# Dynamics and Resilience of the Charge Density Wave in a Bilayer Kagome Metal

Manuel Tuniz  Dipartimento di Fisica, Universita degli studi di Trieste,
34127, Trieste, Italy  Armando Consiglio  Institut für Theoretische Physik und
Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität
Würzburg, 97074 Würzburg, Germany  Denny Puntel  Dipartimento di Fisica,
Universita degli studi di Trieste, 34127, Trieste, Italy  Chiara Bigi  School
of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS,
United Kingdom  Stefan Enzner  Institut für Theoretische Physik und
Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität
Würzburg, 97074 Würzburg, Germany  Ganesh Pokharel  Materials Department,
University of California Santa Barbara, Santa Barbara, California 93106, USA
Pasquale Orgiani  Istituto Officina dei Materiali, Consiglio Nazionale delle
Ricerche, Trieste I-34149, Italy  Wibke Bronsch  Elettra - Sincrotrone Trieste
S.C.p.A., Strada Statale 14, km 163.5, Trieste, Italy  Fulvio Parmigiani
Dipartimento di Fisica, Universita degli studi di Trieste, 34127, Trieste,
Italy  Elettra - Sincrotrone Trieste S.C.p.A., Strada Statale 14, km 163.5,
Trieste, Italy  Vincent Polewczyk  Istituto Officina dei Materiali, Consiglio
Nazionale delle Ricerche, Trieste I-34149, Italy  Phil D. C. King  School of
Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, United
Kingdom  Justin W. Wells  Centre for Materials Science and Nanotechnology,
University of Oslo (UiO), Oslo 0318, Norway.  Ilija Zeljkovic  Department of
Physics, Boston College, Chestnut Hill, MA 02467, USA  Pietro Carrara
Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16,
20133 Milano, Italy  Istituto Officina dei Materiali, Consiglio Nazionale
delle Ricerche, Trieste I-34149, Italy  Giorgio Rossi  Dipartimento di Fisica,
Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy
Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, Trieste
I-34149, Italy  Jun Fujii  Istituto Officina dei Materiali, Consiglio
Nazionale delle Ricerche, Trieste I-34149, Italy  Ivana Vobornik  Istituto
Officina dei Materiali, Consiglio Nazionale delle Ricerche, Trieste I-34149,
Italy  Stephen D. Wilson  Materials Department, University of California Santa
Barbara, Santa Barbara, California 93106, USA  Ronny Thomale  Institut für
Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence
ct.qmat, Universität Würzburg, 97074 Würzburg, Germany  Tim Wehling  Institute
of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607 Hamburg,
Germany  The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149,
22761, Hamburg, Germany  Giorgio Sangiovanni  Institut für Theoretische Physik
und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat,
Universität Würzburg, 97074 Würzburg, Germany  Giancarlo Panaccione  Istituto
Officina dei Materiali, Consiglio Nazionale delle Ricerche, Trieste I-34149,
Italy  Federico Cilento<EMAIL_ADDRESS>Elettra - Sincrotrone
Trieste S.C.p.A., Strada Statale 14, km 163.5, Trieste, Italy  Domenico Di
Sante<EMAIL_ADDRESS>Department of Physics and Astronomy,
University of Bologna, 40127 Bologna, Italy  Center for Computational Quantum
Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA  Federico
Mazzola<EMAIL_ADDRESS>Department of Molecular Sciences and
Nanosystems, Ca’ Foscari University of Venice, 30172 Venice, Italy  Istituto
Officina dei Materiali, Consiglio Nazionale delle Ricerche, Trieste I-34149,
Italy

###### Abstract

Long-range electronic order descending from a metallic parent state
constitutes a rich playground to study the intricate interplay of structural
and electronic degrees of freedom Neupert_2022 ; Arachchige_2022 ; Wang_2021a
; Heumen_2021 ; Luo_2022 . With dispersive and correlation features as
multifold as topological Dirac-like itinerant states, van-Hove singularities,
correlated flat bands, and magnetic transitions at low temperature, kagome
metals are located in the most interesting regime where both phonon and
electronically mediated couplings are significant Kang_2020 ; Kang_2020b ;
Lin_2018 ; Ye_2019 ; Pokharel_2021 ; Hu_2022 . Several of these systems
undergo a charge density wave (CDW) transition, and the van-Hove
singularities, which are intrinsic to the kagome tiling, have been conjectured
to play a key role in mediating such an instability. However, to date, the
origin and the main driving force behind this charge order is elusive. Here,
we use the topological bilayer kagome metal ScV6Sn6 as a platform to
investigate this puzzling problem, since it features both kagome-derived
nested Fermi surface and van-Hove singularities near the Fermi level, and a
CDW phase that affects the susceptibility, the neutron scattering, and the
specific heat Arachchige_2022 , similarly to the siblings $A$V3Sb5 ($A$ = K,
Rb, Cs) Neupert_2022 ; Kang_2023  and FeGe Teng_2022 . We report on our
findings from high—resolution angle-resolved photoemission, density functional
theory, and time-resolved optical spectroscopy to unveil the dynamics of its
CDW phase. We identify the structural degrees of freedom to play a fundamental
role in the stabilization of charge order. Along with a comprehensive analysis
of the subdominant impact from electronic correlations, we find ScV6Sn6 to
feature an instance of charge density wave order that predominantly originates
from phonons. As we shed light on the emergent phonon profile in the low-
temperature ordered regime, our findings pave the way for a deeper
understanding of ordering phenomena in all CDW kagome metals.

