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Emergence of a resistance anomaly by Cu-dopingin TaSe3
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TaSe3: Relationship between
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A. Nomura et al

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July 2017
EPL, 119 (2017) 17005
doi: 10.1209/0295-5075/119/17005

www.epljournal.org

Emergence of a resistance anomaly by Cu-doping in TaSe3
A. Nomura1 , K. Yamaya2 , S. Takayanagi2 , K. Ichimura1,2 , T. Matsuura3 and S. Tanda1,2
1

Department of Applied Physics, Hokkaido University - Sapporo 060-8628, Japan
Center of Education and Research for Topological Science and Technology, Hokkaido University
Sapporo 060-8628, Japan3
Department of Electrical and Electronic Engineering, National Institute of Technology, Fukui College
Sabae, 916-8507, Japan2

received 30 May 2017; accepted in ﬁnal form 23 August 2017
published online 14 September 201771.45.Lr – Charge-density-wave systems
72.15.-v – Electronic conduction in metals and alloys
PACS 74.70.-b – Superconducting materials other than cuprates
PACS
PACS

Abstract – We have synthesized single crystals doped with Cu atoms in TaSe3 which exhibits
no Charge Density Wave (CDW) transition, and measured precisely the temperature dependenceof the resistance. We discover an anomalous sharp dip in the temperature derivative of theresistance (dR/dT ) at about 91 K in Cu-doped TaSe3 , which is never observed in pure TaSe3 .
The dip suggests that there is a phase transition with a relative increase in resistance. In addition,
the dip is “γ” shaped. We reveal that the same “γ”-shaped dip in dR/dT is commonly observedat the CDW transition temperature in many CDW conductors, which is a universal consequence
resulting from the opening and growth of a CDW gap on a Fermi surface. Furthermore, the resultof the single-crystal X-ray diﬀraction (XRD) analysis implies that Cu-doping increases the lattice
parameter of the a-axis and c-axis and decreases that of the b-axis, leading to an improvementin the nesting condition. Based on the “γ”-shaped dip and the result of the single-crystal XRD
analysis, we conclude that a CDW emerges by Cu-doping in TaSe3 .
c EPLA, 2017
Copyright Introduction. – The induction of superconductivity
has helped in the search for new superconducting characteristics and in answering unresolved questions about
superconductivity. For example, high-temperature superconductivity has been induced by doping carriers in insulators [1]. As a result, a new superconductivity mechanism
was found, and the transition temperature (TC ) achieved
164 K under high pressure [2]. In addition, it was foundthat conventional superconductivity appears in a sulfur
hydride system under high pressure [3]. This discovery
brought the leap of TC to 203 K and showed the possibility of realizing a higher TC in other hydrogen-based materials. Moreover, superconductivity was induced in some
Charge Density Wave (CDW) compounds by employing
doping or high pressure, and the coexistence or competition of induced superconductivity with CDW was investigated [4–9]. Thus, the induction of superconductivity
provides many opportunities to study superconductivity.
CDW is a macroscopic quantum state as well as superconductivity. CDWs occur in low-dimensional metals
as the result of the Peierls instability of Fermi surface.
Previous CDW studies have provided a lot of knowledge about the mechanisms and the dynamics of CDW

by targeting materials with intrinsic CDW states [10,11].
However, the next stage of this research should involve inducing a CDW in materials that do not normally exhibit
one, because new CDW characteristics might be obtained
and it will provide many opportunities to deal with unresolved issues as well as superconductivity. For example,
new driving mechanisms other than conventional Fermi
surface nesting might be found as reported for NbSe2 [12]and TiSe2 [13]. Moreover, if a CDW is induced in materials that exhibit superconductivity, we can study the
relationship between induced CDW and superconductivity and compare it with the conventional coexistence orcompetition.
TaSe3 is a predominant candidate material capable ofinducing a CDW. TaSe3 is one of the transition metaltrichalcogenides, MX3 (M: Nb, Ta; X: S, Se). MX3 arequasi–one-dimensional conductors with chain structures,in which electric currents are passed well in the direction of the chain axis. Generally, the Fermi surface of aquasi–one-dimensional conductor is close to a plane. If the
Fermi surface was translated by a wave vector, it would
overlap well with that before translation, i.e., the nesting
condition is good. This indicates the intrinsic instability

