# Highly anisotropic transient optical response of charge density wave order
in ZrTe3

Li Yue<EMAIL_ADDRESS>International Center for Quantum Materials, School
of Physics, Peking University, Beijing 100871, China  Amrit Raj Pokharel
Institute of Physics, Johannes Gutenberg University, 55128 Mainz, Germany
Jure Demsar  Institute of Physics, Johannes Gutenberg University, 55128 Mainz,
Germany  Sijie Zhang  International Center for Quantum Materials, School of
Physics, Peking University, Beijing 100871, China  Yuan Li  International
Center for Quantum Materials, School of Physics, Peking University, Beijing
100871, China  Tao Dong  International Center for Quantum Materials, School of
Physics, Peking University, Beijing 100871, China  Nanlin Wang
<EMAIL_ADDRESS>International Center for Quantum Materials, School of
Physics, Peking University, Beijing 100871, China  Beijing Academy of Quantum
Information Sciences, Beijing 100913, China

###### Abstract

Low dimensionality in CDW systems leads to anisotropic optical properties, in
both equilibrium and non-equilibrium conditions. Here we perform polarized
two-color pump probe measurements on a quasi-1D material ZrTe3, in order to
study the anisotropic transient optical response in the CDW state. Profound
in-plane anisotropy is observed with respect to polarization of probe photons.
Below $T_{\mathrm{CDW}}$ both the quasi-particle relaxation signal and
amplitude mode (AM) oscillation signal are much larger with
$\mathbf{E}_{\mathrm{pr}}$ nearly parallel to $a$ axis
($\mathbf{E}_{\mathrm{pr}}\parallel a$) than for $\mathbf{E}_{\mathrm{pr}}$
parallel to $b$ axis ($\mathbf{E}_{\mathrm{pr}}\parallel b$). This reveals
that $\mathbf{E}_{\mathrm{pr}}\parallel a$ signal is much more sensitive to
the variation of the CDW gap. Interestingly, the lifetime of the AM
oscillations observed with $\mathbf{E}_{\mathrm{pr}}\parallel b$ is longer
than $\mathbf{E}_{\mathrm{pr}}\parallel a$. Moreover, at high pump fluence
where the electronic order melts and the AM oscillations vanish for
$\mathbf{E}_{\mathrm{pr}}\parallel a$ , the AM oscillatory response still
persists for $\mathbf{E}_{\mathrm{pr}}\parallel b$. We discuss possible
origins that lead to such unusual discrepancy between the two polarizations.

###### pacs:

Valid PACS appear here

Low dimensionality plays a key role for the formation of charge density waves
(CDWs). CDWs usually appear in quasi-1D or -2D materials Monceau (2012);
Rossnagel (2011), where the low-dimensional electronic structure supports good
Fermi surface nesting. The electronic susceptibility, especially for quasi-1D
systems, tend to diverge at the nesting wave vector 2$\mathbf{k}_{F}$ Grüner
(2018, 1988), resulting in electronic instability and periodic modulation of
the conducting electrons. Another important factor for CDW formation is
electron-phonon coupling. At 2$\mathbf{k}_{F}$, phonon modes tend to soften,
leading to a new periodic modulation of the lattice structure Grüner (1988,
2018); Pouget  _et al._ (1991); Hoesch  _et al._ (2009).

A typical experimental characterization of CDW phase is the measurement of
optical properties, in both equilibrium and non-equilibrium conditions.
Optical conductivity spectroscopy is a powerful tool to identify the single-
particle gap in the CDW state, where profound spectral weight redistribution
happens in the low-energy range Li  _et al._ (2022); Lin  _et al._ (2020);
Chen  _et al._ (2014, 2017). CDWs also induce new collective excitations
consisting of amplitude (AM) and phase modes. The AM excitations involves
ionic displacement around the periodically distorted atomic displacements, and
can be observed in Raman spectroscopy as a soft optical mode with
$A_{\mathrm{1g}}$ symmetry Hu  _et al._ (2015); Snow  _et al._ (2003). Besides
these time-averaging spectroscopies which detect the equilibrium properties,
ultrafast pump probe techniques have been widely utilized to study the non-
equilibrium dynamical evolution of the system after optical excitation Li  _et
al._ (2022); Lin  _et al._ (2020); Chen  _et al._ (2014, 2017); Demsar  _et
al._ (1999a, 2002); Schaefer  _et al._ (2014). The single-particle gap opening
and the appearance of collective AM are manifested in the time-domain spectra
as changes in quasi-particle (QP) relaxation signals and coherent
oscillations, respectively. Moreover, time-resolved probes can provide much
more information of the system that is inaccessible in the equilibrium state,
including non-thermal ultrafast phase transitions driven by pump excitation
Tomeljak  _et al._ (2009); Schmitt  _et al._ (2008), and selective detection
of the order parameter components during the relaxation processTomeljak  _et
al._ (2009); Schäfer  _et al._ (2010).

