PHYSICAL REVIEW B 85, 184513 (2012)

Mixed bulk-filament nature in superconductivity of the charge-density-wave conductor ZrTe3
Kazuhiko Yamaya,1 Shigeru Takayanagi,1 and Satoshi Tanda1,2
1Center of Education and Research for Topological Science and Technology, Hokkaido University, Kita 13,
Nishi 8 Kita-Ku, Sapporo 060-8628, Japan2
Department of Applied Physics, Hokkaido University, Kita 13, Nishi 8 Kita-Ku, 060-8628 Sapporo, Japan(Received 26 July 2011; revised manuscript received 6 April 2012; published 11 May 2012)

We have shown that the superconducting transitions in ZrTe3 are successive from filamentary to bulk, based on
experimental results obtained for a superconducting specific-heat anomaly and the anisotropic superconducting
transition curve of resistivity. A small jumplike superconducting specific-heat anomaly with a large and widelyextended tail was observed to closely follow the anisotropic zero-resistance transition. We concluded that thejumplike anomaly signifies the onset of the long-range order of Cooper pairs with the opening of a superconducting
gap at TC , while the large and widely extended tail indicates behavior induced by Cooper pairs with a very shortcoherence length. As a limit for a very short coherence length, we propose local pairs with Bose characteristics.
As a result, we can understand that the filamentary superconductivity is caused by the local pairs, and the large
and widely extended tail is in a crossover region between superconductivity induced by local pairs and thatinduced by Cooper pairs. Based on a discussion about the origin of the change in the pair coupling from thestarting of local pairing to Cooper pairing in ZrTe3 , we conclude that “mixed bulk-filament superconductivity”
results from unique electronic structural changes in the quasi-1D + 3D (D, dimensional) Fermi surfaces after the
CDW transition.
DOI: 10.1103/PhysRevB.85.184513

PACS number(s): 74.25.Bt, 71.45.Lr, 74.25.F−, 74.70.Ad

I. INTRODUCTION

Superconductivity and charge density waves (CDWs) arecooperative electronic phenomena caused by Fermi surface(FS) instabilities and electron-phonon coupling. Superconducting transitions generally occur in three-dimensional (3D)electronic systems, while CDW transitions occur in lowdimensional electronic systems, but rarely in 3D systems. Indeed, CDW transitions have been observed in low-dimensional
conductors such as layered MX2 compounds and chain-based
MX3 compounds, where M is a group four or five metals
and X = S, Se, or Te.1–5 A number of CDW compounds
are also superconducting at temperatures lower than the
CDW transition temperature (TCDW ) (this is called a CDW
superconductor).1,5,6 The issue whether superconductivity and
CDW states are competing or coexisting electronic states at
low temperatures is a fundamental topic in condensed-matterphysics.7–9
Noteworthy among CDW superconductors is ZrTe3 , which
exhibits a CDW transition around 63 K and superconductivity below 2 K. This is because ZrTe3 has characteristicfeatures regarding its FS topology10,11 and the nature of its
superconductivity.5,12 Band-structure calculations for ZrTe3
have predicted a 3D FS sheet, quasi-one-dimensional (1D)
FS sheets, and a van Hove singularity (vHs) consisting ofa quasi-1D FS intersecting a 3D FS (quasi-1D + 3D FSs).
The topology of a quasi-1D + 3D FS is unique and is neverseen in the FSs of chain-based compounds such as NbSe3
and TaS3 .13 A quasi-1D FS sheet obtained by band-structure
calculations forms a nesting vector consistent with the CDW
vector obtained in electron microscopy and x-ray diffraction
studies.14,15 A CDW gap driven by the nesting of the FS isobserved on a quasi-1D FS in angle-resolved photoemission
spectroscopy (ARPES) spectra, whereas no gap is observed
on a 3D FS.16,17 Furthermore, the spectra at and near thevHS show no gap opening, but a large enhancement is1098-0121/2012/85(18)/184513(6)observed in the electronic density of states at the Fermi
energy EF , D(EF ). The FSs that remain after the CDW
formation, which are mainly 3D and quasi-1D + 3D FSs, arerelevant to the superconductivity. Indeed, the superconducting
transition of ZrTe3 can be observed below 2 K by measuring
the electrical resistivity and diamagnetic susceptibility.5,12
However, it has been concluded that the superconductivity
is filamentary rather than bulk on the basis of results obtained
for anisotropic superconducting transitions, which depend on
the direction of applied currents and magnetic fields.12 The
filamentary behavior reported for NbSe3 18 is extrinsic, whereas
the filamentary behavior observed for ZrTe3 is intrinsic.
However, the filamentary behavior observed for ZrTe3 is
uncommon if the FSs that remain after the CDW formation
respond normally to superconductivity as found with as other
CDW superconductors such as NbSe2 , Nb3 Se4 , and Cux TiSe2 ,etc., because these all are bulk superconductors.19–21 Since
resistivity and diamagnetic susceptibility measurements do
not directly reflect the bulk properties of a sample, theseproperties must be detected directly to clarify the nature of
the superconductivity in ZrTe3 .
In this paper, the temperature dependence of the specificheat of ZrTe3 measured from 0.6 K up to 10 K is reported
together with a reexamination of the anisotropic superconducting transition caused by electrical resistivity. A small jumplikesuperconducting specific-heat anomaly with an extended tailwas observed to closely follow the anisotropic zero-resistancetransition, showing successive superconducting transitions
moving from filamentary at high temperatures to bulk at low
temperatures below 2 K. We concluded that the jumplikeanomaly signifies the onset of the long-range order of Cooper
pairs with the opening of a superconducting gap at TC , while
the large and widely extended tail indicates superconducting
behavior caused by Cooper pairs with a very short coherence
length. As a limit for a very short coherence length, we

