LETTER

Effect of Cu doping on superconductivity in TaSe3: Relationship between
superconductivity and induced charge density wave
To cite this article: A. Nomura et al 2018 EPL 124 67001

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December 2018
EPL, 124 (2018) 67001
doi: 10.1209/0295-5075/124/67001

www.epljournal.org

Eﬀect of Cu doping on superconductivity in TaSe3: Relationshipbetween superconductivity and induced charge density wave
A. Nomura1 , K. Yamaya2 , S. Takayanagi2 , K. Ichimura1,2 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, Japan2

received 23 August 2018; accepted in ﬁnal form 5 December 2018
published online 8 January 201974.70.-b – Superconducting materials other than cuprates
71.45.Lr – Charge-density-wave systems
PACS 72.15.-v – Electronic conduction in metals and alloys
PACS
PACS

Abstract – By measuring the temperature dependence of the resistance, we investigated theeﬀect of Cu doping on superconductivity (SC) in Cu-doped TaSe3 in which the charge density
wave (CDW) transition is induced by Cu doping. We observed an emergence of a region where theSC transition temperature (TC ) decreased in samples with higher Cu concentrations and foundthat the region tended to expand with increasing Cu concentration. In addition, the temperaturedependence of the upper critical ﬁeld (HC2 ) of Cu-doped TaSe3 was found to diﬀer from that ofpure TaSe3 . Based on these experimental results and the fact that the SC of TaSe3 is ﬁlamentary,
we conclude that SC is suppressed locally by Cu doping and competes with the CDW in Cu-doped
TaSe3 . The resistance anomaly due to the CDW transition was extremely small and the size ofthe anomaly was enhanced with increasing Cu concentration but the temperature at which theanomaly appeared hardly changed. These results of the anomaly and the local suppression of
SC suggest that the induced CDWs have short-range order in the vicinity of Cu atoms. We also
discuss the eﬀect of the pinning of CDWs on the relationship between SC and short-range order
CDWs.
c EPLA, 2019
Copyright Introduction. – The relationship between superconductivity (SC) and charge density wave (CDW) has beena major research topic in condensed-matter physics. For
example, in ZrTe3 in which SC and a CDW exist underatmospheric pressure, the application of pressure below
2 GPa enhances the CDW and eliminates the SC transition [1]. On the other hand, the CDW is suppressed
above 2 GPa while the SC transition emerges again at∼5 GPa. Moreover, in NbSe3 with a typical CDW material, Ta doping suppresses two CDWs and induces theSC transition [2]. These results show that the SC or the
CDW is enhanced while the other is suppressed, whichis ascribed to the competition between SC and the CDW
on a Fermi surface. On the other hand, in a Cux TiSe2
system where Cu atoms are doped in 1T -TiSe2 with acommensurate CDW material, a unique SC and CDW
phase diagram is observed and a new relationship between SC and CDW has been discussed. According to
the temperature dependence of the resistance, the CDW
is suppressed by Cu doping while SC is induced, and thedependence of the SC transition temperature (TC ) on Cu

concentration has a dome-like structure [3]. However, precise measurements performed with scanning tunneling microscopy (STM) and X-ray diﬀraction (XRD) reveal thatshort-range order CDWs survive up to high Cu concentrations where the SC emerges and the transition temperature of the short-range order CDWs is independent of
the TC [4,5]. This result suggests that short-range order
CDWs are not necessarily in competition with SC and cannot be explained solely in terms of the competition for thedensity of states at the Fermi level. Moreover, according
to the XRD result, the short-range order CDWs change
from commensurate to incommensurate at the Cu concentration where SC emerges in Cux TiSe2 [5]. The result
suggests that the incommensuration of the CDWs may
aﬀect the relationship between SC and the CDWs. However, the reason for this is unclear. As described above,
the relationship between SC and CDW has been investigated in many materials. However, previous studies wereactually limited to two cases: the ﬁrst is where SC and a
CDW intrinsically exist; the second is where SC is induced
in a CDW material. Here, in addition to these two cases,