17005-p1

A. Nomura et al.
Table 1: The synthesis condition and result of ICP-AES.

CrystalNominal value of Cu (x)Growth temperature

Pure TaSe3
Cu-doped TaSe3
Cu-doped TaSe3
Cu-doped TaSe3

00.00750.05
0.05

678 ◦ C678 ◦ C678 ◦ C708 ◦ Cof the Fermi surface, and as a result, a CDW develops below the transition temperature in a quasi–one-dimensional
conductor. In fact, CDW transitions are observed in
NbSe3 , TaS3 , and NbS3 [14–16]. On the other hand,
TaSe3 exhibits no CDW transition over the entire temperature range, but the superconductivity transition occurs
at about 2 K although it is a quasi–one-dimensional conductor [17,18]. It is considered that the irregular behavior
arises because TaSe3 is more three-dimensional than theother MX3 compounds. Actually, the electrical conductivity anisotropy (σ /σ⊥ ) of TaSe3 is 3–15, while that of
TaS3 is ∼100 and that of NbSe3 is 10–20 [19–22]. Furthermore, according to the band calculation, TaSe3 has twodimensional Fermi surfaces, which are described as fusedtunnels running in the (−a∗ + c∗ ) direction in contrast
to the one-dimensional ﬂat Fermi surfaces of NbSe3 and
TaS3 [23]. Conversely, if we can reduce the dimensionality,
TaSe3 may also exhibit a CDW.
There is impurity doping as a predominant candidate
method capable of reducing the dimensionality in TaSe3 .
In TaSe3 , the chains are weakly bonded by van der Waals
forces. Therefore, if impurities are doped in TaSe3 , theimpurities are expected to enter in the van der Waals
gap and to increase the distance between chains. Actually, in the transition metal dichalcogenides, MX2 (M: Ti,
Nb, Ta; X: S, Se), where MX2 layers are weakly bonded
by van der Waals forces, impurities enter between layers and increase the distance between layers, as reported
for Cux TiSe2 [5,24]. If Cu-doping increases the distance
between chains in TaSe3 as well as Cux TiSe2 , the overlap between electron wave functions perpendicular to thechain axis decreases, leading to an increase in electricalconductivity anisotropy. As a result, the dimensionality
may be reduced.
In our research, we tried to induce a CDW in TaSe3 by
Cu-doping, and investigated the presence of a CDW bymeasuring the resistance as a function of temperature.
Experimental. – We prepared single crystals of pure
TaSe3 and Cu-doped TaSe3 synthesized by the vapor
phase transport method. We obtained three kinds of Cudoped TaSe3 crystals by changing the nominal value ofCu (x) and the growth temperature. First, Ta, Se andCu materials (99.95%, 99.999%, and 99.9% respectively,
Nilaco Corp.) were sealed with a molar ratio of 1 to 3 to x
(x = 0, 0.0075, and 0.05) in evacuated quartz tubes. They
were then heated at 678 ◦ C (x = 0, 0.0075, and 0.05) and

Ratio of amount of substance
Ta
Se
Cu
1
2.79 ± 0.10
012.86 ± 0.10 0.0051 ± 0.0010
1
2.91 ± 0.10 0.0095 ± 0.0010
1
2.89 ± 0.10 0.0112 ± 0.0010