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YAMAYA, TAKAYANAGI, AND TANDAPHYSICAL REVIEW B 85, 184513 (2012)

propose local pairs with Bose characteristics. And as a result,filamentary superconductivity is understood to be induced by
local pairs, and the large and widely extended tail is understood
to be a crossover region between local pairs and Cooper pairs.
We show that “mixed bulk-filament superconductivity” iscaused by a change in the pair coupling from local pairing with
Bose characteristics to Cooper pairing. Based on a discussionof the origin of the change in pair coupling in ZrTe3 , weconclude that the “mixed bulk-filament superconductivity”
results from the unique electronic structural changes in thequasi-1D + 3D FSs after the CDW transition, where there
is a large enhancement in D(EF ) near the vHs and thesimultaneous presence of narrow and wide bands at EF .
II. EXPERIMENTS

Single crystals of ZrTe3 were prepared by the iodine (I2 )vapor transport method. Starting materials were Zr sheetsof 99.99% purity and Te ingot of 99.999%. The Zr sheets
preheated in a vacuum and Te ingot were simultaneously
reacted and transported with I2 in a 2-cm-diam 20-cm-longquartz tube. After 14 days a number of single crystals up to∼5 × 8 × 0.5 mm3 were obtained at the cool end of tube. Two
samples were used in the heat capacity measurements. Sample
A consists of single crystals grown in the temperature gradientfrom 750 to 700 ◦ C, and its total mass is 230 mg. While Sample
B consists of single crystals grown in the temperature gradientfrom 730 to 680 ◦ C, and its total mass is 200 mg. Each sample
consists of 10 single crystals brought into thermal contact
using Apiezon N grease (total mass of 20 mg).
The heat capacity from 0.6 to 10 K was measured withthe heat pulse method using a conventional handmade 3 He
cryostat. The sample temperature was determined using acalibrated resistance thermometer (Cernox Resistor, Lake
Shore Cryotronics, Inc.). The overall accuracy was 2%, with a
precision that was determined by performing measurements
using two typical samples. One was a 200-mg standard
aluminum (A) plate of 99.99% purity (the superconducting
transition temperature, TC = 1.21 K).22 The other was a
250-mg typical CDW superconductor NbSe2 (TC = 7.22 K)
that consisted of 13 single crystals contacted thermally as with
the ZrTe3 sample.23 The total addenda (including the Cu-Be
sample stage and the Apiezon N grease) amounted to nearly
20% of the total heat capacity.
For the resistivity measurement, the samples were selectedfrom the single crystals of Samples A and B. Parallel-pipedsamples were cut from the same crystal. One was cut parallelto the a axis, and the other was cut parallel to the b axis.
The resistance from 0.6 to 295 K was measured with theconventional dc-four-probe method. Carbon paste was used
for the electrical contacts. The thermometer was a Cernox
Resistor as in the heat capacity measurement.
III. RESULTS AND DISCUSSION