The low dimensionality of CDW systems can lead to strongly anisotropic optical
responses. Optical conductivity experiments have built a thorough
understanding of the anisotropy in the equilibrium state. For in-plane optical
conductivities of many quasi-1D CDW systems, the gap signature mainly appears
with the polarization direction along the in-plane projection of
2$\mathbf{k}_{F}$ vector (which is often the structural chain direction) Li
_et al._ (2022); Perucchi  _et al._ (2004). In contrast, for the non-
equilibrium dynamical relaxation process, the anisotropy of the transient
optical response was seldom studied. Such studies would be meaningful for
clarifying the dynamical evolution of CDW state, and expand the understanding
of the cooperative phenomena. Here we report polarized femtosecond pump probe
measurements on a prototypical quasi-1D CDW material ZrTe3, which has not been
previously studied with pump probe methods. Our data reveal interesting and
pronounced anisotropic transient optical responses of the system.

ZrTe3 is a quasi-1D CDW metal with $T_{\mathrm{CDW}}$=63 K. It belongs to the
space group $P2_{1}/m$, with $a=5.89$ Å, $b=3.93$ Å, $c=10.09$ Å,
$\beta=97.8^{\circ}$, $\alpha=\gamma=90^{\circ}$ Hu  _et al._ (2015); Stöwe
and Wagner (1998). The structure consists of prisms stacking along $b$ axis.
The sample has stripes-like $ab$ surface, with the long edge parallel to $b$
axis and short edge parallel to $a$ axis. The ordering wave vector
$\mathbf{q}_{\mathrm{CDW}}=(0.07\mathbf{a}^{*},0,0.33\mathbf{c}^{*})$
corresponds to the nesting of the quasi-1D Fermi sheets near the Brillouin
zone boundary Yokoya  _et al._ (2005); Hu  _et al._ (2015); Yue  _et al._
(2020). Unlike other quasi-1D CDW materials such as NbSe3, K0.3MoO3, etc.,
$\mathbf{q}_{\mathrm{CDW}}$ is perpendicular to the structural chain
direction. According to ARPES experiments, the quasi-1D Fermi sheets are
partially gapped around the Brillouin zone $D$ pointYokoya  _et al._ (2005);
Hoesch  _et al._ (2019), where the electron-phonon interaction is strongest Hu
_et al._ (2015). Optical conductivity measurements showed the anisotropic gap
feature which is more prominent along the in-plane $a$ direction Perucchi  _et
al._ (2005), with a depletion of spectral weights below 1000 cm-1.

Figure 1: (a) and (b) Time resolved reflectivity under different polarization
conditions at room temperature and 10 K, respectively, with pump fluence $\sim
60$ $\mu$J/cm2. The inset of panel depicts the reflection geometry of the
experiment. The $a$ axis lies in the horizontal plane of incidence, and the
$b$ axis is along the vertical direction.

We performed two-color pump probe reflection measurements on the $ab$ surface
of ZrTe3 single crystal SM . Fig. 1 displays the polarization-dependent
transient reflectivity changes at room temperature and at 10 K. It is clear
that the polarization of probe photons makes the major difference to the
signal amplitudes. In the CDW state (Fig. 1(b)), the difference between the
two probe polarizations is much more profound than in the normal state (Fig.
1(a)). Since the polarization dependent spectra are dominated by the
$\mathbf{E}_{\mathrm{pr}}$ direction, we focus on the results obtained with
$\mathbf{E}_{\mathrm{pu}}\parallel a$. Considering the rather small incident
angle of the probe beam, the $s$ and $p$ polarizations can be approximated as
nearly parallel to $b$ ($\mathbf{E}_{\mathrm{pr}}\parallel b$) and $a$
($\mathbf{E}_{\mathrm{pr}}\parallel a$) axis.

Figures 2(a-b) present the temperature evolution of the transient reflectivity
change with $\mathbf{E}_{\mathrm{pr}}\parallel a$ and
$\mathbf{E}_{\mathrm{pr}}\parallel b$, respectively. In Fig. 2(a), at 300 K
the relaxation dynamics is given by a fast decaying negative signal with a
small long-lived background signal extending far over the 10 ps time-window.
As temperature is decreased towards $T_{\mathrm{CDW}}$, the long-lived
background signal changes sign. Across the CDW transition, a second
exponential decay process with positive sign and longer relaxation time
becomes apparent while the amplitude of the long-lived background response
rapidly increases with decreasing temperature. Upon cooling to the lowest
temperature, the two exponentially decaying signals, as well as the long-lived
signal are further enhanced, and the oscillatory response due to the CDW
amplitude mode with $\sim 2$ ps period becomes apparent. The spectra for
$\mathbf{E}_{\mathrm{pr}}\parallel b$ (Fig. 2(b)) show a similar trend, but
with substantially lower signal amplitudes.

