetics in Eq. S6.1 convoluted with the 0.75 ps instrument time resolution, applied to the dynamics of Bragg$\uparrow$, Bragg$\downarrow$ and superlattice peaks for different excitation fluences of 1.5 mJ cm-2, 1.75 mJ cm-2 and 2.3 mJ cm-2. Fit ( ) Residual ( )  Supplementary Table 2: Values of amplitude (A) and time constant ($\tau$) recovered from fits of time-dependent curves of Bragg$\uparrow$, Bragg$\downarrow$ and Superlattice peaks at 1.5 mJ cm-2, 1.75 mJ cm-2, and 2.3 mJ cm-2. Errors associated with the extracted values are the standard errors of the fit.  | 1.5 mJ cm-2 |  | 1.75 mJ cm-2 |  | 2.3 mJ cm-2
---|---|---|---|---|---
| A |  $\tau$ (ps) |  | A |  $\tau$ (ps) |  | A |  $\tau$ (ps)
Bragg$\uparrow$ | $3.0\pm 0.6$ | $1.4\pm 1.6$ |  | $4.9\pm 0.5$ | $1.4\pm 0.7$ |  | $8.0\pm 0.9$ | $2.4\pm 0.8$
Bragg$\downarrow$ | $-10.3\pm 2.8$ | $3\pm 1.6$ |  | $-11.2\pm 2.1$ | $1.6\pm 1.3$ |  | $-13.1\pm 2.3$ | $2.3\pm 1.3$
Superlattice | $-13.5\pm 3.4$ | $1.1\pm 1.5$ |  | $-29.6\pm 2.8$ | $0.9\pm 0.4$ |  | $-46.6\pm 2.4$ | $1.4\pm 0.3$

## Supplementary Note 7: Sample optical properties from reflectivity mapping

Supplementary Figure 14: Reflectivity of TaTe2 sample. a Reflectance map
across the TaTe2 flake measured at 1030 nm wavelength at 77 K. b, c Zoomed-in
maps at 77 K of region over Si-supported Si3N4 and region over suspended
Si3N4. d, e Reflectance contrast spectra from region over Si-supported Si3N4
and region over suspended Si3N4.

In thin films, optical propagation involves coherent interference between
waves transmitted through and reflected from each interface between layers.
The reflectivity, absorbance, and transmittance of a thin film sample depends
not only on the thickness and dielectric function of the film, but also on
that of the substrate materials. Here, we take advantage of this behaviour to
extract the dielectric function of TaTe2 in the near-infrared range and
estimate the absorption of the sample. We measure the reflectance in two
regions of the flake over different substrates and, using the transfer-matrix
method to model the reflectance in these cases, we retrieve the complex
refractive index.

We use the tmm python package62 to model the optical propagation, employing
previously measured dielectric functions for Si3N463, Si64, and SiO265. In
using this method, we approximate the laser as a plane wave and the in-plane
dielectric function as isotropic.

Reflectance mapping was performed in a confocal laser scanning microscope. A
mode-locked Ti:Sapphire laser (Coherent Chameleon) generates the incident
beam, which is focused by a Nikon 40x objective lens with a numerical aperture
of 0.6NA onto the surface of the sample. The reflected light was collected
through the same objective lens, coupled in free space into an Andor Kymera
328i spectrometer equipped with a 50 g mm-1, 600-nm blaze grating and detected
on an Andor iDus CCD camera. The output wavelength of the laser was scanned
from 690 nm to 1080 nm in steps of 10 nm, with a FWHM of about 9 nm at each
wavelength, and a hyper-spectral map of the light reflected on the surface of
the sample was measured at every step. The microscope’s alignment and focus
were adjusted before each measurement. A continuously variable ND filter wheel
was used to compensate for the power fluctuations of the laser emission as a
function of wavelength.

The sample was mounted in a Janis ST-500 flow cryostat using liquid nitrogen
to reach a base temperature of 77 K. We mapped the reflectivity by scanning
ASI MS-2009B XY motorised translation stages supporting the sample and
collecting the reflected spectrum at each position. This hyperspectral
measurement was controlled using the open-source ScopeFoundry software
platform66; 67.

To calibrate the reflectance, we measured the reflected signal from a 100 nm
thick gold film and the Si3N4-covered Si TEM chip under the same conditions.
For instance at 1030 nm, after correcting for the reflectivity of gold (99%),
we obtained a reflectance from the Si chip of about 28%. Using this and the
measured reflectance contrast, $\frac{\Delta R}{R}$, as a function of laser
wavelength between freestanding Si3N4 and the Si chip, we fit the thickness of
the membrane and the Si native oxide, finding a best fit for 28 nm of Si3N4
and a 2 nm SiO2 native oxide layer on the Si chip.

Reflectance maps at 77 K for 1030 nm light are shown in Supplementary Figure
14a-c. We observe that the reflectivity is largely homogeneous across the
flake, with deviations at topographic features such as flake edges and small
pieces of additional TaTe2 sitting on top from the sample transfer process
(see AFM map in Supplementary Note 2). We also observe similar reflectivity
between regions over the Si chip and the suspended Si3N4 membrane.