The room-temperature resistivities of ZrTe3 were ρa 
ρb = 3 × 10−4 cm, which are in good agreement withpreviously reported values.5 Figure 1 shows the temperaturedependencies of the resistivities below 8 K for Samples A-1,
A-2, B-1, and B-2. The resistivities were almost independent of

FIG. 1. (Color online) Temperature dependencies of the a and bcomponents of resistivity of ZrTe3 measured on samples A-1, A-2,
B-1, and B-2.

current for the measured current values. The data agreed wellwithin measurement accuracy, indicating good compositional
homogeneity. An anisotropic superconducting transition wasobserved. The transition of the a component started at ∼5 K
and was broad (∼2 K), while that of the b component was
relatively narrow at only ∼0.6 K from ∼2.1 to ∼1.5 K.
The b component did not exhibit any noticeable changes
through the transition of the a component. The normal
resistance of the b component showed a gradual decrease withdecreasing temperature even when the a component exhibited
zero resistance below 2.5 K. Both resistivity components
became zero below 1.5 K. These results are almost the sameas previously reported results,12 suggesting the presence offilamentary superconducting channels along the a axis.
In addition to the anisotropic transition curves of resistivity, Nakajima et al. observed anisotropic ac diamagnetic
susceptibilities depending on the direction of applied magnetic
fields, which occurred at low temperature below the zeroresistance transition temperature.12 They proposed a modelin which the superconductivity of ZrTe3 is filamentary, but
not bulk. According to the model, superconducting filaments
are aligned parallel to the a axis with the spacing of about
40 Å, and they are coupled weakly each other. However,with decreasing temperature the coupling becomes stronger.
A zero-resistance transition along the perpendicular direction
is observed at lower temperature. However, the origin offilamentary superconductivity remains unclear.
In contrast to the resistive transition result, specific-heatmeasurements Cp (T ) show unambiguous evidence of bulk
superconductivity. Figure 2 shows the specific heat divided
by temperature, Cp /T as a function of T 2 for Sample B.
Cp /T decreases linearly with decreasing T 2 ; that is, it iswell represented as a function of Cp /T = γ + βT 2 observedin Cp (T ) of a typical normal metal. Here γ is an electronic
specific-heat coefficient, and β is a lattice specific-heat coefficient. Figure 2(b) shows that at around 2 K Cp /T deviates fromthe linear relation for T 2 observed in the high-temperature

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PHYSICAL REVIEW B 85, 184513 (2012)

FIG. 2. (a) Temperature dependence of specific heat Cp (T ) of
ZrTe3 (sample B) plotted as Cp /T vs T 2 . The dotted line is a leastsquare fit (see text). (b) Cp /T vs T 2 for T 2 < 5 K2 (T < ∼2.2 K).