Figure 2: (a) and (b) $\Delta R/R$ as a function of time delay at different
temperatures with pump fluence $\sim 60$ $\mu$J/cm2. (c-f) Temperature
dependence of the several parameters characterizing the QP relaxation
dynamics. The red and blue markers correspond to spectra obtained with
$\mathbf{E}_{\mathrm{pr}}\parallel a$ and $\mathbf{E}_{\mathrm{pr}}\parallel
b$, respectively. The solid lines in (c) are the fitted curves with RT model
using $T$-independent gap Demsar  _et al._ (1999b). The dashed lines are
guides-to-the-eye.

The QP relaxation dynamics can be fit by a convolution of a Gaussian response
function and the following model function

$\displaystyle(\frac{\Delta
R}{R})_{i}=A_{fi}\mathrm{e}^{-\frac{t}{\tau_{fi}}}+A_{si}\mathrm{e}^{-\frac{t}{\tau_{si}}}+B_{i}t+C_{i}$
(1)

Here $i=a$ or $b$ denotes the $\mathbf{E}_{\mathrm{pr}}$ polarization,
$A_{fi}$ and $\tau_{fi}$ are the amplitude and relaxation time of the fast
negative exponential decay seen at all temperatures, $A_{si}$ and $\tau_{si}$
are the the amplitude and relaxation time of the picosecond positive component
arising in the CDW phase. The long-lived background signal should, in
principle, be fitted with a third exponential decay with very long relaxation
time. However, since we are focusing on the short time dynamics on the
timescales of about 10 ps, we approximate the long lived response by
$B_{i}t+C_{i}$.

In the pump probe experiment, the pump pulse injects QPs into the system. If a
gap exists near the Fermi level, photo-generated carriers will accumulate
above the gap, the presence of the latter resulting in a relaxation
bottleneck. However, in ZrTe3, only parts of the Fermi surface are gapped by
the CDW formation Yokoya  _et al._ (2005). Therefore, part of the photo-
generated carriers may rapidly relax to ungapped region of the Fermi surface
and relax via normal electron-phonon thermalization process. The two
exponentially decaying components in Eq. 1, with the faster one being present
at all temperatures, likely stem from the two relaxation channels.

The amplitudes of both exponentially decaying components exhibit anomalies
near $T_{\mathrm{CDW}}$. In Fig. 2(c), $A_{si}$ is nearly zero at high
temperatures, and increases rapidly below $T_{\mathrm{CDW}}$. $A_{fi}$ are
also enhanced in the CDW state (Figs. 2(d)), however they remain pronounced
far above $T_{\mathrm{CDW}}$. Compared to the value at 10 K $A_{fi}$ above
$T_{\mathrm{CDW}}$ is about $40\%$ of its low temperature value for
$\mathbf{E}_{\mathrm{pr}}\parallel a$ and $80\%$ for
$\mathbf{E}_{\mathrm{pr}}\parallel b$, consistent with the assignment of the
fast decay component to the normal relaxation processes in the un-gapped
regions. The relaxation times $\tau_{fi}$ are on the order of $\sim$ 100 fs,
displaying no anomalies near $T_{\mathrm{CDW}}$, consistent with this
scenario. The long-lived signal $C_{i}$ also changes dramatically near
$T_{\mathrm{CDW}}$. This signal may be in part related to the bolometric
response as well as to the localized in-gap carriers Demsar  _et al._ (1999a,
2002), whose contribution is reduced above $T_{\mathrm{CDW}}$, consistent with
the pronounced drop in $C_{i}$ at temperatures above $T_{\mathrm{CDW}}$.

Previously, the anisotropic optical response to the CDW gap formation was
mainly studied by optical conductivity measurement of the equilibrium state.
Here, in quasi-1D systems, the gap feature is more prominent along the Fermi
nesting direction and is weak along the perpendicular direction. In the near-
infrared range, far above the CDW gap, the optical conductivity is very weakly
influenced by the CDW transition and is usually not resolved in the
equilibrium spectra. In the optical pump probe experiment, however, thanks to
the high sensitivity of the technique, one can measure the pump induced
reflectivity changes due to the photoinduced gap suppression, even if they are
much smaller than $10^{-4}$. Our polarized pump-probe study, even at 0.95 eV
(1300 nm) probe photon energy, clearly demonstrates a profound anisotropic
transient optical response in the CDW state, where
$\mathbf{E}_{\mathrm{pr}}\parallel a$ signal in the CDW state is about an
order of magnitude larger than for $\mathbf{E}_{\mathrm{pr}}\parallel b$. At
temperatures above $T_{\mathrm{CDW}}$, however, the difference between the
responses in the two probe polarizations is quite small (see Fig. 1(a) and
Fig. 2(d)). We note that such an anisotropy of the response in the CDW state
should not be taken for granted in quasi-1D CDW systems. E.g., in studies of
K0.3MoO3, the anisotropy between the probe polarizations along the chain or
perpendicular to the chain directions is quite weak (see Supplementary
material in Ref. Schäfer  _et al._ (2010)).

