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Symmetry-dependent carrier relaxation dynamics
and charge–density–wave transition in DyTe3
probed by polarized femtosecond spectroscopy
To cite this article: S Tsuchiya et al 2015 J. Opt. 17 085501

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Satoshi Tsuchiya et al

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Journal of Optics
J. Opt. 17 (2015) 085501 (7pp)

doi:10.1088/2040-8978/17/8/085501

Symmetry-dependent carrier relaxation
dynamics and charge–density–wavetransition in DyTe3 probed by polarized
femtosecond spectroscopy
S Tsuchiya1, Y Sugawara1, S Tanda1,2 and Y Toda1
1

Department of Applied Physics, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan
Center of Education and Research for Topological Science and Technology, Hokkaido University,
Sapporo 060-8628, Japan2

E-mail: satoshi.tsuchiya@eng.hokudai.ac.jp
Received 6 November 2014, revised 24 June 2015
Accepted for publication 25 June 2015
Published 31 July 2015
Abstract

Photo-induced quasi-particle (QP) relaxation dynamics with different symmetries have been
investigated for the multiple charge–density–wave (CDW) compound DyTe3 by using ultrafast
polarized pump-probe spectroscopy. By performing symmetry analysis, the QP dynamics withisotropic A1g and anisotropic B2g symmetry were found to show unique anomalies at the ﬁrst andsecond CDW transitions. Both the temperature dependence and pump ﬂuence dependence
indicate that the B2g response is very sensitive to the underlying lattice deformation, which
provides critical insight into the multiple CDW formations.
Keywords: time resolved reﬂection spectroscopy, charge–density–wave systems, opticalproperties
1. Introduction

Recently, the coexistence of multiple charge–density–
waves (CDW) has been reported in quasi-two-dimensional(Q2D) rare-Earth tritelluride compounds, RTe3, where R is arare-Earth ion (R = Dy, Ho, Er, Tm). RTe3 consists of squareplanar Te sheets (a–c plane) and insulating RTe3 layers,which are alternately stacked along the b direction [30]. The
weakly interacting 5p electrons of the Te atoms construct a
Q2D Fermi surface. Electron and x-ray diffraction measurements and angle-resolved photoemission spectroscopy(ARPES) have revealed that, in these compounds, the ﬁrst
CDW occurs along the c axis at high temperatures and thesecond CDW forms along the direction perpendicular to theﬁrst CDW direction (the a axis) at low temperatures [31–33].
However, in the pump-probe measurements for the series of
RTe3, the temperature dependence of the magnitude of transient reﬂectivity changes and relaxation time did not show
clear evidence of the second CDW transition [34]. This isbecause the response associated with the second CDW formation can be buried in that of the ﬁrst one. Thus, the QP
dynamics of multiple CDW states have not been completely
understood so far.

Optical pump-probe time-resolved spectroscopy has been
widely used to study chemical reaction, [1] dynamics ofphoto-excitation in semiconductors [2, 3] and optical devices[4, 5], and photo-induced phase transition in spin-crossoversolid [6, 7] and strongly correlated electron systems [8, 9].
Moreover, the pump-probe spectroscopy has made a great
contribution to researches of the coexistence and competitionof different kinds of ordered states such as superconductivity(SC) and pseudogap (PG) state in cuprate superconductors[10, 11]. When multiple ordered states co-exist together, thosephoto-excited quasi-particle (QP) dynamics can be distinguished from each other by differences in relaxation time,magnitude of transmission reflectivity changes, and thetemperature dependences between them [12–17, 19–29].
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S Tsuchiya et al

J. Opt. 17 (2015) 085501

Figure 1. (a) Schematic of deﬁnition of the probe polarization angle θ. (b) Schematic of the Fermi surface and nesting vectors q 1 and q2. A1g,
B1g, and B2g indicate the selectivity of the probe in the k-space according to the Raman-like process. (c)–(e) Intensity plots of ΔR R transientfor F = 36 μJ cm−2 as a function of angle at 310, 200, and 20 K, respectively. (f)–(h) Polar plots of the maximum values of ΔR R .