range, then rapidly increases near 1.4 K, and beyond a peak at
1.2 K it gradually decreases. The humplike anomaly of Cp /Temerges below the zero-resistance transition temperature. The
same result was obtained with Sample A. Here it should be
noted that the temperature at which the specific-heat anomaly
emerges corresponds well with that of the previously reported
ac diamagnetic susceptibilities.5,12 This strongly indicates thatthe superconductivity of ZrTe3 is thermally and magneticallybulk at low temperatures below 2 K.
When we compare the temperature dependences of boththe specific heat and the resistivities, three main features canbe summarized as follows. The first is that no specific-heatanomaly is observed in the zero-resistance transition region of
the a component (between ∼2.5 and ∼5 K). The second is thatthe deviation from the linear T 2 dependence of Cp /T is near
the onset of the zero-resistance transition of the b component.
The third is that the specific-heat anomaly rapidly increases
around a temperature corresponding to the zero resistanceof the b component (T0b ), and the peak of the specific-heatanomaly is below T0b . The comparison shows that superconducting filaments aligned parallel to the a axis are coupledweakly to each other in the high-temperature region,12 butwith decreasing temperature the coupling becomes stronger
with an increasing volume of superconducting filaments. Bulk
superconductivity is induced over the entire sample at low
temperature. Thus, we find successive superconducting transitions ranging from filamentary behavior at high temperatures
to bulk behavior at low temperatures below 2 K. This contrasts
with the case of TaSe3 , which is known to be a filamentarysuperconductor that exhibits no bulk characteristics even at low
temperatures below 1 K,24,25 except in recently published workon ring-shaped crystals of TaSe3 .26 Hence, we conclude that
ZrTe3 exhibits mixed bulk and filamentary superconductivity,
but is neither bulk nor filamentary. This is a new type ofsuperconductivity, which can be called “mixed bulk-filament
superconductivity.”

Let us now discuss the values of γ and β of a function of
Cp /T = γ + βT 2 determined by the least-square method. The
dotted line in Fig. 2 represents calculated values of Cp /T with
γ = 2.15 mJ/mol K2 and β = 0.985 mJ/mol K4 determined inthe 3 to 6 K temperature range (T 2 = 9 ∼ 36 K2 ) for Sample B.
For Sample A, the obtained values were γ = 2.23 mJ/mol K2
and β = 0.97 mJ/mol K4 , showing good agreement between
the two samples. It should be noted that with ZrTe3 , the γ value
is obtained in the metallic CDW state below TCDW (=63 K), but
not in the normal metal state above TCDW . The γ value obtained
here is expected to be proportional to D(EF ) on the remaining
FSs after CDW formation, D(EF )CDW , but not D(EF )metal ,which is D(EF ) in the normal metal state. In fact, the decreasein D(EF ) due to the CDW transition has been estimatedby Chung et al.27 We try to estimate the relative change inD(EF ) caused by the CDW transition, D(EF )CDW /D(EF )metalfrom the size of the resistance anomaly at TCDW using an
α parameter introduced by Kawabata; D(EF )CDW = (1 −α)D(EF )metal .9 The α value of ZrTe3 obtained here is 0.4,
which is in good agreement with the reported values.8 Hence,
D(EF )CDW /D(EF )metal is 0.6. This is nearly three times aslarge as that of NbSe3 , which is a CDW conductor, but not
a superconductor.9 The large value of D(EF )CDW /D(EF )metal
may be due to the existence of the vHs, which may makesuperconductivity possible at low temperature.
To investigate the electronic states of bulk superconductivity of ZrTe3 , we estimate the electronic specific heat Ce (T )by subtracting the phonon contribution (βT 3 ) from Cp (T ) in
the normal state, that is, Ce (T ) = Cp (T ) − βT 3 , assuming nochange in the phonon contribution in the superconducting
state. Figure 3 shows Ce divided by temperature and γ ,Ce /γ T as a function of the normalized temperature, tN , heretN = (T − TC )/TC , and TC is the temperature corresponding
to the peak of Ce (T ) (TC = 1.17 K for Samples A and
B). Data of A (TC = 1.15 K) that is a typical BCS bulk
superconductor are added for comparison. The γ values used

FIG. 3. (Color online) Temperature dependencies of electronic
specific heat Ce (T ) of ZrTe3 (samples A and B) plotted as Ce /γ T vstN , where tN is the normalized temperature by TC [tN = (T − TC )/TC ]and γ is an electronic specific-heat coefficient in the normal state (seetext). A data are added for comparison. The dotted line represents acurve calculated using the BCS theory.