Figure 3: (a) and (b) The oscillation part of transient reflectivity change
for $\mathbf{E}_{\mathrm{pr}}\parallel a$ and
$\mathbf{E}_{\mathrm{pr}}\parallel b$ with pump fluence. Lines are vertically
shifted for clarity. (c) and (d) correspond to the Fast Fourier transformation
of the oscillation part for $\mathbf{E}_{\mathrm{pr}}\parallel a$ and
$\mathbf{E}_{\mathrm{pr}}\parallel b$, respectively. (e) The temperature
dependence of AM peak frequency obtained by fitting the peak position in the
FFT spectra of panel (d). (f) The lifetime of AM oscillation for different
probe photon polarizations, obtained by fitting the time-domain oscillation.

Figures 3(a-b) display the oscillatory component of the spectra along two
polarizations, obtained by subtracting the fitted QP relaxation curve of Eq. 1
from the raw traces in Figs. 2(a-b). Figs. 3(c-d) present the corresponding
fast Fourier transformation. Several distinct modes are observed at around
0.47, 1.74, 3.5, 4.5, 6.55 THz, among which the 0.47 THz mode, disappearing
above $T_{\mathrm{CDW}}$, shows clear signatures of the amplitude mode. As the
temperature rises, the AM intensity decays and the mode softens (Fig. 3(e)),
consistent with the Raman measurements Hu  _et al._ (2015). Comparing the two
polarizations, the AM oscillation intensity for
$\mathbf{E}_{\mathrm{pr}}\parallel a$ is much stronger than that for
$\mathbf{E}_{\mathrm{pr}}\parallel b$. Since the AM collective dynamics
involves the oscillation of the CDW gap Schmitt  _et al._ (2008, 2011), the
larger AM amplitude for $\mathbf{E}_{\mathrm{pr}}\parallel a$ implies that
$\mathbf{E}_{\mathrm{pr}}\parallel a$ provides a much larger response to the
photoinduced variation of the CDW gap. This is consistent with the larger QP
relaxation signal for the probe polarized along the $a$-axis due to the gap
formation below $T_{\mathrm{CDW}}$, as discussed in the preceding section.

The oscillatory AM signal can be described with a damped oscillator

$\displaystyle\frac{\Delta
R_{\mathrm{osc}}}{R}(t)=A_{\mathrm{AM}}\mathrm{e}^{-t/\tau_{\mathrm{AM}}}\mathrm{sin}(\omega_{\mathrm{AM}}t+\phi)$
(2)

where $A_{\mathrm{AM}}$, $\tau_{\mathrm{AM}}$, $\omega_{\mathrm{AM}}$, $\phi$
correspond to the amplitude, lifetime, frequency and phase. An interesting
result of our measurements is that the AM lifetime also exhibits anisotropy
(see Fig. 3(f)): the lifetime is shorter for
$\mathbf{E}_{\mathrm{pr}}\parallel a$ than for
$\mathbf{E}_{\mathrm{pr}}\parallel b$. This difference can also be directly
seen in the time-domain traces, where the oscillations in Fig. 3(b) extend
longer than in Fig. 3(a). We discuss the possible origins of this observation
later.

We also studied the pump fluence dependence of the dynamics at 10 K (Figs.
4(a-b)). By increasing the pump fluence, the system will go from a linear,
weak perturbation, regime to quenching the CDW state. This has been observed
in other CDW materials, showing that strong perturbation leads to an ultrafast
melting of the electronic order where the gap is closed and the amplitude mode
amplitudes saturate and eventually vanish Tomeljak  _et al._ (2009); Schmitt
_et al._ (2008). In ZrTe3, with increasing fluence, the fast negative
exponential increases monotonically, but becomes less anisotropic, as expected
from the T-dependence measurements. The slower positive exponentially decaying
component, which corresponds to the QP relaxation across the CDW gap, also
grows linearly at first but then fades away (Figs. 4(b) inset). Such changes
of QP relaxation signals are consistent with ultrafast melting of the
electronic order. At high pump fluence, a broad hump appears on the higher-
frequency side of the AM peak in the FFT spectra, which may be related to
enhanced anharmonicity under strong perturbation. Along with the melting of
electronic order, the AM oscillation gradually vanishes for
$\mathbf{E}_{\mathrm{pr}}\parallel a$ (Figs. 4(c, f)). Interestingly, for
$\mathbf{E}_{\mathrm{pr}}\parallel b$ the AM oscillation exist till the
highest fluences (Figs. 4(d, g)).