** These authors contributed equally
Bilayer kagome metals are an emerging class of correlated topological
compounds with chemical formula $R$V6Sn6 ($R$: rare earth - hereafter also
dubbed as the 166 family), featuring unconventional topological phases and
collective magnetic excitations at low temperature Pokharel_2021 ; Hu_2022 ;
Arachchige_2022 ; Peng_2021 ; Ishikawa_2021 ; Rosenberg_2022 ; Lee_2022 ;
Chen_2021 . Similarly to the sister compounds $A$V3Sb5 ($A$: alkali atoms -
hereafter also nicknamed as the 135 family), the electronic structure of
$R$V6Sn6 is a rich platform for the emergence of unconventional phase
diagrams, boasting the simultaneous presence of itinerant Dirac electrons,
non-trivial flat bands, and van-Hove singularities at the Fermi energy
Kang_2020 ; Kang_2020b ; Lin_2018 ; Ye_2019 ; Guo2009 ; Mazin2014 ; Kiesel2013
; DiSante2020 ; Neupert_2022 . Among the 166 family, ScV6Sn6 exhibits a unique
three-dimensional charge density wave (CDW) transition, with a motif
dissimilar to those observed in other kagome compounds Kang_2023 . Here, the
CDW phase provokes a weak atomic lattice displacement, which might generate
unconventional phenomena, such as metal-insulator transitions of fermions,
vortexes at the surface, chiral currents, and bond orders Arachchige_2022 ;
Guo_2022 ; Nishimoto_2010 ; Kiesel_2013 ; Denner_2021 ; Feng_2021 ; Park_2021
; Jiang_2021 ; Liang_2021 . The major goal of contemporary research thus is to
reveal the underlying mechanism of the charge order in ScV6Sn6 and the
specific role of structural and electronic degrees of freedom, the
interdependence of whom has so far remained uncharted territory.
Previous works have highlighted important differences between the CDW in
ScV6Sn6, $A$V3Sb5, and FeGe Teng_2022 . In $A$V3Sb5, the charge order has been
thought to be connected to the nesting of the Fermi surface, exemplified by
the van-Hove singularity electron filling Wu2021 ; Kang2022 ; Ortiz2020 ;
Kang_2023 . In these systems, the charge order has been conjectured to be
linked to the emergence of superconductivity and stripe orders Yu_2021 ;
Liang_2021 ; Du_2021 ; Oey_2022 ; Li_2021a ; Wang_2021b ; Zhao_2021 . In
addition, the atomic displacement following the onset of the CDW involves
mostly the V atoms and their in-plane positions. ScV6Sn6, surprisingly, does
not undergo any superconducting transition at low temperature and the motif of
the CDW, generated by the ordering vector $Q=(1/3,1/3,1/3)$, does not give
rise to either the Star of David or trihexagonal arrangement, as for the
$A$V3Sb5 compounds, for which the ordering vectors are $Q=(1/2,1/2,1/4)$ and
$Q=(1/2,1/2,1/2)$ Ortiz_2021 ; Ortiz2020 ; Nie_2022 . This is ascribed to the
involvement of Sn and Sc atoms in the lattice modulation. The differences
between these two systems, are also reflected in a much more rapid CDW
suppression for ScV6Sn6 under the application of pressures Zhang_2022 ,
offering an increased ease of tuneability compared to $A$V3Sb5.
In CDW materials, the simultaneous occurrence of a lattice displacement and a
change in the electronic structure, often associated with the opening of gaps
in the electronic spectrum challenges the understanding of the main driving
force behind the charge order and limits the access to possible consequent or
concomitant cascade of collective phases and their control. While there is
compelling evidence of CDW in kagome systems, its microscopic origin and
dynamics are still debated. We stress that the understanding of such origin
and dynamics is a task of paramount importance given the peculiar electronic
structure of kagome with van-Hove singularities at the Fermi level and the
presence of a nested Fermi surface, which hints at an energy gain upon a gap
opening as an underlying driver. For 166, which has also a topological nature,
it becomes crucial to understand the dynamics of the CDW, to uncover not only
the relationship between subsequent ordered phases, but to elucidate the
interplay between phase transition and electron spins Hu_2022 ; Yin_2022 ;
Sun_2022 ; Tanaka_2020a ; Ortiz2020 ; NagaosaPRB2019 . In the present study,
we used time-resolved optical spectroscopy (TR-OS) to unveil the dynamics of
the CDW in the 166 bilayer kagome ScV6Sn6. Specifically, by using TR-OS, we
disclose the energy scales involved in the charge order, which points towards
a major robustness of the lattice degree of freedom for the observed
transition.
First, we describe the electronic properties of ScV6Sn6, then we will show by
using ARPES, DFT, and TR-OS how the electronic and structural degrees of
freedom are affected by the CDW order. Along with the crystal structure (both
with and without CDW) and the Brillouin zone (Figs.1 a-b), we show the
expected electronic structure from density functional theory (DFT), above and
below the transition temperature, in Fig.1 c (red color without CDW, green
shades with CDW). In both CDW and pristine cases, the Dirac-like states and
the van-Hove singularities are similar and identifiable, with negligible
variation in their electronic dispersion along the $\Gamma$-K-M-$\Gamma$ path.
According to the calculations, the van-Hove singularities are located around
the Fermi level. It is thus noteworthy that large changes at EF are not seen
upon inclusion of the CDW nested systems Whangbo_1991 ; Carpinelli_1996 ;
Tam_2022 ; Bosak_2021 . Along the $\Gamma$-K-M-$\Gamma$ high-symmetry
direction, the main changes occur at the $\Gamma$ point within the energy
window [-0.75, -1] eV. Below the transition temperature, the separations
between the bands increase by approximately 30 meV compared to the electronic
structure without CDW (see red box in Fig.1 c). Other changes along the same
direction, even if smaller, are indicated by the blue arrows (labeled as ’2’).
If in the plane that comprises the $\Gamma$ point, the changes are rather
subtle, our DFT calculation reveals that the CDW has its major effect along
the A-H and A-L directions (see yellow arrows labeled as ’3’). There, we
notice that the charge order opens several energy gaps along the entire
$k$-space path. Nonetheless, we also notice that the spectral weight
immediately fades away from the gap openings. In addition, the spectral
intensity in the CDW phase is still located around the poles of the electronic
structure of the bands above $T_{CDW}$. As a result, the gaps themselves are
expected to be challenging to detect experimentally given the vicinity to the
poles, the $k_{z}$ broadening, and the experimental resolution ($\sim$ 15 meV,
that is larger than the gap value itself) Sunko_2020 .
Similarly to other 166 materials, as shown in Fig. 2, ScV6Sn6 shows the
presence of surface states, after the ultrahigh vacuum (UHV) cleave (see
Methods for details about the samples’ preparation). These surface states have
been extensively discussed for other kagome systems Kang2022 ; Kang_2020 ;
Kang_2020b  and members of the 166 family Pokharel_2021 ; Peng_2021 ;
Ishikawa_2021 ; Rosenberg_2022 ; Hu_2022 . While they offer an interesting
platform for exploiting spin-momentum locking because of their non-trivial
topology Hu_2022 ; Li_2014 ; Li_2018 ; Jiang_2016 ; Luo_2017 , they could
challenge the clear visualization of small changes occurring in the bulk
electronic structure as a consequence of the charge order, because they could
obfuscate subtle spectroscopic features. Thus, to exclude this avenue, we
measured the electronic structure above and below the transition temperature
$T_{CDW}$ and along the $\Gamma$-K-M-$\Gamma$ high symmetry direction, with