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YAMAYA, TAKAYANAGI, AND TANDAPHYSICAL REVIEW B 85, 184513 (2012)

FIG. 4. (Color online) (a) Temperature dependencies of superconducting electronic specific-heat Ces (T ) of ZrTe3 (samples A andB) plotted as Ces /γ TC vs tN . A data are added for comparison(see text). The temperature dependencies of resistivity normalized by
7 K (solid lines) refer to the right axis (see Fig. 1). (b) Temperaturedependencies of Ces (T ) of ZrTe3 (samples A and B) are plotted on asemilogarithmic scale.

are obtained in the metal state for A (γ = 1.24 mJ/mol
K2 ) and in the CDW metal state for ZrTe3 . We can see large
differences when we compare the results of ZrTe3 and A.
A exhibits typical behavior of a BCS superconductor; that
is, Ce (T ) shows a jump at TC and falls below the γ value
at low temperatures of tN < −0.5(T < TC /2). The jump of
the specific heat Ce (TC ) was ∼1.74 mJ/mole K, and theparameter Ce /(γ TC ) was calculated as ∼1.36, which is close
to the BCS value of 1.43. On the other hand, Ce /γ T of ZrTe3
exhibits a humplike anomaly with an extended tail above TC .
To estimate the unclear jump at TC of ZrTe3 , we used thedifference between Ce at TC and γ TC [Ce = Ce (TC ) − γ TC ].
The Ce (TC ) values of Samples A and B were ∼2.30 and∼2.13 mJ/mole K, respectively. The parameter Ce /(γ TC )obtained of Samples A and B were 1.03 and 0.99, respectively,
which were ∼30% smaller than the BCS value. Ce /γ T below
TC gradually decreases with decreasing temperature, and its
value remains about 1.6 times higher than the γ value even at
low temperatures of tN < −0.5 (T < TC /2). An extrapolation
to T = 0 K of Ce /γ T seems to be nonzero (a residual
electronic specific heat, γ0 = 0), although the measurementof Ce /γ T in ZrTe3 is needed down to well below TC /2. This
is in contrast to the exponential temperature dependence of
Ce /γ T in A calculated by the BCS theory as shown by thedotted line in Fig. 3. Unconventional behavior such as the
reduced value of Ce /(γ TC ), the γ0 = 0 and the extended tailsuggest that ZrTe3 is a non-s-wave superconductor.28–31
The most interesting feature as regards the specific-heatanomaly is the extended tail above TC . To determine the T
dependence of the extended tail, the specific-heat anomaly
caused by the superconducting transition Ces (T ) may be obtained from an extrapolation of the temperature dependence of
Ce (T ) in the normal state. This extrapolation allows Ces (T ) as
the difference between Ce (T ) and γ T , Ces (T ) = Ce (T ) − γ T .
Figure 4(a) shows the T dependencies of Ces normalized by