Figure 4: (a) and (b) The transient reflectivity change at different pump
fluence at 10 K, with $\mathbf{E}_{\mathrm{pr}}\parallel a$ and
$\mathbf{E}_{\mathrm{pr}}\parallel b$ respectively. The inset of (b) shows the
amplitude of the slower positive exponential at different fluence. For
$\mathbf{E}_{\mathrm{pr}}\parallel b$ the we can only obtain reasonable
fitting parameter $A_{sb}$ below 179 $\mu$J/cm2. (c) and (d) The oscillation
part of the time-domain spectra of (a) and (b), data is taken from 2 ps to
avoid the residual quasi-particle relaxation signal which is not perfectly
subtracted. (e) The fluence dependence of the amplitude (upper panel) and
lifetime (lower panel) of the AM oscillation, obtained by fitting the time-
domain oscillation spectra with Eq. 2. The shaded region in the upper panel
expected intensity range in the condition that the existence of AM signal at
high fluence with $\mathbf{E}_{\mathrm{pr}}\parallel b$ is purely induced by
the mismatch of penetration depth SM . (f) and (g) The Fast Fourier
transformation of the time-domain oscillation signal for different probe
polarizations.

Generally, one would expect the amplitude mode to saturate and subsequently
disappear as the electronic order is melted by high fluence, regardless of the
probe photon polarization. Yet here, the AM oscillation for
$\mathbf{E}_{\mathrm{pr}}\parallel b$ survive above $\approx$ 100 $\mu$J/cm2,
with its amplitude and lifetime nearly independent on fluence above $\sim$ 100
$\mu$J/cm2 (Fig. 4(e)). The different fluence dependence of the AM amplitudes
between two probe polarizations, as well as the different lifetimes shown in
Fig. 3(f), have not been reported thus far. In the following we discuss the
possible origins that may be responsible for these observations.

First, given the non-linearity of the AM response, we consider the influence
of penetration depths mismatch. The optical penetration depths are determined
from the reported reflectivity data by Herr et al. Herr and Brill (1986),
using Kramers-Kronig analysis. The penetration depth at 1300 nm probe
wavelength is 28.2 nm for $\mathbf{E}_{\mathrm{pr}}\parallel a$ and 89.2 nm
for $\mathbf{E}_{\mathrm{pr}}\parallel b$ while at 847 nm pump wavelength it
is $22.5$ nm for $\mathbf{E}_{\mathrm{pu}}\parallel a$ and 47.8 nm for
$\mathbf{E}_{\mathrm{pu}}\parallel b$.

The large mismatch can thus be responsible for different fluence dependences
of the AM signal. Let us first consider the fluence dependence of the response
for the case, where pump and probe mismatch is negligible, or when optical
penetration depth is larger than that of the probe. For weak perturbations,
the amplitude of the AM signal is usually linearly proportional with the pump
fluence. Above the absorbed energy density corresponding to quenching the
electronic order, however, the signal will saturate Tomeljak  _et al._ (2009)
and eventually disappear. Indeed, this scenario well accounts for our
observations with $\mathbf{E}_{\mathrm{pr}}\parallel a$. For the case, where
the pump penetration depth is shorter that the probe penetration depth, i.e.,
for $\mathbf{E}_{\mathrm{pr}}\parallel b$, however, the situation is more
complicated. Beyond the linear response regime, the high incident pump fluence
result in quenching of the electronic order in the surface layer given by the
pump penetration depth. However, for the deeper regions (still probed by the
probe), the absorbed energy density is still below the CDW melting threshold,
resulting in a contribution to the reflectivity transient of the perturbed CDW
state. Indeed, our observations with $\mathbf{E}_{\mathrm{pr}}\parallel b$ are
qualitatively consistent with this scenario. E.g., the quenched surface region
may be responsible for the broad hump feature and broadened phonon peaks in
the FFT spectra, with the deeper, weakly perturbed regions giving rise to the
AM response far beyond the threshold seen in
$\mathbf{E}_{\mathrm{pr}}\parallel b$ experiment.