67001-p1

A. Nomura et al.
we should also investigate the relationship in a third casewhere a CDW is induced in a superconducting material, if
we are to understand the whole picture of the relationshipbetween SC and CDW.
TaSe3 provides a stage on which to investigate the relationship in the third case. TaSe3 is one of the transition
metal tri-chalcogenides, MX3 (M: Nb, Ta; X: S, Se). MX3
has a structure consisting of chains made of transition
metals and chalcogens, and the chains are weakly bonded
by van der Waals forces. Owing to this structure, MX3
is a quasi–one-dimensional conductor in which an electric current travels well in the direction of the chain axis
(b-axis). Most forms of MX3 (NbSe3 , TaS3 , and NbS3 )exhibit CDW transitions because the Fermi surfaces are
ﬂat and the nesting condition is good [6–9]. On the other
hand, TaSe3 exhibits no CDW transition over the entire
temperature range [10]. It is considered that the irregularbehavior arises because TaSe3 is far from one-dimensional
compared with the other MX3 compounds as you can see
from the electrical conductivity anisotropy and the Fermi
surfaces [9,11–14]. Instead of a CDW transition, TaSe3
exhibits an SC transition at ∼2 K [15]. The SC transition
curve in the temperature dependence of the resistivity is
anisotropic [16]. The resistivity parallel to the b-axis falls
to zero at TC , while that perpendicular to the b-axis exhibits a partial drop at TC and a ﬁnite value even below
TC . Moreover, the diamagnetism induced by the SC transition is not observed in relation to the temperature dependence of the magnetic susceptibility [17]. From theseresults, it is considered that the SC of TaSe3 is ﬁlamentary and composed of superconducting ﬁlaments parallelto the b-axis.
Recently, we reported changes in the properties of TaSe3
due to Cu doping [18]. The result of single-crystal XRD
analysis at room temperature implies that Cu atoms intercalated in the van der Waals gap change the lattice parameters, leading to an improvement in the nesting condition.
Furthermore, we found an anomalous “γ”-shaped dip in
the temperature derivative of the resistance (dR/dT ) at
∼91 K in Cu-doped TaSe3 , which is never observed in pure
TaSe3 . Based on these results, we concluded that a CDW
is induced by Cu doping in TaSe3 .
Therefore, in this study, we investigated SC in Cu-doped
TaSe3 by measuring the temperature dependence of theresistance to clarify the eﬀect of Cu doping on SC and therelationship between SC and an induced CDW.
Experimental. – We prepared single crystals of pure
TaSe3 and Cu-doped TaSe3 synthesized by the vapor
phase transport method in the same way as our previous study [18]. The growth temperature was 660 ◦ C. The
nominal value of Cu to Ta was 10% in Cu-doped TaSe3 .
Crystals were ribbon-shaped with typical dimensions of
5 μm × 10 μm × 5 mm. The ribbon plane is (2̄01) [19].
The temperature dependence of the resistance along theb-axis from 0.6 to 280 K was measured with a dc four-probe
technique. The whisker crystal was cut to about 2 mm.

Sampleb-axisRibbon plane (201)

Conducting direction

H
Fig. 1: Schematic of the conduction direction and the magnetic
ﬁeld direction.

Current terminals were attached to both ends of the crystal with carbon paste, and voltage terminals were attachedinside. The cross-section at both ends of the crystal wascovered with carbon paste. We measured the resistance
while the samples were being warmed from 2 to 280 K overabout 30 hours and from 0.6 to 2 K over about 30 minutes.
The measurements from 0.6 to 2 K were performed applying static magnetic ﬁelds (0–80 mT) perpendicular to theribbon plane as shown in ﬁg. 1 after the zero ﬁeld cooling.
Results. – The resistance was measured for two samples of pure TaSe3 and for four samples of Cu-doped
TaSe3 . Figure 2 shows a typical result from 2 K to
280 K for pure TaSe3 and Cu-doped TaSe3 . As shownin ﬁg. 2(a), all the samples showed that resistance had
a metallic temperature dependence as with the resultsin our previous study [18]. The residual resistance ratio (RRR = R(280 K)/R(4.5 K)) of Cu-doped TaSe3 wassmaller than that of pure TaSe3 . The normalized residual
resistance (R(4.5 K)/(R(280 K) − R(4.5 K))) of Cu-doped
TaSe3 was larger than that of pure TaSe3 as shown inﬁg. 2(b). The characteristics of all the samples are summarized in table 1. Matthiessen’s rule holds for the Cu-doped
TaSe3 system, and the normalized residual resistance increases almost as a linear function of the Cu concentration
determined by inductively coupled plasma atomic emission spectroscopy (ICP-AES) [18]. We obtained the empirical formulay = 0.41x + 0.02,(1)