The recent study has demonstrated that, by varying theprobe-polarization, the SC and PG responses were distinguishedindividually by spatial symmetry breaking accompanied by
the SC and PG transitions in the cuprate superconductor
Bi2Sr2CaCu2O 8 + δ (Bi2212) [29]. Since, on the CDW transition
in a Q2D system spatial (translational and rotational) symmetries are broken, such a polarization-dependent pump-probe
measurement will provide new information, especially on QP
dynamics in terms of the second CDW transition.
In this paper, we report the use of pump-probe spectroscopy for a multiple CDW system of DyTe3 with different
probe polarizations. By performing concise symmetry analysis, we found that the observed anisotropic response for theprobe is not only attributed to the CDW formation but alsothat it is quite sensitive to changes in the underlying latticesymmetry. Moreover, the ratio between anisotropic and isotropic responses shows unique anomalies associated with theﬁrst and second CDW transitions.

under vacuum. Respective mixture were heated at 550 and
850 °C for 2 d. After heating, the mixtures were cooled gradually to 450 °C at a rate of 2 °C h−1 and quenched to room
temperature. Clean sample surfaces were prepared by cleavage with adhesive tape. The crystalline axes were determined by x-ray diffraction measurement at room temperature.
However, it was difﬁcult to distinguish between the a and caxes because the resolution of the instrument was insufﬁcient
to detect a difference in their lattice constants.
In the optical pump-probe experiments, the pump beam
excites carriers to a nonequilibrium high-energy state. This resultsin immediate relaxation of the excited carriers to states near the
Fermi level by electron–electron and electron–phonon scattering[36]. When a gap for electronic excitation, such as a superconducting or CDW gap, is present, a relaxation bottleneck may
occur and QPs accumulate just above the gap. The relaxation
across the gap is caused gradually because of interaction between
QPs and high-frequency phonons [12, 13]. The probe beam,
which is delayed with the time t, measures the change ofreﬂectivity, ΔR (t), which is connected with the non-equilibrium
distribution of the QPs, Δf , as a function of t. The optical measurements were performed using 120 fs pulses centered at 400 nm
for a pump (F = 36 μJ cm−2) and 800 nm for a probe from acavity-dumped Ti:sapphire oscillator with a repetition rate of
270 kHz. The pump and probe beams were coaxially overlappedby a dichroic mirror and irradiated perpendicular to the a–c plane.
The probe pulse polarization was rotated by a half-wave plate. θis the angle between the probe electric ﬁeld and the direction
tilted by 45°from a crystalline axis, as shown in ﬁgure 1(a).

2. Experimental
DyTe3 was chosen from among the RTe3 compounds because
the CDW formation occurs along two directions. It is thus
expected to provide more information for symmetry analysis
than the other unidirectional CDW compounds. The ﬁrst
CDW forms along the c axis just at room temperature (Tc1 ≈305 K) and along the the second a axis at Tc2 of 50 K. In theseries of RTe3, a structural phase transition has not beenreported except for the lattice modulation due to the CDW
formation. This fact allows us to carry out simple analysis interms of spatial symmetry breaking.
Single crystals of DyTe3 were grown by a self-ﬂux
technique [35]. High-quality starting elements with the molar
ratio Dy:Te = 1:10 were put into a quartz tube and sealed

3. Results
Figures 1(c)–(e) show transient reﬂectivity ΔR R as a functionof θ and ΔR R for θ = 0◦ at T = 310, 200, and 20 K,
2

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J. Opt. 17 (2015) 085501

Figure 2. (a), (b) ΔR R transients of the A1g and B2g components for various temperatures, respectively. The data are shifted for clarity. (c)Temperature dependence of the amplitude A of the A1g and B2g components. (d) Temperature dependence of the decay time τ of the A1g andB2g components The dashed lines display the result ﬁtted by the theoretical model. (e) Oscillatory responses of the A1g and B2g components
at 20 K. (f) Fourier-transform spectrum of the data in (e).