In order to check this scenario, we performed quantitative analysis with the
above model, presented in the Supplementary material SM . The model, taking
into account the optical penetration length mismatch, is qualitatively
consistent with our experimental observations. However, after quenching of the
electronic order in the surface layer, by further increasing the pump fluence,
the volume fraction of the quenched CDW state will increase, leading to
decrease of the AM signal intensity. According to the model the AM signal
intensity should drop faster with increasing fluence as compared to our
experimental results. The predicted dependence of the amplitude of the AM is
given by the dashed blue region in Fig. 4 (e) SM , showing that for fluences
beyond $\approx$ 100 $\mu$J/cm2, the AM signal intensity for
$\mathbf{E}_{\mathrm{pr}}\parallel b$ should start to decay. However, the
measured AM signal intensity for $\mathbf{E}_{\mathrm{pr}}\parallel b$ is
nearly constant and may even be increasing with increasing pump fluence.
Moreover, we note that the lifetimes of AM oscillations in Fig. 1(b) do not
change much when switching pump polarization to from $a$ to $b$ direction
(Supplementary Fig. 2) SM , even though the difference in the pump penetration
depths is about a factor of two. Thus, the penetration depth mismatch may not
be solely responsible for our observations. We should note, however, that the
non-linearity of the AM signal can be more complicated than our simple
phenomenological model.

Next we discuss an alternative scenario that may be responsible for the
observe anisotropy in the fluence dependent AM response. We first note that
the CDW order parameter comprises electronic and lattice parts, and the
amplitude mode involves oscillation of the electronic gap Schmitt  _et al._
(2008, 2011); Dolgirev  _et al._ (2020) and the periodic lattice displacements
Moore  _et al._ (2016). Usually, the two parts are considered to be
adiabatically coupled due to electron-phonon coupling. However, at least on
the timescales shorter that the AM period, this assumption may be invalid
Schäfer  _et al._ (2010); Schaefer  _et al._ (2014). First, in earlier
studies, different techniques have been utilized to probe the ultrafast
dynamics of the two components of the CDW order. In TbTe3, time-resolved
photoemission demonstrated the oscillation of CDW gap at the $\sim 2.4$ THz AM
frequency Schmitt  _et al._ (2008, 2011). Here, above $\sim 1$ mJ/cm2, the gap
is closed by strong excitation and the AM oscillation are no longer resolved.
However, the time-resolved X-ray diffraction study on TbTe3 showed that with 3
mJ/cm2 fluence the superlattice peak intensity still oscillates at the AM
frequency Moore  _et al._ (2016). In K0.3MoO3, X-ray studies suggest a
critical fluence of 1 mJ/cm2 for the collapse of the superlattice Huber  _et
al._ (2014), but optical reflectivity probe showed a critical fluence of $\sim
0.3$ mJ/cm2, where damping and disappearance of the AM oscillation is observed
Tomeljak  _et al._ (2009). Finally, at fluences much higher than those needed
to collapse the electronic order, a collapse and revival of the periodic
lattice modulation has been observed Huber  _et al._ (2014); Neugebauer  _et
al._ (2019). Thus, it can be inferred that the non-equilibrium dynamics of the
electronic and lattice subsystems are not always strictly entangled. Under
strong perturbation, the electronic order is melted and CDW band oscillation
vanish (or become to small to detect), but the lattice part may still display
well resolved oscillatory dynamics. Such a disentangled dynamics may be
responsible for the observed anisotropy in the fluence dependence of AM in
ZrTe3, as discussed below.

To describe this scenario, we first point out the fact, that transient
reflectivity in the infrared range far above the CDW gap is neither a direct
probe of the lattice motion or of the CDW gap. In fact, the reflectivity
probes both components with different weights. The weights may depend on the
photon energy. E.g., when the probe photon energy is close to the CDW gap, one
can expect a dominant contribution to the signal from the CDW gap oscillation,
while in the case of a resonance with an interband transition, the probe may
be more sensitive to lattice part of the order parameter, where the whole
electronic band structure will experience shifts due to the driven atomic
motion Schaefer  _et al._ (2014). The weights may also depend on photon
polarizations, given the anisotropic CDW gap which affects the optical
conductivities mainly along $a$ direction Perucchi  _et al._ (2005). With the
highly anisotropic electronic structure, manifested by a large anisotropy in
the dielectric function up to the visible range Herr and Brill (1986), it is
possible that transient reflectivities in the $a$ and $b$ polarizations are
mainly probing the collective dynamics of the electronic and lattice
subsystems, respectively. Such a scenario is also consistent with our
observation of AM at high fluences for $\mathbf{E}_{\mathrm{pr}}\parallel b$.
Here, at high fluence, the disappearance of AM signal for
$\mathbf{E}_{\mathrm{pr}}\parallel a$ corresponds to the strong suppression of
the AM oscillations of the electronic gap, while the AM signal for
$\mathbf{E}_{\mathrm{pr}}\parallel b$ corresponds to the dynamics of the
lattice part of the order parameter. This scenario may be realized in ZrTe3
given the fact that $\mathbf{E}_{\mathrm{pr}}\parallel a$ provides much larger
response to the variation of the CDW gap, as shown by the profound intensity
of the quasiparticle relaxation and the AM oscillation signals in this
polarization. For $\mathbf{E}_{\mathrm{pr}}\parallel a$, the measured AM
oscillation is dominated by the dynamical evolution of CDW gap. For
$\mathbf{E}_{\mathrm{pr}}\parallel b$, the signal is not as sensitive to the
variation of gap, so the response would be dominated by the AM vibration.
Indeed, such a scenario agrees with the different amplitudes of individual
components to transient reflectivity in the two probe polarizations - see Fig.
1(b). Here for $\mathbf{E}_{\mathrm{pr}}\parallel a$ the QP exponential decay
is very prominent, but for $\mathbf{E}_{\mathrm{pr}}\parallel b$ the signal is
dominated by the coherent AM oscillation.