and without surface states such that one can better distinguish the bulk from
the surface-derived signal (see Fig.2 for the clean surface case with both
light polarizations and Supplementary Information Figs. 1 and 2 for data where
the surface states have been suppressed and how). Along the selected high-
symmetry path, we have the most favorable photoemission matrix elements and
the intensity of the bands is the most prominent. Notably, no remarkable
differences are observed across $T_{CDW}$, besides a constant thermal
broadening which affects the spectra collected above $T_{CDW}$.
To still check possible effects of the charge order, from the ARPES spectra
collected along the $\Gamma$-K-M-$\Gamma$ path, we extracted energy-
distribution curves (EDCs) across the $\Gamma$ point, where we expect the
strongest changes induced by the CDW (Fig.2 i-l and red box of Fig.1 c). By
using linear-horizontal (LH) polarized light, it is hardly possible to see the
relevant states affected by the charge order (see Fig.2 i). By using linear-
vertical (LV), instead, the missing spectral weight is recovered. In this
condition, we resolve a 70 meV splitting at approximately $0.8$ eV of binding
energy. Such a splitting might be consistent with the calculated increase in
the energy separation produced by the CDW, however, we cannot exclude that
this might be an effect of the band sharpening due to the lower temperature
(see Fig.2 l). Despite having weaker intensity due to photoemission matrix
elements, we also collected ARPES spectra along the A-L and A-H high-symmetry
directions (shown in Supplementary Information Figs. 3, 4, and 5). Along these
paths, the DFT analysis predicts the strongest changes in the electronic
structure. Unfortunately, the changes from above to below $T_{CDW}$ are very
small and not well-resolved experimentally. This is likely due, as anticipated
above, to the combination of $k_{z}$ broadening, finite experimental
resolutions, small energy values of the gaps, and expected spectral weight
concentrated along the poles of the bands above the CDW transition.
The ARPES data depict a situation where most of the electronic spectral weight
is only weakly affected by the CDW order in the proximity of the Fermi level
(within the experimental resolutions). This is in line with DFT only showing a
partial gap opening, which involves only certain bands but not the majority of
the V-derived spectral weight. In addition, the partial gap calculated in the
electronic structure agrees well with recent optical measurements in the
static regime performed for ScV6Sn6, which show a sharp first order transition
without the development of full gaps in the optical spectra Arachchige_2022 .
Importantly, this behaviour describes a rather rare phenomenology, which is
different from the most commonly observed second-order density condensation
gaps, found in systems which undergo a CDW transition. In other words, the
inability to spectroscopically resolve changes in the Fermi surfaces across
the transition temperature makes ScV6Sn6 reminiscent of the CDW behaviour
discovered for IrTe2 , TaTe2, and BaNi2As2 Li_2014b ; Hu_2022 ; Fang_2013 .
This aspect is intimately related to the underlying electronic structure of
the compound; the vanadium states indeed contribute in a significant way to
the density of states around $E_{F}$, while the corresponding atoms are not
influenced by the CDW displacement. Conversely, tin and scandium states are
not predominant at $E_{F}$ while the corresponding atoms’ positions are
particularly influenced by the CDW transition. Additionally, ScV6Sn6 shows a
very peculiar ordered phase, with a marked peak in the specific heat and an
increased metallic character below the transition Arachchige_2022 . However,
the origin of the charge order is still an open question. It is then crucial
to separate the time- and energy-scales of the electronic and lattice degrees
of freedom and to determine their robustness and involvement in the CDW order.
To this aim, we use TR-OS and we measure the time-resolved reflectivity
dynamics of ScV6Sn6. Fig.3 a presents the temperature (T) dependence of the
photoinduced reflectivity transients, $\Delta R/R$, recorded upon increasing
the temperature (T from approximately 18 K; the fluence was F $\approx$ 0.2
mJ/cm2). The $\Delta R/R$ can be described by two features: an incoherent
(non-oscillating) response and a coherent oscillatory behaviour. In our data,
clear oscillations in the $\Delta R/R$, showing a strong T-dependence, are
detected up to the transition temperature $T_{CDW}$ (Fig.3 a-b). The
incoherent (non-oscillating) response consists of two decays, a fast and a
slow one, with characteristic times $\tau_{1}$ and $\tau_{2}$, respectively
(see Supplementary Information for details about the data analysis and their
extraction) that appear in the data as a fast peak and a slowly-decaying
component. Similarly to the coherent response, the incoherent one is also
strongly T-dependent and it shows the indication of a phase transition around
T $\approx$ 90 K (see Fig.4 a), which matches well with the nominal $T_{CDW}$
Arachchige_2022 . Above $T_{CDW}$, the $\Delta R/R$ becomes smaller and, after
the fast exponential decay, it changes sign becoming negative (see trace ’5’
of Fig.3 b).
In general, below the critical CDW temperature, the pump pulse induces an
abrupt change in the reflectivity, followed by a fast decay within a
picosecond and a slower recovery on a timescale of the order $\approx$ 10 ps
Tomeljak_2009 ; Yusupov_2008 ; Pokharel2022 ; Vorobeva_2011 ; Ravnik_2018 .
The first, which slows down critically upon approaching the transition
temperature, is attributed to the re-opening of the CDW gap, while the second
one, as confirmed by detailed studies of the dynamics as a function of the
excitation fluence and applied external electric field, is attributed to a
second stage of the CDW recovery Eichberger2010 ; TOMELJAK2009_physB ;
Huber_2014 ; Storeck_2020 . In ScV6Sn6, the T-evolution of the incoherent part
of the $\Delta R/R$ shows a rather peculiar behavior: in contrast to the well-
studied one dimensional CDW systems, the lifetime of the first fast decay
$\tau_{1}$ increases linearly with the temperature and shows a rapid drop at
$T_{CDW}$ (Fig.4 a). Remarkably, no divergence of the lifetime $\tau_{1}$ is
observed during the phase transition. This peculiar behavior, in combination
with our ARPES measurements and DFT analysis, suggests an unusual origin for
the CDW phase in this material, where no gaps are observed in the near Fermi
level region. Indeed, a divergence of the lifetime $\tau_{1}$ is usually
linked to the closing of the electronic gap that develops in conventional CDW
transitions. This is also different from what has been observed in the kagome
metal CsV3Sb5, where TR-OS measurements have highlighted the divergence of the
lifetime of the fast decay process during the onset of the charge order
Wang_2021b .
Interestingly, from the fits to the data (see Supplementary Information for
more details), the frequency of the oscillatory mode and the damping show a
pronounced temperature dependence, as we show in Fig.4 b. In particular, at
low temperature the mode is characterized by a frequency of $\sim$ 1.45 THz,
in excellent agreement with our ab-initio estimate of 1.42 THz from the
quadratic fit of the DFT total energy around the minimum of CDW ordered
structure (see Fig.4 c and Methods for more details), and we observe a
$\approx$ 6 $\%$ softening of the mode frequency and an exponential increase