γ TC as a function of tN . The resistivities normalized by 7 K areshown by solid lines for comparison. A jumplike anomaly isobserved in the vicinity of TC , and an extended tail is observed
above tN ∼ 0.1. Figure 4(b) shows the T dependencies of Ces
by a semilogarithmic plot. The temperature dependence of theextended tail is almost logarithmic, indicating superconducting
fluctuations. Ces deviates from the log T dependence aroundtN ∼ 0.1, and then rapidly jumps very near TC , signifying theonset of a long-range order of Cooper pairs with the openingof a superconducting gap at TC , although the magnitudeof the jump of Ces is fairly small compared with that ofa BCS superconductor. Here, it should be noted that thesuperconducting fluctuation region appears from a temperaturenear tN ∼ 1.0, and the magnitude of the extended tail reaches
nearly 50% of the peak value of Ces ; it is a large and widelyextended tail. Such large fluctuations have never previously
been observed in s-wave or non-s-wave superconductors.28–31
A comparison of the region of superconducting fluctuations
with that of cup-rate superconductors, which are known tohave a short coherence length of about 10 Å,32 shows that the
ZrTe3 region is wider than that of cup-rate superconductors
and comparable to that observed in the λ transition in liquid
4
He II.33 This result suggests that the coherence length of
ZrTe3 is extremely short and below 10 Å. On the other hand,the coherence length at 0 K, which was estimated by theanisotropic clean Ginzburg-Landau theory from the upper
critical field defined as the magnetic field where the Meissner
diamagnetism vanishes, is over 600 Å and much longer thanthe lattice constants5 . From the contradictory estimations of
the coherence length, we suggest that the very short coherence
length is a feature of filamentary superconductivity rather
than the fluctuations observed for the superconducting state
formed below TC . As a limit for a very short coherence
length, it is reasonable to assume local pairs that interact
strongly with each other in an attractive way over shortdistances, and that have Bose characteristics.34,35 Assumingthat filamentary superconductivity is induced by local pairs
with Bose characteristics, it would not be inconsistent withthe result of the direction-dependent zero-resistance transition
observed as being filamentary, because local pairs with
Bose characteristics result from real space pairing. Thus, weconclude that “mixed bulk-filament superconductivity” resultsfrom a change in the pair coupling starting from local pairs
with Bose characteristics to Cooper pairs. The large and widelyextended tail of Ces may be adopted as a feature in the crossover
region from superconductivity induced by local pairs to thatinduced by Cooper pairs.
Next we discuss the origin of the change in the pair couplingfrom local pairing to Cooper pairing in ZrTe3 . We noticecharacteristic changes in the electronic band structure acrossthe CDW transition, in which D(EF ) very close to the vHs isgreatly enhanced in addition to significant electronic structuralchanges in the quasi-1D FS.16,17 It is known that the presenceof a vHs at EF can induce Fermi surface instabilities andlead to the superconducting state36,37 or the CDW state.38
The CDW-induced enhancement in D(EF ) near the vHs maylead again to superconductivity or CDW stability. Particularly,
in the narrow band that constructs the quasi-1D + 3D FSs
together with the wide band,11,16,17 electrons can form local
pairs that interact attractively with each other over short

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PHYSICAL REVIEW B 85, 184513 (2012)