where y is the normalized residual resistance and x is the
Cu concentration [%]. Using this empirical formula, weestimated the Cu concentration of each Cu-doped TaSe3
sample from the normalized residual resistance that we
observed in this research (table 1). The estimated Cu concentration varied in the 0.78–1.04% range among samples
from the same batch. As shown in ﬁg. 2(c), a “γ”-shaped
dip in dR/dT was observed at ∼91 K in Cu-doped TaSe3 .
The dip size tended to increase with increasing estimated
Cu concentration, which is consistent with the result inour previous study [18].
Figure 3 shows the temperature dependence of the resistance of pure TaSe3 and Cu-doped TaSe3 from 0.6 K
to 2 K. All the samples exhibited a sharp drop in resistance due to the SC transition below 1.7 K. As shown in
the inset of ﬁg. 3(a), the SC transition exhibited electric
current dependence, which matches the results of previous

67001-p2

R(T)R(280 K)−R(4.5 K)

8

(c)
−1

(b)

(10 K )(a) 1
R(T)/R(280 K)

Eﬀect of Cu doping on superconductivity in TaSe3

Cu−doped TaSe3 No.1
pure TaSe3 No.1

3

0.5

0

Cu−doped TaSe3 No.1
pure TaSe3 No.1
0

0

100

200

4

2
Cu−doped TaSe3 No.1
pure TaSe3 No.1
0

0

300

6

dR(T)/dT
R(280 K)−R(4.5 K)

0.5

1

100

200

300

0

100

T (K)

T (K)

200

300

T (K)

Fig. 2: (Colour online) Typical resistance measurement results for pure TaSe3 and Cu-doped TaSe3 from 2 K to 280 K. The
normalization was in accordance with our previous study [18]. (a) The temperature dependence of the resistance normalized by
the resistance at 280 K. (b) The temperature dependence of the resistance normalized by the diﬀerence between the resistances
at 280 K and 4.5 K. (c) The temperature derivative of the normalized resistance in panel (b). The curve of Cu-doped TaSe3 isshifted vertically by 0.001 K−1 .
Table 1: Characteristics of samples of pure TaSe3 and Cu-doped TaSe3 .

SampleR(4.5 K) (Ω)

R(280 K) (Ω)

RRR

y∗

pure TaSe3 No. 1
pure TaSe3 No. 2
Cu-doped TaSe3 No. 1
Cu-doped TaSe3 No. 2
Cu-doped TaSe3 No. 3
Cu-doped TaSe3 No. 4

2.278
1.385
5.613
67.05
9.908
11.77

135.39181.256
20.695217.2237.116
46.58

59.43
58.67
3.687
3.240
3.746
3.957

0.017110.01734
0.37220.44650.3642
0.3382x (%)∗∗TC (K)

0.86
1.04
0.83
0.78

1.72
1.54
(1.6)∗∗∗ , 1.07
(1.5)∗∗∗ , 1.14
1.51, 1.15
1.69

∗ y is the normalized residual resistance deﬁned as R(4.5 K)/(R(280 K) − R(4.5 K)).
∗∗ x is Cu concentration estimated from y.
∗∗∗ Approximate temperature at which the resistance begins to decrease.

(a)

(b)

pure TaSe3
1

1 20 μΑ No.1

Cu−doped TaSe3

0

No.2

1.5 TC 2

1

R(T)/Rn

R(T)/Rn

1

No.1

1

0.5

0
0.5

0.99

No.2

3

0.5

1

No.1

1

10
5

0.5

1.5

2

No.1
No.3
No.2

No.4

0
1

1.5

2

T (K)

0.5

1

1.5

2

T (K)

Fig. 3: (Colour online) The temperature dependence of the resistance from 0.6 K to 2 K normalized by the normal-state resistance(Rn ) of pure TaSe3 and Cu-doped TaSe3 . (a) Pure TaSe3 No. 1 (I = 1.00 μA) and No. 2 (I = 0.40 μA). The inset shows theSC transition curves for various electric currents of pure TaSe3 sample No. 1, and the deﬁnition of TC . We deﬁne TC as theintersection between a straight line ﬁtted to the data of R = 0.25Rn –0.75Rn and the straight line of R = Rn . (b) Cu-doped
TaSe3 No. 1 (I = 0.30 μA), No. 2 (I = 0.30 μA), No. 3 (I = 0.30 μA), and No. 4 (I = 0.30 μA). The inset is an enlarged view
for Cu-doped TaSe3 No. 1 and 2. The data of sample No. 1 in the inset is for I = 20.00 μA, whose scattering is smaller thanthat for I = 0.30 μA.