of the damping constant, when the temperature of the system approaches the
critical temperature of the CDW transition. Such a temperature dependence has
been observed in many CDW systems and it constitutes the fingerprint of an
amplitude mode (AM) of the CDW phase Demsar_1999 ; Chen_2017 ; Yusupov2010 ;
Yoshikawa2021 ; Vorobeva_2011 ; Ravnik_2018 . This observation confirms that
the coherent response is not due to a trivial phonon, but rather to the
excitation of the AM of the CDW phase, confirming the onset of CDW physics in
ScV6Sn6. We also note that no fingerprints of an AM have been hitherto
detected in CsV3Sb5 by previous reflectivity studies Wang_2021b .
By varying the excitation density (fluence), additional information about the
nature of the phase transition can be obtained. The melting of electronic
modulation is generally achieved on a timescale much faster than the
characteristic timescale related to the relaxation of the periodic lattice
modulation, which is given by the period of the characteristic amplitude modes
of the system. This results in the disentanglement of electronic and lattice
degrees of freedom on the sub-picosecond time scale, with a subsequent rapid
recovery of the electronic degrees of freedom Schaefer2013 ; Yusupov2010 ;
Vorobeva_2011 ; Stojchevska_2011 . Additionally, the characteristic energy
required to fully drive the phase transition, i.e. quenching the periodic
lattice distortion and the electronic degrees of freedom, is that one which
leads to the disappearance of the (oscillatory) amplitude mode Pokharel2022 ;
Schaefer2013 . This provides a means to quantify the strength of the lattice
degree of freedom compared to the electronic one. We report this in Fig. 3 c,
where the evolution of the scaled $\Delta R/R$ signal as a function of the
fluence is shown, in a range from $\sim 50$ to $\sim
1000~{}\mathrm{\mu}$J/cm2. The traces are scaled to the fluence to better
visualize the qualitative behavior of the response upon approaching the
photoinduced phase transition. Note that the sample is kept at a temperature
well-below $T_{CDW}$. In the low perturbation regime, the signal scales
linearly with excitation density (traces A, B, C in Fig. 3 d), while upon
approaching the photoinduced phase transition the $\Delta R/R$ signal related
to CDW order shows saturation Schaefer2013 ; Pokharel2022 . The maximum change
that can be induced in the signal is generally achieved when the electronic
degree of freedom associated to the CDW order is collapsed. We find that the
fast electronic component with relaxation time $\tau_{1}$ saturates at a
fluence, where the oscillations linked to AM involving the lattice degrees of
freedom persist Schaefer2013 ; Tomeljak_2009 ; Pokharel_2022 . By
progressively increasing the excitation fluence, the oscillations in the
$\Delta R/R$ due to the AM get also suppressed, with an exponential increase
of the damping constant and a softening of the frequency of the mode.
Remarkably, our measurements highlight the robustness of the lattice
reconstruction of the CDW in this material. Indeed, even at high excitation
fluences ($\sim 700\ \mu$J/cm2), the oscillations due to the AM are still
detected. This behavior is again markedly different from what has been
observed in the sister compound CsV3Sb5, where already at a pump fluence as
small as $\sim 55\ \mu$J/cm2, the CDW order is melted Wang_2021a . In our
study, we show that the oscillation disappears completely only at a fluence of
$\sim 1000\ \mu$J/cm2, meaning that the lattice order can be melted, although
at a fluence larger than the one required to saturate the purely electronic
response at around $\approx$ 240 $\mu$J/cm2. The electronic states that
maximally couple to this CDW span an energy window around the Fermi level of
about 0.25 eV, because smearing over that window greatly affects the AM, as we
show in Fig. 4 d. Indeed, taking into account the electronic specific heat of
ScV6Sn6, an absorbed fluence of $\approx$ 240 $\mu$J/cm2 leads to an increase
of the electronic temperature of $\approx$ 2100 K, which is in reasonable
agreement with the smearing obtained by DFT calculations (See Fig. 4 d).
Finally, it is only when the average lattice temperature exceeds the CDW
critical temperature because of the average power deposited by the pump pulse,
that one might expect to detect the transient signal of the high-temperature
phase. We estimate the pump-induced average heating to be in a $\Delta
T\approx$ 20 K at a fluence of $\approx$ 1 mJ/cm2. Hence, in order to reach
$T_{CDW}$, very large fluences are required, which are not attainable because
sample damage would occurr.
In conclusion, by using the combination of experimental techniques, i.e. ARPES
and TR-OS, as well as theoretical calculations, we disclose the dynamics of
the unusual CDW transition in ScV6Sn6 and we simultaneously demonstrate
marginal energy gaps at the Fermi level. In particular, temperature dependent
TR-OS reveals the hallmarks of the CDW. In addition, our fluence dependent
study disentangles the electronic and structural degrees of freedom, showing
persisting AM oscillation up to unusually high values of fluence,
corroborating the robustness of the lattice distortions compared to the sudden
disruption of the purely electronic component. Such dynamics is in favor of a
CDW with the lattice degrees of freedom and electron-phonon interaction
playing the dominant role. We believe that our comprehensive study sheds light
onto the collective modes emerging in the low-temperature phase of ScV6Sn6. It
paves the way for the understanding of unconventional many-body phases in
correlated kagome metals, which all share a similarly nested Fermi surface,
and deepens our understanding of cooperative lattice and electronic symmetry
breaking at this new frontier. Therefore, we think that our discovery is the
crucial step to understand the origin and drive of the CDW also in the
archetypal family AV3Sb5.
Methods
Experimental details – Single crystals of ScV6Sn6 were grown using a flux-
based growth technique as reported in the reference PhysRevMaterials.6.104202
. Sc (chunk, 99.9$\%$), V (pieces, 99.7$\%$), and Sn (shot, 99.99$\%$) were
loaded inside an alumina crucible with the molar ratio of 1:6:20 and then
heated at 1125 ∘C for 12 h. Then, the mixture was slowly cooled to 780 ∘C at a
rate of 2 ∘C/h. Thin plate-like single crystals were separated from the excess
Sn-flux via centrifuging at 780 ∘C. The samples were cleaved in ultrahigh
vacuum (UHV) at the pressure of 1$\times$10-10 mbar. The ARPES data were
acquired at the APE-LE end station (Trieste) using a VLEED-DA30 hemispherical
analyzer. The energy and momentum resolutions were better than 12 meV and 0.02
Å-1, respectively. The temperature of the measurements was kept constant
throughout the data acquisitions (16 K and 120 K, below and above $T_{CDW}$
respectively). Both linear polarizations were used to collect the data from
the APE undulator of the synchrotron radiation source ELETTRA (Trieste). The
photon energy used for the ARPES data was 75 eV. This choice was such that the
spectra intensity was the most prominent, especially near the region of the
quadratic minimum of the electronic structure, where the major changes with
the CDW are expected.
Time-resolved reflectivity experiments were performed at the T-ReX laboratory
(FERMI, in Trieste) with a probe photon energy of $\approx$ 0.95 eV (1300 nm).
The measurements were performed using a Ti:sapphire femtosecond (fs) laser
system, delivering, at a repetition rate of 250 kHz, $\approx 50$ fs light