708 ◦ C (x = 0.05), and maintained at the temperature forabout seven days. Finally, the tubes were quenched inwater. In this way, we obtained whisker crystals with atypical dimension of 5 μm × 10 μm × 5 mm.
To examine the actual concentration of Cu in the crystals, we performed inductively coupled plasma atomic
emission spectroscopy (ICP-AES) using an ICPE-9000(Shimadzu Corp.). We determined the average Cu concentration for a bundle of the whisker crystals (a few
milligrams).
The crystal structure was examined by single-crystal
X-ray diﬀraction (XRD) analysis with Cu Kα radiation(λ = 1.5418 Å) using a Rigaku XtaLAB P200 diﬀractometer. The lattice parameters were extracted by ﬁtting the
XRD spectra using CrysAlisPro.
The temperature dependence of the resistance along theb-axis (parallel to the chain axis) was precisely measured
with a dc four-probe measurement. We measured thetemperature dependence of the resistance, while the samples were warmed from 4.2 to 280 K for about 30 hours.
The temperature was measured with a Cernox resistancesensor.
Results. – The synthesis condition and the result of
ICP-AES are listed in table 1. From the ratio of theamount of substance determined by ICP-AES, we deﬁne
the Cu concentration as the ratio of Cu to Ta given asa percentage. The Cu concentrations of the Cu-doped
TaSe3 were 0.51 ± 0.10%, 0.95 ± 0.10% and 1.12 ± 0.10%.
Thus, together with pure TaSe3 , we prepared four kinds ofcrystals with diﬀerent Cu concentrations. The Cu concentration did not exceed 1.2% even when the nominal value
for Cu was more than 5%.
Figure 1 shows the lattice parameters determined bysingle-crystal XRD analysis as a function of Cu concentration. The crystal structure of TaSe3 is monoclinic. The a-axis and c-axis are perpendicular to theb-axis, which is the direction of the chain axis, and β
is the angle between the a-axis and the c-axis. The
lattice parameters obtained for three samples of pure
TaSe3 were a = 10.402–10.409 Å, b = 3.498–3.500 Å, c =9.824–9.828 Å and β = 106.24–106.27◦ , which showed little sample dependence. However, the obtained values werein good agreement with previously reported values of a =10.402 ± 0.004 Å, b = 3.495 ± 0.002 Å, c = 9.829 ± 0.004 Å,β = 106.26 ± 0.03◦ [25], and a = 10.374 Å, b = 3.501 Å,c = 9.827 Å, β = 106.11◦ [26]. The lattice parameters we

17005-p2

Emergence of a resistance anomaly by Cu-doping in TaSe3

10.415b−axis (Å)

a−axis (Å)

3.500

10.41010.405

3.499

3.498

3.497
0

0.5

0

1

1

Cu concentration (%)

Cu concentration (%)

9.835

106.35°9.830

106.30°βc−axis (Å)

0.5

9.825

106.25°

0

0.5

1

0

Cu concentration (%)

0.5

1

Cu concentration (%)

Fig. 1: The lattice parameters of pure TaSe3 and Cu-doped TaSe3 determined by single-crystal XRD analysis. Three samples
for each Cu concentration are measured. The ﬁlled circles show the data for each sample, and the open circles show the averagevalue for each Cu concentration.

obtained for three samples of each Cu-doped TaSe3 also
exhibited sample dependence in almost the same range asthat of pure TaSe3 . The Cu concentration dependenceof lattice parameters does not show a clear change which
satisﬁes Vegard’s law. However, the average values for thea-axis, c-axis and β tended to increase slightly as the Cu
concentration increased, while that of the b-axis tended todecrease slightly.
The temperature dependence of the resistance was measured for several samples for each Cu concentration.
Figure 2 shows typical data for pure TaSe3 and Cudoped TaSe3 . In all the samples, as the temperature
increased, the resistance monotonically increased with aconvex downward curvature in the low-temperature range(T < 70 K) and with a convex upward curvature in
the high-temperature range (T > 70 K) unlike the linear R-T curve for typical metals. The residual resistance ratios (RRR = R(280 K)/R(4.5 K)) were 43.2–57.1

in pure TaSe3 , 5.3–6.3 in Cu-doped TaSe3 (0.51%), 3.2–3.5
in Cu-doped TaSe3 (0.95%) and 3.0–3.3 in Cu-doped
TaSe3 (1.12%). The RRR decreased with increasing Cu
concentration.
Figure 3(a) shows the temperature dependence of theresistance normalized by the diﬀerence between the resistance at 4.5 K and that at 280 K to compare thetemperature-dependent parts of the resistance of pure
TaSe3 and Cu-doped TaSe3 . The temperature dependence of the resistance shows almost the same functional
form for all samples. As the Cu concentration increased,
the normalized resistance at 4.5 K increased almost as
a linear function of the Cu concentration as shown inﬁg. 3(b). Therefore, Matthiessen’s rule holds for the Cudoped TaSe3 system.
To compare these temperature dependences of the resistance in detail, we plot the temperature derivative of theresistance (dR/dT ) in ﬁg. 3(c). In pure TaSe3 , the dR/dT