67001-p3

A. Nomura et al.
Cu−doped TaSe3 No.3 (I=0.30 μΑ)(a)(a) pure TaSe3 No.1 (I=1.00 μΑ)20255

I1−I2 (two−probe)

2

15

R(Ω)

10

R(Ω)

R(Ω)

250
V1−V2 (four−probe)

10 mT
5.5 mT
10.5 mT
15.5 mT
20.5 mT
30.5 mT
40.5 mT245
V2−I2 (two−probe)

5

0

240
I1−V1 (two−probe)

0
0.5

1

1.5

0.5

1

2

80

TC~1.5 K

TC~1.15 K

I2

HC2

TC~1.35 K

Sample(201)

pure TaSe3:

60

HC2 (mT)

I1

2

(b)

T (K)

Cu-doped TaSe3 No.3

1.5

T (K)

40

No.1

No.2

Cu−doped TaSe3:
No.1
No.3

No.2
No.4

20

b-axisV1

Lead line

Carbon
paste

0
1

V2

1.5

T (K)

Fig. 4: (Colour online) (a) The temperature dependence ofthe resistance between the voltage terminals, between the current terminals, and between a current terminal and a voltage
terminal in Cu-doped TaSe3 sample No. 3. (b) Schematic of
spatial distribution of TC in Cu-doped TaSe3 sample No. 3 derived from panel (a). The distribution of the regions with the
TC ’s of ∼1.6 K and ∼1.15 K between the voltage terminals is
deduced.

studies [17,20]. With increasing current, the onset of theSC transition did not move while the oﬀset shifted to the
low-temperature side. Therefore, we determine TC as deﬁned in the inset of ﬁg. 3(a) from the SC transition curve
observed for the smallest electric current in this measurement. The SC transition temperature (TC ’s) are summarized in table 1. Pure TaSe3 samples No. 1 and 2 exhibiteda one-step SC transition with a TC of 1.54 K and 1.72 K,
respectively. In Cu-doped TaSe3 samples No. 1 and 2, theresistance began to decrease at ∼1.6 K and 1.5 K, respectively, as shown in the inset of ﬁg. 3(b), and droped mostly
at 1.07 K and 1.14 K. Sample No. 3 exhibited a two-step
SC transition with TC ’s of 1.51 K and 1.15 K. Sample No. 4
exhibited a one-step SC transition with a TC of ∼1.69 K.
The ratio of the value of the drop in resistance at ∼1.1 K
to the normal-state resistance is ∼0.99 for No. 1, ∼0.93 forNo. 2, ∼0.63 for No. 3, and 0 for No. 4. The samples were
No. 4, 3, 1 and 2 in ascending order of Cu concentration
as shown in table 1. Thus, the ratio tended to be higher
with increasing Cu concentration.

Fig. 5: (Colour online) (a) The temperature dependence of theresistance of pure TaSe3 sample No. 1 from 0.6 K to 2 K undervarious magnetic ﬁelds perpendicular to the ribbon plane (2̄01).
(b) The temperature dependence of HC2 perpendicular to theribbon plane (2̄01) of pure TaSe3 and Cu-doped TaSe3 . We
deﬁne HC2 for the TC shown in the inset of ﬁg. 3(a).

Cu-doped TaSe3 sample No. 3 exhibited a two-step SC
transition. To investigate the cause of this result, we measured the resistance between the current terminals, andthe resistance between a current terminal and a voltage
terminal with a dc two-probe measurement. Figure 4(a)shows the results. Sharp drops in resistance due to the SC
transition were clearly observed between any pair of terminals, although the resistance measured with a two-probe
method did not become zero because of the resistances due
to contacts and lead lines (∼ 240 Ω). The SC transition
diﬀered according to the combination of terminals, showing that various regions with diﬀerent TC ’s are aligned inseries in the b-axis direction as shown in ﬁg. 4(b). Thus,
the two-step SC transition of sample No. 3 was caused by
the coexistence of two regions with TC ’s of ∼1.6 K and∼1.1 K between voltage terminals, and the value of thedrop in resistance for each TC corresponded to the size ofthe region with the TC . Cu-doped TaSe3 samples No. 1
and 2 also exhibited a non-single SC transition, where
the resistance began to decrease at ∼1.6 K and dropped
mostly at ∼1.1 K. Therefore, two regions with TC ’s of∼1.6 K and ∼1.1 K would coexist and the region with the
TC of ∼1.1 K would occupy most of these samples.