respectively. The maximum values of ΔR R are plotted inﬁgures (f)–(h). For T = 310 K (T > Tc1), the ΔR R shows noangular dependence (isotropic). On the other hand, an anisotropic response is observed for T = 200 K (Tc2 < T < Tc1).
The signals are enhanced along the 135◦ and 315◦ directions,which correspond to the a or c axis. The anisotropy for theprobe can be associated with the ﬁrst CDW formation alongwith c axis. For T = 20 K (T < Tc2 ), the angular dependences isqualitatively similar to that for T = 200 K, although the second CDW occurs along the a axis.
The probe-polarization-dependent ΔR R can be associated with two different types of pump excitation processe,
stimulated Raman excitation and dissipative excitation (DE).
The former is a coherent process and depends on the pumppolarization, whereas the latter shows no pump polarization
since information about the pump polarization is lost due toinelastic scattering. In our results, the observed anisotropy is
independent of the pump polarization, indicating that DE isdominant. For the case of DE, the probe-polarization dependence of ΔR R arises from the anisotropy of excited statesaffected by some symmetry breaking owing to the structural
or electronic phase transition [29].
For DyTe3, because the lattice constant of a is very close
to that of c (a ≈ c), it is reasonable to assume the tetragonal(D4h point group symmetry). Under this assumption, theangular dependence of ΔR R for the probe can be analyzed in
the same way as the case of Bi2212 [29]. As a result, thephoto-induced change of reﬂectivity is derived as
ΔR∝ ΔR A1g + ΔR B1g cos (2θ ) + ΔR B2g sin (2θ ),R

Figures 2(a) and (b) present ΔR R transients of the A1g
and B2g components, respectively, for various temperatures.
As a result of the decomposition, the A1g and B2g components
are found to develop with decreasing temperature, whereas
the B1g component is negligible at all temperatures. In the A1g
response, a combination of positive and negative components
is observed at 310 K. As the temperature decreases, only the
positive component develops, whereas a negative component
dominates in the B2g response. Oscillatory responses are seen
in both the A1g and B2g channels at low temperatures, as
shown later.
Since the maximum values A of ΔR R are associated withthe photo-induced QP density, nqp, A is plotted as a functionof temperature, as shown in ﬁgure 2(c). The curve of B2g isqualitatively similar to that of the A1g component. As thetemperature decreases from 310 K and crosses Tc1, A increases
steeply, indicating growth of the CDW gap. To explore thequalitative validity, we ﬁtted the data with the theoreticalmodel [13]. When nqp is small as compared to the equilibrium
conditions, ΔR R is given by
ΔR∝
R( ΔCDW (T ) + k B T 2)−1
⎛ ΔCDW (T ) ⎞kB T
1+g
exp ⎜ −⎟ΔCDW (T )kB T ⎠⎝,(2)

where ΔCDW (T ), kB, and g indicate the BCS-type gap
function, Boltzmann constant, and the ratio of bosonic andelectronic densities of states that contribute to nqp, respectively. The ﬁts yield ΔCDW (0) = 91 and 88 meV for the A1g
and B2g components, respectively. These values are close to
those obtained in ARPES [32] and the previous pump-probe
measurements [34].With a further decrease in temperature,
the A values start to deviate from the model at around 130 K.
Similar deviation has been observed in other RTe3
compounds [34]. In the previous study, such a deviation
may be associated with the resonant coupling between the(1)

where A1g, B1g, and B2g correspond to symmetries in the kspace, as shown in ﬁgure 1(b), respectively. By ﬁtting
equation (1) to the angular dependences of ΔR R, we
decomposed the data into the components of isotropic A1g,
anisotropic B1g, and B2g symmetries.
3S Tsuchiya et al

J. Opt. 17 (2015) 085501

Figure 3. (a), (b) ΔR R transients of the A1g and B2g components for various pump ﬂuences at 20 K, respectively. (c), (d) Fluence dependenceof amplitude and decay time of the A1g, B1g, and B2g components, respectively. The dashed lines are linear ﬁts. (e), (f) Fluence dependenceof amplitude of the A1g and B2g components at 296 and 310 K, respectively.

collective excitation (amplitude mode) of CDW and thetotally symmetric phonon [34]. Below 50 K, the A values
tend to increase with decreasing temperature. The slightincrease can be attributed to the occurrence of thesecond CDW.
Figure 2(d) shows the temperature dependences of the
decay time obtained by ﬁtting the rapid decline of the transient with a single-exponential function A exp − τt . Before
ﬁtting, to eliminate the contribution of the temperature-independent component from the data, we subtracted the result at
310 K from each results below 305 K for the A1g response.
The τ of both the A1g and B2g components show a clear
divergence as Tc1 is approached from below, whereas no
pronounced anomaly is observed at Tc2 . Theoretically, therelaxation time is associated with the CDW gap as τ ∝ 1/
ΔCDW (T ) when T → Tc1 [13] . This behavior agrees well withthe divergence at Tc1. Therefore, we conclude that the positive
component of the A1g and B2g response are associated with
the CDW formation.
Figure 2(e) shows the oscillatory responses of the A1g
and B2g components at a low temperature, where therelaxation component has been subtracted. The oscillations
are observed not only in the A1g channels but also the B2gchannels, although the oscillation amplitude in B2g is morethan 4 times smaller than that in A1g. Figure 2 (f) exhibits theFourier transform spectrum of the A1g and B2g oscillations.
For the A1g spectrum, the peak positions agree well withthose in a previous report, [34] in which a mode at 2.2 THzcorresponds to the collective excitation of CDW (amplitudemode) and the others are attributed to oscillations of thetotally symmetric phonons. On the other hand, the spectrumof the B2g component partly includes different modes. The