pulses at a wavelength of 800 nm (1.55 eV). The single color probe
measurements were performed at a probe wavelength of 1300 nm, obtained by
filtering a broadband (0.8–2.3 eV) supercontinuum probe beam, generated using
a sapphire window.
Theoretical details – DFT calculations have been performed using both Quantum
Espresso and VASP packages. Phonon calculations are based on density
functional perturbation theory, as implemented in Quantum Espresso
doi:10.1063/5.0005082 ; Giannozzi_2009 ; Giannozzi_2017 . Exchange and
correlation effects were included with the generalized gradient approximation
(GGA) using the Perdew-Burke-Ernzerhof (PBE) functional PhysRevLett.77.3865 ;
the pseudopotentials are norm-conserving and scalar relativistic, containing
core corrections PhysRevB.88.085117 . Self-consistent calculations and ionic
relaxation of the unit cell have been performed with a 9$\times$9$\times$6
$k$-grid; convergence threshold for both ionic minimization and electronic
self-consistency are set to be $10^{-15}$ Ry. The kinetic energy cutoff for
the wavefunctions is equal to 90 Ry. A ordinary Gaussian spreading of 0.006 Ry
has been used. Once the structure was properly at equilibrium, with vanishing
forces acting on each atom, we proceeded with the actual phonon calculations.
The dynamical matrices have been obtained and computed for a $q$-grid of
3$\times$3$\times$6, with a self-consistency threshold of $10^{-15}$ Ry. These
dynamical matrices are consequently Fourier-transformed to obtain the inter-
atomic force constants (IFC) in real space; three translational acoustic sum
rules have been imposed, via correction of the IFC. Finally, both phonon
dispersion and phonon density of states are obtained. In particular, for the
density of states calculations (see results in the Supplementary Information)
we used 30$\times$30$\times$30 $q$-points. The presence of imaginary phonon
modes has been verified also for a 6$\times$6$\times$9 and a
9$\times$9$\times$12 $q$-grid, during the dynamical matrices’ calculation. The
remaining DFT calculations have been performed with VASP. To study the
dependence of the CDW phase with respect to the smearing we used a plane-wave
cutoff of 500 eV and a 9$\times$9$\times$9 $\Gamma$-centered $k$-mesh. Ionic
relaxations have been performed with a constant volume. The relaxations of the
ionic and electronic degrees of freedom were considered converged respectively
below a threshold of $10^{-5}$ eV and $10^{-10}$ eV. Subsequently, for each
smearing value, we computed the norm of the 351-dimensional (117 atoms
$\times$3) displacement vector among the CDW and the pristine phases. Spin-
orbit coupling has not been included for this set of calculations. To study
the structural interpolation among the CDW and pristine systems, leading to
the double-well potential profile, we computed the 351-dimensional
displacement vector $\vec{e}$ between the two configurations. This has a norm
of $\sim 0.64$ Å. The two structures hence are gradually interpolated, moving
the atoms along the direction defined by $\vec{e}$. For each step, a self-
consistent calculation with 500 eV for the kinetic energy cutoff and a
$\Gamma$-centered 12$\times$12$\times$12 $k$-grid has been performed. The
smearing here is constant and equal to 0.005 eV. The electronic calculations
are considered converged below a threshold of $10^{-8}$ eV. This process has
been studied while keeping the volume constant. Also here the spin-orbit
coupling has not been included. To compute the frequency of the phonon mode we
started from a quadratic fit around the minimum of the Born-Oppenheimer
potential, corresponding to the CDW phase; the resulting fit has equation
$y=0.379x^{2}$. From here it is possible to obtain the ”spring” constant $k$,
as $k=2$$\times$0.379202 eV/Å2. The effective mass $m^{*}$ is computed using
the normalized displacement vector $\hat{n}=\vec{e}/\norm{\vec{e}}$ and the
mass tensor $\mathbf{M}=$ diag($m_{1}$, $m_{1}$, $m_{1}$, …, $m_{117}$,
$m_{117}$, $m_{117}$) via $m^{*}=\vec{e}\cdot(\mathbf{M}\cdot\vec{e})$; we
obtain $m^{*}=91.02$ u. Note that this mass value is intermediate among the Sn
and Sc ones, i.e. the atoms which mostly participate to the CDW transition.
Finally the frequency $\nu$ can be computed as $\nu=\omega/(2\pi)$, with
$\omega=\sqrt{k/m^{*}}$, giving us $\nu=1.42$ THz. When considering the
unfolding of the CDW supercell, the Kohn–Sham wave functions are expanded in
plane waves up to a 400 eV energy cutoff, with a $k$-mesh resolution for the
self-consistent electronic structure calculations of 0.02 reciprocal
Angstroms. For the non-self-consistent calculations, the $k$-mesh resolution
corresponds to 0.01 reciprocal Angstroms. In this case, the spin-orbit
coupling has been considered and included self-consistently. The initial CDW
supercell corresponds in every case to the experimental one Arachchige_2022 .
Band structures have been visualized using the VASPKIT postprocessing tool
vaspkit . VESTA vesta  has been used to visualize the crystal structures.
Acknowledgements The authors acknowledge Andrea Cavalleri for the fruitful
discussions on this work. The research leading to these results has received
funding from the European Union’s Horizon 2020 research and innovation program
under the Marie Skłodowska-Curie Grant Agreement No. 897276. We gratefully
acknowledge the Gauss Centre for Supercomputing e.V. (https://www.gauss-
centre.eu) for funding this project by providing computing time on the GCS
Supercomputer SuperMUC-NG at Leibniz Supercomputing Centre
(https://www.lrz.de). We are grateful for funding support from the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s
Excellence Strategy through the Würzburg-Dresden Cluster of Excellence on
Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project ID
390858490) as well as through the Collaborative Research Center SFB 1170
ToCoTronics (Project ID 258499086) and the Hamburg Cluster of Excellence “CUI:
Advanced Imaging of Matter” (EXC 2056, Project No. 390715994). This work has
been performed in the framework of the Nanoscience Foundry and Fine Analysis
(NFFA-MUR Italy Progetti Internazionali) facility. The Flatiron Institute is a
division of the Simons Foundation. S.D.W. and G. Po. acknowledge support via
the UC Santa Barbara NSF Quantum Foundry funded via the Q-AMASE-i program
under award DMR-1906325. F.M. greatly acknowledges the SoE action of pnrr,
number SOE_0000068. I.Z. acknowledges the support from U.S. Department of
Energy (DOE) Early Career Award DE-SC0020130.
Author contributions F.M., D.D.S and F.C. conceived and designed the project.
G.Po. and S.W. grew the crystals. F.M., C.B., J.F., I.V., and P.C. carried out
the ARPES measurements, while F.C., M.T., D.P., and W. B. obtained the pump
and probe results. A.C. and S.E. performed the numerical calculations and
theoretical analysis supervised by D.D.S, G.S., T.W. and R.T. All the authors
participated in the discussion and crucially contributed to understanding and
the writing of the manuscript.
Additional information Extended data is available for this paper at
https://xxxx
Supplementary information The online version contains supplementary material
available at https://xxx
Correspondence and requests for materials should be addressed to Federico
Mazzola, Domenico Di Sante and Federico Cilento.
Data availability The data that support the findings of this study are
available from the corresponding authors upon reasonable request.
Competing financial interests
The authors declare no competing financial interests.