67001-p4

Eﬀect of Cu doping on superconductivity in TaSe3

superconducting
filament

TC~1.6 K

TC~1.1 K

b-axisCuatom(a) pure TaSe3(b) Cu-doped TaSe3 No. 4 (c) Cu-doped TaSe3 No.1, 2, 3
(lowest Cu concentration)(higher Cu concentration)

Fig. 6: (Colour online) Model of the superconducting ﬁlament structures of pure TaSe3 and Cu-doped TaSe3 . The TC of
suppressed SC is represented by 1.1 K overall.

Figure 5(a) shows a typical temperature dependence ofthe resistance from 0.6 K to 2 K under various magnetic
ﬁelds. As the magnetic ﬁeld increased, the SC transition
curve shifted to the low-temperature side. Figure 5(b)shows the temperature dependence of the upper criticalﬁeld (HC2 ). As the temperature decreased, HC2 of pure
TaSe3 sample No. 1 increased with an upward curvature,and HC2 of pure TaSe3 sample No. 2 increased with temperature dependence as a linear function near TC andwith an upward curvature at low temperatures. HC2 of
Cu-doped TaSe3 sample No. 2 increased with an upwardcurvature, and HC2 of Cu-doped TaSe3 sample No. 4 increased with a downward curvature near TC of ∼1.6 K
and with an upward curvature at low temperatures. In
Cu-doped TaSe3 sample No. 3, HC2 for the ﬁrst-step SC
transition exhibited an upward curvature and that for thesecond-step SC transition exhibited a slightly downward
curvature. The curvature for Cu-doped TaSe3 sample
No. 1 was unknown because there were only two points.
Discussion. – The SC of TaSe3 is ﬁlamentary, andadjacent superconducting ﬁlaments are coupled to eachother by the Josephson eﬀect [16,17]. An superconducting
ﬁlament is considered to be composed of multiple TaSe3
chains. In our result, pure TaSe3 exhibits a one-step SC
transition at ∼1.6 K (see ﬁg. 3(a)). As shown in ﬁg. 6(a),superconducting ﬁlaments with a TC of ∼1.6 K parallel tothe b-axis are bundled in pure TaSe3 . On the other hand,
Cu-doped TaSe3 samples No. 1, 2 and 3 with higher Cu
concentrations exhibit a coexistence of two regions with
TC ’s of ∼1.6 K, ∼1.1 K, and the region with the TC of∼1.1 K tends to be larger with increasing Cu concentration (ﬁg. 3(b) and ﬁg. 4). This result indicates that the Cu
doping suppresses the SC of TaSe3 . However, Cu-doped
TaSe3 sample No. 4 with the smallest Cu concentration
exhibits a one-step SC transition at ∼1.6 K as with pure
TaSe3 (ﬁg. 3(b)). Moreover, there is a region with a TC of∼1.6 K in Cu-doped TaSe3 samples No. 1, 2 and 3. The Cu
concentrations of the present four Cu-doped TaSe3 samples (table 1) are lower than that of the Cu-doped TaSe3
sample with the highest Cu concentration observed in ourprevious study [18]. The lower Cu concentrations and thelocation dependence of the TC in a sample (ﬁg. 4) suggestthat there are some areas that no Cu atom enters in asample and the area increases with decreasing Cu concentration. In addition, the suppression of SC by a Cu atom
might be limited within a superconducting ﬁlament rather
than the entire sample because the SC of TaSe3 is ﬁlamentary. Therefore, it is believed that, in a sample, there
are ﬁlaments where Cu atoms enter and SC is suppressed,
and ﬁlaments where Cu atoms do not enter and SC is
not suppressed. If there is a superconducting path composed of superconducting ﬁlaments where no suppression
remain, the partial suppression of SC cannot be observedby measuring the resistance because the electric current
ﬂows through the superconducting path with zero resistance. Therefore, as regards the invariant SC transitionin Cu-doped TaSe3 sample No. 4 and the region where
TC does not change in samples No. 1, 2 and 3, it canbe interpreted that more than one superconducting pathwith a TC of ∼1.6 K remains as shown in ﬁg. 6(b), (c).
Inhomogeneous SC as observed in Cu-doped TaSe3 hasbeen extensively studied theoretically and experimentallyin other systems [21–23].
We compare the temperature dependence of HC2 forpure TaSe3 and Cu-doped TaSe3 . HC2 is derived fromthe Pauli paramagnetic and orbital eﬀects. However, thePauli paramagnetic limit will not matter in the present
range of magnetic ﬁelds (0–80 mT). Considering orbital
eﬀects based on the Ginzburg-Landau (GL) theory, thetemperature dependence of the HC2 of bulk superconductors is expressed as