observed peaks in the B2g channel may correspond to Ramanactive phonon modes coupled with QPs in the B2g symmetry.
Figures 3(a) and (b) present the ΔR R transients of the
A1g and B2g components, respectively, for various ﬂuences at
20 K. For the A1g response, in addition to a positive component, which is ascribed to the CDW formation, a long-lived
negative component is seen at high ﬂuences. This component
probably corresponds to that observed at 310 K, indicatingthat it is unrelated to the CDW formation. In the B2g response,
two negative components seem to emerge at high ﬂuences.
The maximum values of the A1g and B2g signals areplotted as a function of ﬂuence in ﬁgure 3(c). Both theamplitudes have qualitatively similar ﬂuence dependence. As
the ﬂuence increases, amplitudes increase linearly and showsa kink, followed by a gradual increase. We determined thatthe threshold ﬂuence Fth = 39 μJ cm−2 for both the A1g andB2g components by using the saturation model [20] . The Fthvalues are reasonable as compared to 47 μJ cm−2 for TbTe3,
which has a higher CDW transition temperature of 336 K[27]. Figures 3(e) and (f) show the ﬂuence dependences of theamplitude of the A1g and B2g components, respectively, athigh temperatures. The saturation behaviors are observed up
to 310 K (> Tc1), indicating a precursor of CDW.
Figure 3(d) indicates the ﬂuence dependence of decay
time for the A1g and B2g signals. The τ value increases withincreasing ﬂuence, showing saturation behavior for bothcomponents. In the Rothwarf–Taylor (RT) model under thestrong bottleneck condition [12], τ is given by

( )

(

)

τ −1 = 2 n qp + nT γ ,(3)where nqp is the photo-induced QP density, nT is the QP
density under the thermal equilibrium condition, and γ is the4

S Tsuchiya et al

J. Opt. 17 (2015) 085501

Figure 4. (a) Magnitude of transient reﬂectivity normalized by A in the A1g component for various temperatures. The dashed and solid lines
indicate the A1g and B2g components. The data are shifted for clarity. (b) Absolute values of ratio of A between the A1g and B2g components
as a function of normalized temperature. Right axis is ratio of the lattice parameter between a and c in TbTe3 adopted from [7]. (c) Fluence
dependence of absolute values of ratio of A between the A1g and B2g components as a function of ﬂuence for various temperatures. (d)Schematic of Te plane for three temperature regions.

effective relaxation rate. At low temperatures, nT decreases ascompared to nqp, leading to the relation τ −1 ∝ nqp at low
ﬂuences. Our results are in contrast to the RT model.
Although A increases linearly (ﬁgure 3(c)), τ seems to be
proportional to nqp, i.e., τ ∝ nqp . Within the framework of the
RT model, our results may be explained by the change of γ. If
γ decreases with increasing ﬂuence, it will lead to τ ∝ nqp .
This means that the bottleneck condition can be changed byvarying the ﬂuence. At high ﬂuences, τ increases gradually.
This behavior may be due to improper ﬁtting. For both the
A1g and B2g channels, ΔR R seems to be two components athigh ﬂuences. Thus, use of a single exponential function will
result in a poor ﬁt. Similar behavior has been observed in
Bi2212 [26].
As observed earlier, the temperature and ﬂuence dependences of amplitude and decay time in the B2g channel arequite similar to those in the A1g channel. However, the following data reveal that the A1g and B2g responses have different origins. Figure 4(a) shows the magnitude of ΔR
normalized by the maximum value A of the A1g component
for various temperatures. The ΔR value in the B2g channel isobviously different from that in the A1g channel. The ratio
between the amplitude of the A1g and B2g components as afunction of the normalized temperature is shown inﬁgure 4(b). Strikingly, the ratio was found to increase near Tc1
and, in contrast, decrease at Tc2 . As the temperature increases
from below Tc1, the ∣ AB2g AA1g ∣ curve shows a steep increase,followed by a rapid decrease. We note that the reduction
above Tc1 can be attributed to a negative component in the A1gchannel, which is not associated with the CDW formation.
For the intermediate temperature range Tc2 < T < Tc1, there
are almost no changes in the ∣ AB2g AA1g ∣ curve. Figure 4(c)shows the ﬂuence dependence of ∣ AB2g AA1g ∣ for various
temperatures. As the ﬂuences increase, the ∣ AB2g AA1g ∣ curveshows a steep increase for 20 K, whereas it decreases for 296
and 310 K. At high ﬂuences, all the curves become almost
constant and monotonically shift downward with increasing
temperature. These results indicate the distinct differences
between A1g and B2g responses.