17005-p3

A. Nomura et al.
(a)

1

1.5

R(T)
R(280 K)−R(4.5 K)

R(T)/R(280 K)

0.8

0.6

0.4
pure TaSe3

1

0.5

pure TaSe3
Cu−doped TaSe3(0.51%)

Cu−doped TaSe3(0.51%)

0.2

Cu−doped TaSe3(0.95%)

Cu−doped TaSe3(0.95%)

Cu−doped TaSe3(1.12%)

Cu−doped TaSe3(1.12%)

0

0

0
0

100

200

100

200

300

T (K)

300

T (K)

(b)

0.5

Fig. 2: (Colour online) The temperature dependence of theresistance normalized by the resistance at 280 K of pure TaSe3
and Cu-doped TaSe3 .
R(4.5 K)R(280 K)−R(4.5 K)

0.4

0.3

Discussion. – The single-crystal XRD analysis showsthat the lattice parameters have sample dependence anddo not show Vegard’s law clearly for increasing Cu concentration, as shown in ﬁg. 1. On the other hand, the
RRR and the depth of the dip change systematically as
the Cu concentration increases (see ﬁgs. 2 and 3(c)). The
beam diameter used in the single-crystal XRD analysis isR(280 K)−R(4.5 K)

dR(T )/d T

3−1(10 K )

increased monotonically from 4.5 K, showed a maximum of
70 K, and decreased monotonically above 70 K. In all Cu0.2
doped TaSe3 with diﬀerent Cu concentrations, the dR/dT
showed a similar temperature dependence to that of pure
0.1
TaSe3 over almost the entire temperature range. However,there was an anomalous sharp dip in the dR/dT at about
91 K in Cu-doped TaSe3 , but never in pure TaSe3 . In Cu00
0.5
1
doped TaSe3 (1.12%) with the maximum Cu concentraCu concentration (%)
tion, the dR/dT suddenly decreased from about 102 K to(c)about 91 K, showed a narrow minimum, and began to increase at about 91 K. Below about 91 K, it gradually re8
turned to a temperature dependence similar to that ofpure TaSe3 . In summary, the anomalous sharp dip was“γ” shaped. The depth of the dip increased with increas6
ing Cu concentration. We call the temperature at which
the dR/dT drops most the dip appearance temperature,4
Tdip . The Tdip was observed as 92 ± 2 K and 91 ± 2 K
for Cu concentrations of 0.95% and 1.12%, respectively.
pure TaSe3
There was no signiﬁcant diﬀerence between the Tdip values
2
Cu−doped TaSe3(0.51%)
of Cu-doped TaSe3 (0.95%) and Cu-doped TaSe3 (1.12%)
Cu−doped TaSe3(0.95%)
beyond the measurement accuracy (±2 K). In Cu-doped
Cu−doped TaSe3(1.12%)
TaSe3 (0.51%), the dip was too small to deﬁne the mini0
mum dR/dT . The dip was reproduced in all samples mea0
100
200
300
sured for the same Cu concentration. Furthermore, theT (K)same Tdip was observed by cooling and heating the Cudoped TaSe3 (1.12%) sample using another mesurement Fig. 3: (Colour online) (a) The temperature dependence ofthe resistance normalized by the diﬀerence between the resisinstrument, that is, no thermal hysteresis is observed.
tance at 4.5 K and that at 280 K of pure TaSe3 and Cu-doped
TaSe3 . (b) The resistance at 4.5 K normalized by the diﬀerence between the resistance at 4.5 K and that at 280 K as afunction of Cu concentration. The average value is shown foreach Cu concentration. (c) The temperature derivative of thenormalized resistance in panel (a). The curves of Cu-doped
TaSe3 (0.51%), Cu-doped TaSe3 (0.95%) and Cu-doped TaSe3(1.12%) are shifted vertically by 0.001, 0.002 and 0.003 K−1 ,respectively.