67001-p5

HC2 (t) = HC2 (0)1 − t2,
1 + t2(2)

A. Nomura et al.
where t is the normalized temperature (t = T /TC ). However, the temperature dependence of the HC2 of pure
TaSe3 and Cu-doped TaSe3 (ﬁg. 5(b)) cannot be expressedby eq. (2). Thus, we require a theoretical model that considers the special feature of the SC of TaSe3 , namely ﬁlamentary SC. According to the GL theory of ﬁlamentary
SC proposed by Turkevich and Klemm (the TK theory), the HC2 for Josephson-coupled superconducting ﬁlaments increases with upward curvature as temperature
decreases [24]. On the other hand, the HC2 for decoupled superconducting ﬁlaments increases with a downward
curvature. The temperature dependence of the HC2 exhibits an upward curvature in the two pure TaSe3 samples(ﬁg. 5(b)). From the TK theory, this result implies the
Josephson coupling of superconducting ﬁlaments. Even in
our model, as shown in ﬁg. 6(a), the SC of pure TaSe3 iscomposed of coupled superconducting ﬁlaments with thesame TC . In contrast, the temperature dependence of theHC2 exhibits a downward curvature near a TC of ∼1.6 K
in Cu-doped TaSe3 sample No. 4 with the same SC transition as pure TaSe3 . Thus, according to the TK theory, thesuperconducting ﬁlaments are decoupled near 1.6 K in thissample. This result is consistent with our model shown inﬁg. 6(b) where the superconducting ﬁlaments with a TCof ∼1.6 K are sparse. In other Cu-doped TaSe3 samples
No. 2 and 3, the temperature dependence of the HC2 exhibits an upward curvature or a downward curvature. Cu
doping results in SC ﬁlaments with diﬀerent TC ’s being
mixed in a sample as shown in ﬁg. 6(c). As a result, there
are regions where superconducting ﬁlaments with the same
TC are adjacent and coupled, and regions where superconducting ﬁlaments with diﬀerent TC ’s are adjacent and notcoupled. This complex conﬁguration of superconducting
ﬁlaments might lead to the complex sample dependence ofthe HC2 -temperature curve.
From the discussions above, we conclude that the SC of
TaSe3 is suppressed by Cu doping. On the other hand,a CDW emerges in Cu-doped TaSe3 [18]. Hence, SC and
the induced CDW would be in a competitive relationshipin Cu-doped TaSe3 .
We discuss the induced CDW in Cu-doped TaSe3 because the CDW property is important when discussing
the relationship between SC and CDW. The SC suppression of TaSe3 is local in the ﬁlament where Cu atoms enteras shown in ﬁg. 6. Therefore, it is possible that there isno coherent CDW in the entire sample, but CDWs exist
locally.
From the viewpoint of the locality of CDWs, we reconsider the resistance anomaly results, that is, the“γ”-shaped dip in dR/dT due to the CDW transition in
Cu-doped TaSe3 . Conventional CDW materials such as
NbSe3 , TaS3 and NbS3 exhibit anomalous increases in resistance at the CDW transition temperatures (TCDW ) because all or part of the Fermi surface disappears and thenumber of carriers decreases [6–8]. On the other hand,
the resistance anomaly of Cu-doped TaSe3 is extremely
small [18]. This result for Cu-doped TaSe3 may arise