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Figure 1: Crystal and calculated electronic structure of ScV6Sn6. a Crystal
structure without CDW. The top-view corresponds to a 2$\times$2 cell. b
Brillouin Zone with high-symmetry points and directions. c Crystal structure
in the CDW phase with the out-of-plane distortions indicated by the arrows.
The length of the arrow is proportional to the displacement. d Electronic
structure of ScV6Sn6 without (red lines) and with CDW (green color) along the
high symmetry directions. For visual clarity, the pristine bands have been
translated in energy by +0.029 eV. In this way the van-Hove singularities and
the $d_{z^{2}}$ flat band of the CDW and pristine systems are aligned. It is
indeed expected that a structural distortion leads to a tuning in the
electronic band structure, especially around EF PhysRevB.105.165146 . A
similar but disentangled figure can be found in the Supplementary Information.
The main changes are here indicated: at $\Gamma$ (red box, label ’1’) the CDW
induces an increment in the bands separation. Along both $\Gamma$-K and
$\Gamma$-M the bands appear to have slightly different k-loci (blue arrow and
label ’2’). The main changes are observed along the A-H and A-L directions
(yellow arrows and label ’3’) and are characterized by a marked Sn
$p_{z}$-states

.

Figure 2: Measured electronic structure of ScV6Sn6 across the CDW critical
temperature. Fermi surface of ScV6Sn6 collected above $T_{CDW}$ by using
linear a horizontal and b vertical light polarizations and c-d corresponding
energy versus momentum dispersion along the $\Gamma$-K-M direction of the
Brillouin zone. Fermi surface of ScV6Sn6 collected below $T_{CDW}$ by using
linear e horizontal and f vertical light polarizations and g-h corresponding
energy versus momentum dispersion along the $\Gamma$-K-M direction of the
Brillouin zone. i Energy distribution curve (EDC) extracted at the
$\Gamma$-point for LH and l LV polarization, across the transition
temperature. LV reveals more spectral details, including a small doublet.