4. Discussion
Let us discuss origin of the isotropic A1g and anisotropic B2g
responses. The A1g component is determined by the CDW
order parameter. Generally, the order parameter of broken
symmetry ground states is complex, written as Δ =∣ Δ ∣ exp (iϕ). Since in the excitation process by the pump pulse
the dielectric constant is involved as powers of ∣ Δ ∣2 , it leads to
the A1g symmetry. Therefore, the steep growth of the A1g
signal below Tc1 is assigned reasonably to the ﬁrst CDW
formation. The second CDW may be minor a contribution to
the A1g channel because there is no remarkable anomaly ataround Tc2 in ﬁgure 2(c). As shown in ﬁgures 2(e) and (f), it isreasonable that the amplitude mode of CDW was observed in
the A1g channel since it originates form the oscillatory
modulation of ∣ Δ ∣.
5

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J. Opt. 17 (2015) 085501

than that at 20 K and it contributes signiﬁcantly to the ﬂuence
dependence of ∣ β ∣.
From the above discussions, the appearance of the B2g
response is interpreted as a consequence of spontaneous
symmetry breaking in terms of the CDW transition. Usually,
for a one-dimensional CDW system, the translational symmetry is broken. On the other hand, for the two-dimensional
system, in addition to the translational symmetry, the rotational symmetry is broken simultaneously due to unidirectional CDW formation. In the case of DyTe3, as a result ofsuch the symmetry breaking, the symmetry of the systemchanges from tetragonal to orthorhombic below Tc1. This isconsistent with the fact that the B2g signal is enhanced along
the crystalline axis (a or c), which corresponds to the ﬁrst
CDW wave vector, q1, or to the direction perpendicular to q1.
In our results, anisotropy in the B2g channel is conserved as
the temperature decreases and crosses Tc2 , indicating that the
reduced rotational symmetry is maintained even though thesecond CDW occurs. Since the absolute value of the second
CDW wave vector, q2, is not identical to that of q1 for ErTe3,[33] the orthorhombicity will not be changed even for DyTe3
below Tc2 . Consequently, the emergence of the anisotropictransients corresponds to occasion of the rotational symmetry
breaking accompanied by the CDW transition. The ﬁrst CDW
transition occurs with the translational along the c axis androtational symmetry breaking, while only the translational
symmetry along the a axis is broken at the second CDW
transition, maintaining the rotational symmetry.
Our results clearly show that the B1g component is absent
in the whole temperature range. The B1g symmetry corresponds to the direction tiled by ∼45◦ from the crystalline axis
(Te–Te bond direction) in real space. In the previous measurements [31, 33], any charge or lattice modulations along
the direction have not been observed in the RTe3 compounds,
which are consistent with our measurements.
Finally, we compare our results with the results of
Bi2212 [29]. In Bi2212, below T ⋆ , not only anisotropic B2g
response but also isotropic A1g response are observed. A ofB2g component is about 9 and 14 times (for over- and underdoped sample) smaller than that of A1g component. The ratio
between the A1g and B2g component in Bi2212 is larger thanthat of in DyTe3. Moreover, the temperature dependenceshows A increases gradually as temperature increases, whichis contrast to that in DyTe3. These differences between
Bi2212 and DyTe3 can be originated from spatial inhomogeneity. In Bi2212, spatial variations of carrier density andsuperconducting gap were observed [39, 40]. Thus, domainsof some electronic ordered state accompanied by the B2g
symmetry breaking can be emerged in the sample below T ⋆.
On the other hand, unidirectional CDW is formed uniformly
in real space below Tc1 in DyTe3. Since order parameter isaveraged totally as the domains are spatially distributed,
magnitude of the order parameter will be smaller than that in
the case where electronic ordered state is spatially homogeneous. This may be the reason why the ratio between the
A1g and B2g component and temperature dependence of A are
different between them.