In summary, we use polarized femtosecond pump probe experiments to investigate
the non-equilibrium dynamical optical response in ZrTe3. Profound anisotropy
is observed with respect to polarization of probe photons. With
$\mathbf{E}_{\mathrm{pr}}\parallel a$, the spectra present much larger
response to the formation of CDW gap below $T_{\mathrm{CDW}}$ as well as to
the variation of CDW gap during AM oscillations. Interestingly, we observe
that the AM oscillation signal present different damping lifetime between
$\mathbf{E}_{\mathrm{pr}}\parallel a$ and $\mathbf{E}_{\mathrm{pr}}\parallel
b$. Moreover, the AM oscillation signal for $\mathbf{E}_{\mathrm{pr}}\parallel
b$ is seen to persist to much higher pump fluence than for
$\mathbf{E}_{\mathrm{pr}}\parallel a$. While the results may be attributed to
the anisotropy of the pump and probe penetration depths, they may also be
linked to the disentangled collective dynamics of electronic and lattice parts
of the order parameter. Although numerous optical pump probe measurements have
been performed on low-dimensional CDW materials, our results suggest that
further, spectrally resolved studies may further our understanding of the
cooperative phenomena in CDW materials as well as correlated materials in
general.

This work was supported by NSFC (No. 11888101 and NO. 2022YFA1403900). L.Y.
further acknowledges support from China Postdoctoral Science Foundation (Grant
No. 2021M700257 and Grant No. BX20200016). A.R.P. and J.D. acknowledge support
by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - TRR
288 - 422213477 (project B08).