Figure 3: Temperature and fluence dependent-dynamics of ScV6Sn6. a Evolution
of $\Delta$R/R as a function of the temperature in the temperature range
across $T_{CDW}$, showing the signatures of the phase transition around 90 K.
In the low temperature CDW phase a clear oscillatory response is observed. b
$\Delta$R/R profiles extracted from a at selected temperatures, showing the
evolution of the dynamics across the phase transition. c Evolution of the
scaled $\Delta$R/R as a function of the fluence across $T_{CDW}$. The traces
are scaled to the fluence to ease the visualization upon approaching the
photoinduced phase transition. d Scaled $\Delta$R/R profiles extracted from c
at selected fluences.

Figure 4: Evolution of significant fit parameters. a Evolution of the lifetime
of the first fast decay ( $\tau_{1}$) as a function of the temperature (top
panel) and evolution of the amplitude of the fast peak as function of fluence
(bottom panel). b Evolution of the frequency and the damping constant of the
amplitude mode as a function of the temperature. c Total energy of the ScV6Sn6
constant-volume superlattice while interpolating between the pristine, the CDW
and the exaggerated CDW phases. $\lambda=0.00$ Å means that the displacement
vector has a vanishing norm, i.e. we are in the reference starting point (the
pristine phase). When $\lambda=0.64$ Å, the norm of the displacement vector is
$\norm{\vec{e}}=\lambda$, hence we are in the CDW phase. When further
increasing the norm of the displacement vector, we are describing an
exaggerated CDW phase. The parabola represented by a continuous line is the
quadratic fit of the energy profile, around the minimum. The quadratic
coefficient is related to the spring constant $k$ and frequency $\omega$ of
the CDW amplitude mode (more details in the Methods section). d Norm of the
351-dimensional displacement vector $\vec{e}$ among the CDW and pristine
structures, as a function of the electronic (gaussian) smearing $\sigma$ used
during the constant-volume ionic relaxation.

##  I Supplementary Information

##  II ARPES and measurements without surface states

The ARPES measurements have been performed across the transition temperature,
i.e. 98 K, for ScV6Sn6 both with and without the present of surface states.
While the surface states presence is guaranteed by a successful UHV cleave, in
order to suppress them and to remain on the same sample’s spot precautions are
needed. Indeed, we noticed that by cleaving the samples both at 16 K and at
120 K (in the CDW phase and above it) the surfaces states are present.
However, if one cleaves the samples at 16 K (or at 120 K) and varies the
temperature up to 120 K (or down to 16 K) the surface states are killed,
possibly to absorption onto the sample’s following a temperature change. To a
suppression of the surface states an overall reduction of the ARPES data
quality was observed. In order to get high quality surface states, as in the
main text, we cleaved the same sample one time at 16 K and one time at 120 K.
Then, in order to detect the bulk electronic structure as in S1, we waited a
sufficient time at the selected temperature until the surface states were
suppressed by aging. This ensures a better overall quality of the ARPES data,
compared to a forced aging by thermal process, and allows us to be sure to be
on the same area of the sample with the light beam. We noticed also a
variation in the aging time. For samples cleaved at 120 K, despite the initial
lower quality, the surface states resisted for a longer time, i.e. 15-24
hours. For samples cleaved at 16 K, we noticed an initial better quality for
the ARPES data, but a faster degradation time of about 4-6 hours. For the data
in the main text, above the transition temperature, the surface states appear
weaker. Such a weaker intensity recorded for the surface states above
$T_{CDW}$ is not surprising given the more pronounced degradation expected for
the highest temperature cleave. In this regard, we even noticed that by
increasing slightly further the temperature, the surface states get completely
suppressed. However, the electronic structure remains the same, with no
changes in van-Hove singularities (red arrows in Fig.2 of the main text) and
overall dispersion.

##  III ARPES and measurements along A-H and A-L directions

As we showed in the main text, the DFT calculations captures very well the
effects of the CDW on the electronic structure of ScV6Sn6. Along the high-
symmetry directions $\Gamma$-M-K, we have the most favorable matrix elements
and the strongest spectroscopic signal. In these conditions, the main changes
are visible at the $\Gamma$ point as an increase in the energy separation of
some states locates around -0.8 eV. Nevertheless, the DFT predicts the largest
changes to occur in the $k_{x}$-$k_{y}$ plane located between two consecutive
$\Gamma$-points. Here we used 65 eV photon energy (with both linear vertical
and horizontal light polarizations) to capture such a plane and also the A-H
and A-L directions, as shown in the Brillouin zone of Fig.1 of the main text.
To note that despite the CDW-induced changes are supposed to be prominent
here, the photoemission matrix elements reduces significantly the intensity of
the electronic structure and, together with a rather significant $k_{z}$
broadening, the CDW changes are not easily detected. This is further
challenged by the fact that in the low temperature phase, the spectral weight
rapidly dimishes away from the gaps and still, the main intensity ’follow’ the
dispersion of the bands above $T_{CDW}$, as visible in the DFT of the main
text. However, we will here show the results in these conditions.

First of all, we show the Fermi surface maps of the systems within the
$k_{x}$-$k_{y}$ plane centred in the A point, along with the dispersion along
the L-A-H-L, in figure 3 and 4, respectively. One can notice that apart from
the better intensity and resolution gained in the low temperature phase and
due to sharper features, overall there are no significant changes observed or
at least, the changes are not big enough to justify them as effect of the CDW.
To better see possible changes, we also report the very-high-resolution ARPES
data along the A-H-L direction. Still, the data corroborate our previous
conclusions.