17005-p4

Emergence of a resistance anomaly by Cu-doping in TaSe3
0.15 mm and, as a result, the lattice parameters are determined as the average value over a local region of 0.15 mm
in comparison with the resistance that is obtained as theaverage value over the region of 1–3 mm between the voltage terminals. Thus, the inhomogeneity in a single crystal
may cause the sample dependence of the lattice parameters. However, the inhomogeneous distribution of Cu
atoms is not the main cause because the sample dependence is observed not only in Cu-doped TaSe3 but also inpure TaSe3 . The ideal value of the molar ratio of Se to
Ta is 3. However, the actual molar ratio obtained using
ICP-AES is 2.8–2.9 as shown in table 1. This fact shows
excess Ta atoms or Se vacancies. It is possible that there is
inhomogeneous distribution of Ta and Se atoms in a single
crystal which disturbs the lattice parameters and obscuresthe eﬀect of Cu-doping, i.e., Vegard’s law.
Therefore, we focus on the average value of the lattice parameter for each Cu concentration and discuss thechange in lattice parameters by Cu-doping. As shown inﬁg. 1, the average lattice parameter value tends to increase on the a-axis and c-axis (perpendicular to the chainaxis) and tends to decrease on the b-axis (parallel to thechain axis) as the Cu concentration increases. The expansion of the a-axis and c-axis indicates that Cu atoms may
be intercalated in the van der Waals gap between chains.
When the distance between chains is increased, and thechain axis is contracted, the dimensionality is expected todecrease because the overlap between wave functions perpendicular to the chain axis decreases and that in the chain
axis direction increases. Therefore, the result of the singlecrystal XRD analysis implies that the change in lattice parameters caused by Cu-doping changes the Fermi surfaces
from two-dimensional tunnel-like to one-dimensional ﬂat.
This would lead to a better nesting condition in Cu-doped
TaSe3 than in pure TaSe3 .
In addition, we can consider the number of carriers to beanother physical quantity that is changed by Cu-doping.
It is reported that the Cu atoms intercalated in the van der
Waals gap are donors contributing delocalized electrons at
the Fermi level [24]. The Cu atoms in Cu-doped TaSe3
are assumed to be intercalated in van der Waals gaps,
and contribute delocalized electrons. TaSe3 is a semimetal
with several Fermi surfaces which consist of a hole andan electron band [23]. In addition, the result of angleresolved photoemission spectroscopy (ARPES) exhibits ahigh density of states near the Fermi level [20]. Thus, thedensity of states at the Fermi energy and the form of the
Fermi surfaces are sensitive to a change in the number ofcarriers. It is possible that the change in the number ofcarriers caused by Cu-doping can also change the nesting
condition although it does not necessarily get better.
We ﬁnd an anomalous sharp dip in the dR/dT value inthe temperature dependence of the dR/dT of Cu-doped
TaSe3 , which is never observed in that of pure TaSe3 , asshown in ﬁg. 3(c). The dip in dR/dT is “γ” shaped witha sudden decrease and a narrow minimum. Thus, thedip suggests a sudden change in state, namely a phasetransition. The emergence of a structural transition issuggested in pure TaSe3 under uniaxial strain [27]. However, the phase transition in Cu-doped TaSe3 would not
be a ﬁrst-order transition because we observe no thermal
hysteresis.
We discuss how the resistance changes in the vicinity ofthe phase transition temperature where a dip in dR/dT ispresent in Cu-doped TaSe3 . When the dR/dT drops, thedecrease in resistance caused by the decrease in temperature is suppressed. Thus, the resistance below the onset
temperature of the dip (102 K) is larger than the resistance extrapolated from the resistance-temperature curve
above 102 K assuming that there is no dip in dR/dT . In
summary, the dip in dR/dT means a relative increase inresistance. MX3 compounds (NbSe3 , TaS3 , NbS3 ) otherthan TaSe3 show anomalous increases in resistance at the
CDW transition temperatures (TCDW ) because the wholeor part of the Fermi surfaces disappears and the number ofcarriers decreases [14–16]. Therefore, the phase transition
with an increase in resistance in Cu-doped TaSe3 is most
likely to be a CDW transition although the resistance increase is relative.
We discuss the “γ”-shaped dip discovered in Cu-doped
TaSe3 by comparison with the temperature dependenceof the dR/dT in CDW conductors such as NbSe3 [28],
DyTe3 [29] and ZrTe3 [30]. These CDW conductors show
the metallic temperature dependence of the resistance inthe normal state above the TCDW , and the resistance increase at the TCDW . However, the temperature dependence of the resistance shows metallic behavior again atlower temperatures because the Fermi surfaces partly remain due to imperfect nesting. Although the magnitude of the resistance increase at TCDW is diﬀerent for
the three CDW conductors, we ﬁnd out a common dip
in the dR/dT value corresponding to the resistance increase. The dR/dT is constant above the TCDW , however with decreasing temperature, it falls sharply at the
TCDW and then starts to increase at the minimum point.
At lower temperatures, it increases more gradually with aconvex upward curvature and approaches a certain value.
In short, the temperature dependence of the dR/dT shows
the common “γ”-shaped dip, indicating the universal law
peculiar to the CDW transition. The law states that a
CDW is formed with an energy gap opening on a Fermi
surface. In the BCS theory on the CDW transition, theenergy gap opens at TCDW and grows obeying the temperature dependence of the gap function. The opening
and growth of the CDW gap reduce the number of conducting carriers with decreasing temperature, leading toan increase in resistance near TCDW , and at the same timethe dR/dT has a “γ”-shaped dip. This fact strongly indicates that the “γ”-shaped dip observed in Cu-doped TaSe3
is caused by the CDW transition.
As shown in ﬁg. 3(c), the Tdip of Cu-doped TaSe3 isabout 91 K, which is lower than the TCDW of the otherMX3 compounds (340 K in NbS3 [16], 218 K in TaS3 [21],and 145 K in NbSe3 [14]). Originally pure TaSe3 has