## References

  * Monceau (2012) P. Monceau, Advances in Physics 61, 325 (2012).
  * Rossnagel (2011) K. Rossnagel, Journal of Physics: Condensed Matter 23, 213001 (2011).
  * Grüner (2018) G. Grüner,  _Density waves in solids_ (CRC press, 2018).
  * Grüner (1988) G. Grüner, Reviews of modern physics 60, 1129 (1988).
  * Pouget  _et al._ (1991) J. P. Pouget, B. Hennion, C. Escribe-Filippini, and M. Sato, Phys. Rev. B 43, 8421 (1991).
  * Hoesch  _et al._ (2009) M. Hoesch, A. Bosak, D. Chernyshov, H. Berger, and M. Krisch, Phys. Rev. Lett. 102, 086402 (2009).
  * Li  _et al._ (2022) R. S. Li, L. Yue, Q. Wu, S. X. Xu, Q. M. Liu, Z. X. Wang, T. C. Hu, X. Y. Zhou, L. Y. Shi, S. J. Zhang, D. Wu, T. Dong, and N. L. Wang, Phys. Rev. B 105, 115102 (2022).
  * Lin  _et al._ (2020) T. Lin, L. Y. Shi, Z. X. Wang, S. J. Zhang, Q. M. Liu, T. C. Hu, T. Dong, D. Wu, and N. L. Wang, Phys. Rev. B 101, 205112 (2020).
  * Chen  _et al._ (2014) R. Y. Chen, B. F. Hu, T. Dong, and N. L. Wang, Phys. Rev. B 89, 075114 (2014).
  * Chen  _et al._ (2017) R. Y. Chen, S. J. Zhang, M. Y. Zhang, T. Dong, and N. L. Wang, Phys. Rev. Lett. 118, 107402 (2017).
  * Hu  _et al._ (2015) Y. Hu, F. Zheng, X. Ren, J. Feng, and Y. Li, Phys. Rev. B 91, 144502 (2015).
  * Snow  _et al._ (2003) C. S. Snow, J. F. Karpus, S. L. Cooper, T. E. Kidd, and T.-C. Chiang, Phys. Rev. Lett. 91, 136402 (2003).
  * Demsar  _et al._ (1999a) J. Demsar, K. Biljaković, and D. Mihailovic, Phys. Rev. Lett. 83, 800 (1999a).
  * Demsar  _et al._ (2002) J. Demsar, L. Forró, H. Berger, and D. Mihailovic, Phys. Rev. B 66, 041101 (2002).
  * Schaefer  _et al._ (2014) H. Schaefer, V. V. Kabanov, and J. Demsar, Phys. Rev. B 89, 045106 (2014).
  * Tomeljak  _et al._ (2009) A. Tomeljak, H. Schäfer, D. Städter, M. Beyer, K. Biljakovic, and J. Demsar, Phys. Rev. Lett. 102, 066404 (2009).
  * Schmitt  _et al._ (2008) F. Schmitt, P. S. Kirchmann, U. Bovensiepen, R. G. Moore, L. Rettig, M. Krenz, J. H. Chu, N. Ru, L. Perfetti, D. H. Lu, M. Wolf, I. R. Fisher, and Z. X. Shen, Science 321, 1649 (2008).
  * Schäfer  _et al._ (2010) H. Schäfer, V. V. Kabanov, M. Beyer, K. Biljakovic, and J. Demsar, Phys. Rev. Lett. 105, 066402 (2010).
  * Perucchi  _et al._ (2004) A. Perucchi, L. Degiorgi, and R. E. Thorne, Phys. Rev. B 69, 195114 (2004).
  * Stöwe and Wagner (1998) K. Stöwe and F. R. Wagner, Journal of Solid State Chemistry 138, 160 (1998).
  * Yokoya  _et al._ (2005) T. Yokoya, T. Kiss, A. Chainani, S. Shin, and K. Yamaya, Phys. Rev. B 71, 140504 (2005).
  * Yue  _et al._ (2020) L. Yue, S. Xue, J. Li, W. Hu, A. Barbour, F. Zheng, L. Wang, J. Feng, S. B. Wilkins, C. Mazzoli, R. Comin, and Y. Li, Nature Communications 11, 98 (2020).
  * Hoesch  _et al._ (2019) M. Hoesch, L. Gannon, K. Shimada, B. J. Parrett, M. D. Watson, T. K. Kim, X. Zhu, and C. Petrovic, Phys. Rev. Lett. 122, 017601 (2019).
  * Perucchi  _et al._ (2005) A. Perucchi, L. Degiorgi, and H. Berger, The European Physical Journal B - Condensed Matter and Complex Systems 48, 489 (2005).
  * (25) See Supplementary Information for additional methods, measurement data and analyses.
  * Demsar  _et al._ (1999b) J. Demsar, B. Podobnik, V. V. Kabanov, T. Wolf, and D. Mihailovic, Phys. Rev. Lett. 82, 4918 (1999b).
  * Schmitt  _et al._ (2011) F. Schmitt, P. S. Kirchmann, U. Bovensiepen, R. G. Moore, J.-H. Chu, D. H. Lu, L. Rettig, M. Wolf, I. R. Fisher, and Z.-X. Shen, New Journal of Physics 13, 063022 (2011).
  * Herr and Brill (1986) S. Herr and J. Brill, Synthetic Metals 16, 283 (1986).
  * Dolgirev  _et al._ (2020) P. E. Dolgirev, A. V. Rozhkov, A. Zong, A. Kogar, N. Gedik, and B. V. Fine, Phys. Rev. B 101, 054203 (2020).
  * Moore  _et al._ (2016) R. G. Moore, W. S. Lee, P. S. Kirchman, Y. D. Chuang, A. F. Kemper, M. Trigo, L. Patthey, D. H. Lu, O. Krupin, M. Yi, D. A. Reis, D. Doering, P. Denes, W. F. Schlotter, J. J. Turner, G. Hays, P. Hering, T. Benson, J.-H. Chu, T. P. Devereaux, I. R. Fisher, Z. Hussain, and Z.-X. Shen, Phys. Rev. B 93, 024304 (2016).
  * Huber  _et al._ (2014) T. Huber, S. O. Mariager, A. Ferrer, H. Schäfer, J. A. Johnson, S. Grübel, A. Lübcke, L. Huber, T. Kubacka, C. Dornes, C. Laulhe, S. Ravy, G. Ingold, P. Beaud, J. Demsar, and S. L. Johnson, Phys. Rev. Lett. 113, 026401 (2014).
  * Neugebauer  _et al._ (2019) M. J. Neugebauer, T. Huber, M. Savoini, E. Abreu, V. Esposito, M. Kubli, L. Rettig, E. Bothschafter, S. Grübel, T. Kubacka, J. Rittmann, G. Ingold, P. Beaud, D. Dominko, J. Demsar, and S. L. Johnson, Phys. Rev. B 99, 220302 (2019).