##  IV Tr-OS analysis and details

In order to describe the incoherent part of the $\Delta R/R$ signal, we used a
double-exponential function, $\Delta R/R\propto
A_{1}e^{-t/\tau_{1}}+A_{2}e^{-t/\tau_{2}}+bkg$, where $A_{1}e^{-t/\tau_{1}}$
describes the fast decay process (first stage of the CDW) while
$A_{2}e^{-t/\tau_{2}}$ describes the slower recovery process (second stage of
the CDW). The $bkg$ term is used to take into account an extremely slow
recovery process that can be described by a constant value in our time window.

In order to quantitatively analyze the oscillatory component of the $\Delta
R/R$ signal, we considered the Fourier transform of the residuals obtained by
considering the difference between the data and the double-exponential fit
function described above. The complete fit function, resulting in the black
lines of Fig.3 of the main text, has been obtained by adding a damped cosine
oscillation, $A_{p}e^{-t/\tau_{p}}cos(w_{p}t+\phi_{p})$.

To give a rough estimate the induced heating by the pump, we assumed,
reasonably, that the heat capacity of ScV6Sn6 is of the same order of
magnitude of the ones reported for similar kagome systems (both binary and
ternary). We do not expect that the temperature deviates more than 20 K upon
pump application.

##  V Electronic and phononic band structures details

In this section are reported complementary figures, supporting the statements
and the results of the main text. In particular, we report the calculated
electronic structure with and without CDW separately (Fig. 8), and the phonon
density of states and the mechanism by which the phonon frequency has been
estimated (Fig. 9). In addition (Fig. 10), we also show the data from time-
resolved optical spectroscopy documenting the evolution of the fast component.
Such evolution is reminiscent of the one observed in time-resolved
photoelectron spectroscopy, and associated to the electronic degrees of
freedom.

Figure 5: Fermi surfaces of ScV6Sn6 kagome metal without surface states. a
Linear horizontal and b linear vertical polarization Fermi surface maps
collected for ScV6Sn6 above the transition temperature. c Linear horizontal
and d linear vertical polarization Fermi surface maps collected for ScV6Sn6
below the transition temperature. In order to be sure about the absence of
surface states, the samples were left for a significant time in the same
positions and same conditions (approximately 24 h) and they showed a natural
aging effect, which resulted in the removal of the surface states manifold.
Figure 6: Energy vs momentum dispersion of ScV6Sn6 kagome metal without
surface states. a linear horizontal and b vertical polarization spectra along
the $\Gamma$-K-M direction of the BZ obtained for ScV6Sn6 after the surface
states were suppressed as in S1, above $T_{CDW}$. c linear horizontal and d
vertical polarization spectra along the $\Gamma$-K-M direction of the BZ
obtained for ScV6Sn6 after the surface states were suppressed as in S1, below
$T_{CDW}$. Figure 7: Fermi surfaces of ScV6Sn6 kagome metal centred in the
plane of the A point, i.e. 65 eV. a Linear horizontal and b linear vertical
polarization Fermi surface maps collected for ScV6Sn6 above the transition
temperature. c Linear horizontal and d linear vertical polarization Fermi
surface maps collected for ScV6Sn6 below the transition temperature. As one
can see, the low temperature data appear sharper due to the reduced thermal
broadening. Figure 8: Energy vs momentum dispersion of ScV6Sn6 kagome metal
centred in the plane of the A point, i.e. 65 eV. a linear horizontal and b
vertical polarization spectra along the L-A-H-L direction of the BZ obtained
for ScV6Sn6, above $T_{CDW}$. c linear horizontal and d vertical polarization
spectra along the L-A-H-L direction of the BZ obtained for ScV6Sn6, below
$T_{CDW}$. Figure 9: High-resolution Energy vs momentum dispersion of ScV6Sn6
kagome metal along the A-H-L directions a linear horizontal and b vertical
polarization spectra along the A-H-L direction of the BZ obtained for ScV6Sn6,
above $T_{CDW}$. c linear horizontal and d vertical polarization spectra along
the A-H-L direction of the BZ obtained for ScV6Sn6, below $T_{CDW}$. Figure
10: Fast decay evolution as function of temperature. Evolution of the lifetime
($\tau_{1}$, left axis) and of the amplitude (I1, right axis) of the first
fast decay as a function of the temperature. As one can see, contrary to the
amplitude decay as function of fluence (Fig. 4 of the main taxt), which shows
a saturation, here, I1 has a very similar behaviour to the lifetime as
function of temperature. Figure 11: Time- and frequency- resolved
reflectivity. The reflectivity is reported as energy versus time for samples
kept at 30 K. Figure 12: Band structure unfolding of the pristine phase vs the
CDW one a Electronic band structure of the pristine phase, with color-bar on
the right side. The plot has been obtained unfolding the same superlattice of
the CDW phase, without the lattice distortion. The bands have been shifted
upward by 0.029 eV. b Electronic band structure of the CDW phase, with color-
bar on the right side. Note how, in this case, a wider range of colors needs
to be employed. Figure 13: Phonon and CDW theoretical details a Density of
states of phonons in ScV6Sn6. The imaginary modes, indicating a dynamical
instability, are only due to the Sc atom, and the Sn atoms with the same
scandium’s $(x,y)$ coordinates. Note that some atoms in the cell are
represented more than once, because of the periodic boundary conditions. b
Schematic sketch of the procedure followed to compute the frequency of the
phonon mode ($\nu=1.42$ THz). Red colors refer to the effective mass $m^{*}$,
obtained from the mass tensor and the (normalized) displacement vector. Blue
color refers to the spring constant, obtained by doubling the quadratic
coefficient of the parabola. This parabola has been obtained via a quadratic
fit, about one of the two minima of the double-well potential energy profile.
Figure 14: Evolution of the rising edge as function of time and temperature.
Evolution of the rising edge of the $\Delta$R/R signal at the arrival of the
pump pulse, for three selected temperatures (below $T_{CDW}$, at $T_{CDW}$ and
above $T_{CDW}$). Above the critical temperature the maximum of the
$\Delta$R/R signal is reached 150 fs faster than in the CDW phase. The three
traces have been normalized at their maximum intensity.