17005-p5

A. Nomura et al.
two-dimensional Fermi surfaces [23], where the nesting
condition is the worst in MX3 compounds, thus it shows
no CDW transition. Even if Fermi surfaces change anda CDW emerges in TaSe3 , the TCDW is expected to belower than the TCDW of the other MX3 . Therefore, itwill be consistent to assume that Tdip in Cu-doped TaSe3
corresponds to TCDW .
From the discussions above, the main features of the
Cu-doped TaSe3 system are summarized as follows: i) The
change in the lattice parameters caused by Cu-doping maychange the form of Fermi surfaces which leads to a better
nesting condition. ii) The dip in dR/dT exhibits a characteristic of phase transition with a relative increase in resistance. iii) The dip in dR/dT is “γ” shaped and the same“γ”-shaped dip is commonly observed in many CDW conductors. Therefore, we can conclude that a CDW emerges
by Cu-doping in TaSe3 .
If the dip in dR/dT in Cu-doped TaSe3 is due to the
CDW transition, the size of the dip, i.e., the size of the relative resistance increase, corresponds to the ratio of the
reduction of the Fermi surfaces due to the CDW transition. For example, in NbSe3 , two large humps with diﬀerent sizes are observed in the temperature dependence ofthe resistance [31]. From the sizes of the two resistance increases, Kawabata estimates that about 30% of the Fermi
surfaces disappears at the higher TCDW and about 70%of the remainder disappears at the lower TCDW . In thepresent case, even if the Cu concentration is 1.12%, the relative resistance increase in Cu-doped TaSe3 is extremely
small. This result indicates that the reduction ratio of the
Fermi surfaces is very small and a large number of normal
carriers remain at temperatures below the TCDW . This result is also supported by the fact that Matthiessen’s ruleholds, as shown in ﬁg. 3(a) and (b).
Here we discuss the relationship between the size of theresistance increase at TCDW and the TCDW value. When
the CDW is suppressed by Cu-doping in TiSe2 or by Sedoping in ZrTe3 , the size of the resistance increase becomes smaller as the doping concentration increases, andthe TCDW value also decreases [5,9]. These results are
consistent with the prediction obtained for CDW with themean-ﬁeld theory, which shows a positive correlation between TCDW and the area of the reduced Fermi surface,that is, the size of the resistance increase. As seen inﬁg. 3(c), in the Cu-doped TaSe3 system, the size of thedip in dR/dT (the size of the relative resistance increase)increases with increasing Cu concentration, while we observe no clear change in Tdip for Cu-doped TaSe3 (0.95%)
and Cu-doped TaSe3 (1.12%); here, Tdip corresponds to
TCDW . In other words, no clear change in TCDW is observed with increasing Cu concentration within our TCDW
measurement accuracy (±2 K). A comparison of our result to Cux TiSe2 and ZrTe3−x Sex shows that the change
in TCDW per x = 0.0017 (0.17% of doping concentration)
is about 4 K in Cux TiSe2 and about 3 K in ZrTe3−x Sex .
These values are almost the same as our TCDW measurement accuracy. It may be hard to detect the change in