The above discussion suggests that anisotropy of the
CDW order parameter is not the origin of the B2g component.
However, our results indicate that both the B2g and A1g
responses are dominated by the CDW order parameter. Thus,
it is reasonable to assume that the origin of the anisotropic
response is associated with changes in the underlying lattice
and that the relation between the B2g and A1g transients is
simply given by ΔRB2g = βΔRA1g , i.e., AB2g = βAA1g , where β
is a coefﬁcient for the anisotropy and ∣ β ∣ corresponds to∣ AB2g AA1g ∣. In this case, we can explore the origin of theanisotropic transients (B2g signal) by investigating the behavior of β. To compare ∣ β ∣ with the anisotropy of the crystal
structure, the ratio of the lattice parameters between a and c in
TbTe3, which is adopted from [33], is plotted on the right axis
in ﬁgure 4(b). The ratio of the lattice parameters changes withdecreasing temperature below Tc1, meaning that the latticeanisotropy grows monotonically. On the other hand, the ∣ β ∣curve shows a maximum just below Tc1 and it is almost
constant in the temperature range Tc2 < T < Tc1. The comparison indicates that ∣ β ∣ does not correspond linearly to thelattice anisotropy. The most remarkable feature is that ∣ β ∣varies only at Tc1 and Tc2 , suggesting that ∣ β ∣ (B2g signal) is not
simply reﬂected by the lattice anisotropy but also by theanisotropy induced by the CDW transitions. When the temperature decreases and crosses Tc1, the underlying Te lattice
deforms from a square to a rhombic shape as shown in theright side and middle of ﬁgure 4(d) owing to the ﬁrst CDW
formation along the c axis. In this case, the lattice anisotropy
becomes strong, corresponding to enhancement of ∣ β ∣ at Tc1.
As the temperature decreases further, the second CDW forms
along the a axis, deforming the lattice as shown on the left
side of ﬁgure 4(d). At Tc2 , the lattice anisotropy is weakened,in contrast to the case at Tc1. The decrease of the lattice anisotropy may lead to the suppression of ∣ β ∣. In this way, theunique temperature dependence of ∣ β ∣ is explained by thechange of the lattice anisotropy induced by the CDW
transitions.
The ﬂuence-dependent variations of ∣ β ∣ presented inﬁgure 4(c) are also explained by the CDW-induced latticeanisotropy. For 20 K, the ∣ β ∣ curve shows a steep increase
with increasing ﬂuence, and then it shows a kink followed, by
a gradual increase. At high ﬂuences, the ∣ β ∣ values approach∼0.35, which is close to the value obtained near Tc1. When the
ﬂuence increases and exceeds Fth, the two CDWs are completely broken. This situation corresponds to the ﬁrst CDW
transition under varying temperature, indicating theenhancement of ∣ β ∣. The contribution accompanied by thesecond CDW transition is difﬁcult to detect since the Fthvalue of the second CDW is signiﬁcantly smaller than that of
the ﬁrst one. Above 296 K, the ∣ β ∣ curves decrease withincreasing ﬂuence. This behavior may trace the steep reduction of ∣ β ∣ near Tc1 with increasing temperature. For instance,at 296 K, the ∣ β ∣ values are ∼0.3 at low ﬂuences and ∼0.2 athigh ﬂuences. These values are consistent with those obtained
at 295 and 300 K. At high temperatures, since the large
negative component in the A1g channel is signiﬁcantly larger
6

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J. Opt. 17 (2015) 085501

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By performing pump-probe spectroscopy with different
polarizations for the probe photons in DyTe3, we detectedsuccessfully not only the ﬁrst CDW transition but also thesecond one in the ratio between the A1g and B2g components.
These polarized measurements enabled us to investigate aburied component in multiple component systems more easily
than we could using normal measurements. It thus provides asigniﬁcant advantage for investigating the competition andcoexistence of multiple electronic ordered phases.

Acknowledgments
The authors would like to thank M Takesada for experimental
support.

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