From the zoomed-in maps taken at each wavelength, we compute the reflectance
contrast spectra between TaTe2 and the two substrate types: the Si chip and
the suspended Si3N4 membrane (Supplementary Figure 14d,e). We observe similar
reflectance values and trends with the wavelength at 77 K and 300 K, though
slightly higher reflectance is observed in the region over the Si chip at 77 K
which may be due to formation of the LT phase.

Supplementary Figure 15: Dielectric function and absorption spectra extracted
using the transfer-matrix method. a Best-fit real part of the refractive index
of TaTe2. b Best-fit imaginary part of the refractive index of TaTe2. c
Calculated absorption of the TaTe2 flake supported by Si3N4. d Calculated
local absorption as a function of depth. Supplementary Figure 16: DFT-
calculated refractive index for light polarised along the b axis. a Real part
for LT and HT phases. b Imaginary part for LT and HT phases.

Using the transfer-matrix method, we optimise the real and imaginary parts of
the refractive index to match the reflectance contrast in both regions, shown
in Supplementary Figure 15a,b. The extracted refractive index shows smooth and
largely monotonic behaviour in this region, and it is similar at both
temperatures. From the refractive index, n we calculated the total absorption
spectrum via the transfer-matrix method of the Si3N4-supported TaTe2 sample
(Supplementary Figure 15c). At 1030 nm wavelength, the fraction absorbed is
about 44% at both 77 K and 300 K. We also compute the absorption profile over
the depth of the film at 1030 nm, shown in Supplementary Figure 15d. As the
absorption depth is 33 nm, we calculate significant variation in absorption
through the 60 nm thickness of the TaTe2 film: Material near the top surface
absorbs more than 1.5 times more photons than average through the depth.

To check whether the obtained refractive index behaviour is reasonable for
this system, we calculate frequency dependent dielectric response of TaTe2
using VASP under independent particle approximation. The calculated refractive
indices of the relaxed LT and HT structures of TaTe2 for light polarised along
the crystal b axis is shown in the range of our measurements in Supplementary
Figure 16. Though direct quantitative comparison to the experiment is
complicated by experimental factors such as sample tilt, laser polarisation
character, laser bandwidth, and angular spread of the laser beam, we make a
few qualitative observations. First, the dielectric function of the LT and HT
phases have similar magnitude over this wavelength range, both in the
calculation and in experiment. Second, the imaginary component corresponding
to absorptivity shows good agreement between simulation and experiment: the
magnitude is between 2.0 and 2.7 and generally increases for longer
wavelengths. Thirdly, the LT phase appears to have higher k over most of the
wavelength range both in measurement and experiment: This is consistent with
the increased density of states around the Fermi level in the LT phase
observed in DFT calculations (see Supplementary Note 1).

## Supplementary Note 8: Fluence dependent dynamics and calculated temperature
rise

Supplementary Figure 17: Photoinduced superstructure melting at varying laser
fluence. a Representative difference images for early (centered around
$\approx\\!~{}4$ ps) time delays for a laser fluence of 1.5 mJ cm-2, 1.75 mJ
cm-2, and 2.3 mJ cm-2. For improved signal-to-noise these are calculated by
averaging difference patterns over a 3–5 ps time range. b Initial superlattice
peak dynamics for varying laser fluence. Exponential fits are superimposed as
solid lines, with time constants of $1.07\pm 0.92$ ps, $0.9\pm 0.32$ ps, and
$1.44\pm 0.27$ ps for the three fluences in increasing order. c Magnitude of
peak subset changes for varying laser fluence, i.e. the amplitudes of the
exponential fits. A linear fit to the superlattice peak intensities is shown
as a black dashed line.

In addition to the experiment at 2.3 mJ cm-2 highlighted in the main text, we
also measured the initial ultrafast optical melting dynamics at 1.5 mJ cm-2
and 1.75 mJ cm-2. Difference patterns averaged over a 3–5 ps time range are
shown in Supplementary Figure 17a. The magnitude of observed changes increases
with the incident fluence over this range, and the mixture of positive and
negative changes at all fluences resembles that observed for the thermal phase
change shown in Fig. 1. The quantitative temporal profiles of the superlattice
peak intensities are shown in Supplementary Figure 17b. The measured time
constants of PLD suppression fall within the range of 1 to 1.5 ps for all
fluences. The increasing magnitude of superlattice peak reduction, as well as
of change in $\text{Bragg}\uparrow$ and $\text{Bragg}\downarrow$, is shown in
Supplementary Figure 17c. This behaviour shows that the threshold fluence to
melt the Ta trimer superstructure is less than 1.5 mJ cm-2.

The final temperature of the sample in our UED experiments after complete
thermalisation following laser absorption at 1030 nm was also calculated. The
estimate was based on the assumption that 44% of the incident light gets
absorbed (based on optical measurements in Supplementary Note 7) in the film
of 61.5 nm thickness (as determined in Supplementary Note 2). We calculated
the corresponding temperature increase using the temperature-dependent heat
capacity $C_{p}(T)$ from ref. 33, by taking into account the material’s
density33 $\rho$ = 9.3 g cm-3 and molar mass M = 436.15 g mol-1. This resulted
in thermally equilibrated temperatures of $T_{therm}$ = 125 K, 130 K and 177 K
for the three fluences, respectively, of $F=1.5$ mJ cm -2, 1.75 mJ cm -2, and
2.3 mJ cm -2.