because of the locality of the existence of the CDWs. In
fact, in Cux TiSe2 , no signal due to the transition of shortrange order CDWs is observed in the temperature dependence of the resistance [3]. Moreover, a comparison of the“γ”-shaped dips of Cu-doped TaSe3 samples with diﬀerent Cu concentrations shows that the dip size increases
with increasing Cu concentration while the temperature
at which the dip appears is almost constant [18]. The
dip size corresponds to the area of the reduced Fermi surface, and the dip appearance temperature corresponds to
TCDW . The relationship between the dip size and the dip
appearance temperature appears to contradict the prediction for long-range order CDW with the mean-ﬁeld theory, which shows a positive correlation between the areaof the reduced Fermi surface and TCDW . However, if theinduced CDWs have short-range order in the vicinity of
Cu atoms and the size of a CDW is shorter than the distance between Cu atoms, we can interpret the conﬂicting result mentioned above consistently, namely that thesize increases with increasing Cu concentration because
the number of short-range order CDWs increases, while
the appearance temperature is constant because the stateof each short-range order CDW is unchanged.
Here, we estimate the size of short-range order CDWs
from a simple calculation of the distance between Cu
atoms. The volume of a unit cell of TaSe3 is estimatedto be ∼0.34 nm3 from the lattice parameters determinedin our previous study, and a unit cell contains four Ta
atoms [18]. In addition, the Cu concentration of Cudoped TaSe3 is at most 1%. Hence, if Cu atoms enter a crystal evenly, each Cu atom enters a space of∼8.5 (= 0.34/(4 × 0.01)) nm3 and the distance between
adjacent Cu atoms is estimated to be ∼2 nm. Therefore,
the size of a CDW must be shorter than ∼2 nm.
The estimated size of the CDWs in Cu-doped TaSe3 ison a nanometer scale and comparable to the size of theshort-range order CDWs in Cux TiSe2 [4]. In Cux TiSe2 ,the short-range order CDWs do not compete with the SC
transition. On the other hand, our results suggest thatshort-range order CDWs compete with SC in Cu-doped
TaSe3 . One of the diﬀerences between the two materials is that the CDWs form on Cu atoms in Cu-doped
TaSe3 while the CDW is suppressed in the area where
Cu atoms enter in Cux TiSe2 [4]. Generally, when there
is an impurity, a CDW is pinned by that impurity [25].
Hence, the CDWs in Cu-doped TaSe3 would be harder tomove than those in Cux TiSe2 . Moreover, in Cux TiSe2 , themodulation period of the CDWs changes from commensurate to incommensurate at the Cu concentration where theSC phase emerges [5]. In general, a commensurate CDW
is harder to move than an incommensurate CDW [25].
Therefore, CDWs may compete with SC when CDWs are
hard to move due to impurity pinning or commensurate
pinning. We should note that, when discussing the relationship between SC and another electron ordering whichis periodically modulated, there is a case where whether
the electron ordering is static or dynamic is important [26].

67001-p6

Eﬀect of Cu doping on superconductivity in TaSe3
Conclusion. – We investigated SC in Cu-doped TaSe3
by measuring the temperature dependence of the resistance. The Cu-doped TaSe3 sample with the smallest Cu
concentration exhibited a one-step SC transition with a
TC of ∼1.6 K as well as pure TaSe3 . On the other hand,those with larger Cu concentrations exhibited a two-step
SC transition with TC ’s of ∼1.6 K and ∼1.1 K, or a nonsingle SC transition where the resistance began to decreaseat ∼1.6 K and dropped mostly at ∼1.1 K. The value ofthe drop in resistance at ∼1.1 K tended to expand withincreasing Cu concentration. The location dependence of
the SC transition showed that the two-step SC transition
and the non-single SC transition are caused by the coexistence of two regions with TC ’s of ∼1.6 K and ∼1.1 Kaligned in series in the b-axis direction in a sample. The
temperature dependence of the HC2 of Cu-doped TaSe3
diﬀered from that of pure TaSe3 . From these SC results
and the fact that the SC in TaSe3 is ﬁlamentary, we conclude that SC is suppressed locally by Cu doping and competes with the CDW in all Cu-doped TaSe3 samples. The
resistance anomaly due to the CDW transition was extremely small. The size of the “γ”-shaped dip increased
with increasing Cu concentration but the temperature atwhich it appeared hardly changed. These results for the
resistance anomaly and the dip, the local suppression of
SC suggest that the CDWs that appear as a result of Cu
doping have short-range order.
∗∗∗
We thank Professor T. Matsuura for helpful discussions. This study is supported by a grant-in-aid for science research from Hokkaido University Clark Memorial
Foundation.
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