TCDW clearly because the change in the Cu concentrationis very small (0.17%) in our study. Therefore, we can conclude that our result regarding the relationship between
the size of the relative resistance increase and TCDW does
not contradict the positive correlation predicted from themean-ﬁeld theory.
The above discussions about the CDW transition are
based on the scenario of the Fermi surface nesting. However, the resistance increase seen in Cu-doped TaSe3 isextremely small, suggesting alternative scenario for the
CDW formation. Rice and Scott propose that Fermi surfaces with saddle points can be unstable against CDW
formation [32]. In this model, only a relatively small areaof Fermi surfaces disappears and a large area of those remains. Furthermore, the saddle points act as scattering
sinks in the high-temperature phase above TCDW and the
conductivity can be enhanced at the TCDW by the disappearance of the saddle points. As a result, the resistanceincrease due to the CDW transition is suppressed. Therefore, the present result suggests the possibility that the
CDW formation is driven by the mechanism of Rice andScott. Although the presence of saddle points in pure
TaSe3 is not mentioned by the result of the band calculation [23], the result of ARPES shows that there is the ﬂatband region with a high density of states near the Fermi
level in pure TaSe3 [20]. This singularity might drive the
CDW transition in Cu-doped TaSe3 . In order to verify
this mechanism, the band structure of Cu-doped TaSe3
has to be investigated by ARPES.
Conclusion. – By measuring precisely the temperature dependence of the resistance in pure TaSe3 and Cudoped TaSe3 , we discovered an anomalous sharp dip in
the temperature dependence of the temperature derivative of the resistance (dR/dT ) in Cu-doped TaSe3 , which
is never observed in pure TaSe3 . The dip suggests that
there is a phase transition with a relative increase in resistance. Furthermore, the dip is “γ” shaped. We revealthat many CDW conductors commonly exhibit the same“γ”-shaped dip in dR/dT at the CDW transition temperature, which is a universal consequence of the opening andgrowth of a CDW gap on a Fermi surface. Furthermore,
the result of the single-crystal X-ray diﬀraction (XRD)
analysis implies that the lattice parameters perpendicular
to the chain axis increase and that parallel to the chain
axis decreases by Cu-doping, leading to an improvementin the nesting condition. From the “γ”-shaped dip and theresult of the single-crystal XRD analysis, we conclude thata CDW emerges by Cu-doping in TaSe3 . Further studies
are needed to obtain direct evidence of the CDW transition. In addition, we are studying the relationship between
the emerging CDW and superconductivity, because TaSe3
exhibits a superconductivity transition at about 2 K.
∗∗∗
We thank Professor S. Noro for performing the singlecrystal X-ray diﬀraction analysis.

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Emergence of a resistance anomaly by Cu-doping in TaSe3
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