distances. In other words, the formation of local pairs ofelectrons with Bose characteristics will be expected.34,35 The
local pairs formed in the narrow bands are delocalized rather
than localized, because of hopping via virtual excitations
into wide-band states in the quasi-1D + 3D FS. Since thenarrow-band electrons have a dominant Te5px characteristic
originating in the Te(2)-Te(3) chain parallel to the a axis,10,11
the local pairs must be dominantly formed along the a axis,
leading to the zero-resistance transition of the a component. If
the number of local pairs with a lower temperature increased,
they would spread into a wide band in the quasi-1D + 3D
FSs and induce Cooper pairs with a very short coherence
length. The zero-resistance transition of the b component andthe extended tail of Ces may be due to Cooper pairs witha very short coherence length. Furthermore, local pairs also
spread into the wide band in the 3D FS and induce Cooper
pairing among the wide-band electrons and vice versa.34,35
This mutual induction rapidly develops the coherent state of
the Cooper pairs, and as a result the single-particle spectrumof the wide-band electrons opens a superconducting gap on the
3D FS, leading to the onset of the long-range order of Cooper
pairs. Thus, there a crossover region appears between the
superconducting state induced by local pairs and that induced
by Cooper pairs in the superconducting transition of ZrTe3 . We
can conclude that “mixed bulk-filament superconductivity”
results from the unique electronic structural changes in thequasi-1D + 3D FSs after the CDW transition, in which there
is a large enhancement in D(EF ) near the vHs and thesimultaneous presence of narrow and wide bands at EF .
The crossover from local pairs to Cooper pairs in ZrTe3
reminds us of the Bose-Einstein condensation (BEC)-BCS
crossover phenomena in ultracold atomic Fermi gases39 andthe BEC-BCS picture proposed in cup-rate superconductors.40
The former is performed while varying the fermionic density
or interaction and the latter while varying the hole doping. On
the other hand, the crossover in ZrTe3 is observed when thetemperature is varied in the superconducting transition region.
They are quite different situations, supporting the view thatthe unique electronic structural changes in the quasi-1D + 3D
FSs after the CDW transition are deeply involved in the originof the crossover of ZrTe3 .
The unconventional superconducting behavior observedin ZrTe3 , which is the reduced value of Ce /(γ TC ), theγ0 = 0 and the extended tail of Ces , has also been observed in
non-s-wave superconductors such as heavy Fermion superconductors, the spin-triplet superconductor Sr2 RuO4 and cup-rate
superconductors.28–31 These compounds are bulk superconductors where no filamentary behavior is observed, while
ZrTe3 is a “mixed bulk-filament superconductor.” Whether
the unconventional behavior observed here can be explainedby non-s-wave superconductivity or “mixed bulk-filament
superconductivity” will constitute a future issue. Furthermore, to confirm the nature of “mixed bulk-filament superconductivity,” ARPES and scanning tunneling spectroscopy(STS) studies will be needed at temperatures above andbelow TC . A recent study has reported the coexistence ofbulk superconductivity and CDW in Cu intercalated ZrTe3 ,Cu0.06 ZrTe3 .41 It is interesting to note that “mixed bulkfilament superconductivity” turns to bulk superconductivity
with increasing Cu intercalation.

1

5

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2

IV. CONCLUSION

We have shown that the superconducting transitions in
ZrTe3 are successive from filamentary to bulk, based on experimental results for a superconducting specific heat anomaly andthe anisotropic superconducting transition curve of resistivity.
The result shows that the superconductivity is in a mixed bulk
and filamentary state, but is neither bulk nor filamentary; it canbe called “mixed bulk-filament superconductivity.” A small
jumplike superconducting specific-heat anomaly with a large
and widely extended tail was observed to closely follow theanisotropic zero-resistance transition. We concluded that thejumplike anomaly signifies the onset of the long-range orderof Cooper pairs with the opening of a superconducting gap at
TC , while the large and widely extended tail indicates superconducting behavior induced by Cooper pairs with a very shortcoherence length. As a limit for a very short coherence length,
we proposed local pairs with Bose characteristics. The existence of local pairs can allow us to understand the directiondependent zero-resistance transition observed in filamentarysuperconductivity. The large and widely extended tail of Ces
was understood to be a superconducting feature that appears in
the crossover from superconductivity induced by local pairs tothat induced by Cooper pairs. The “mixed bulk-filament superconductivity” of ZrTe3 is explained by the change in the paircoupling starting from local pairs with Bose characteristics to
Cooper pairs. Based on a discussion of the origin of the change
in the pair coupling from local pairing to Cooper pairing in
ZrTe3 , we concluded that the “mixed bulk-filament superconductivity” results from the unique electronic structural changes
in the quasi-1D + 3D FSs after the CDW transition, where
there is a large enhancement in D(EF ) near the vHs and thesimultaneous presence of narrow and wide bands at EF .
ACKNOWLEDGMENTS

We are grateful to K. Inagaki and K. Ichimura for fruitful
discussions. This work was supported by Hokkaido University,
the 21st Century COE Program “Topological Science andTechnology.”

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