RAPID COMMUNICATIONSPHYSICAL REVIEW B 85, 220506(R) (2012)

Fluctuating superconductivity in the strongly correlated two-dimensional organic superconductor
κ-(BEDT-TTF)2 Cu(NCS)2 in an in-plane magnetic field
Satoshi Tsuchiya,1,* Jun-ichi Yamada,2 Satoshi Tanda,3,4 Koichi Ichimura,3,4 Taichi Terashima,1 Nobuyuki Kurita,1Kota Kodama,1,5 and Shinya Uji1,51National Institute for Materials Science, Ibaraki 305-0003, Japan
Graduate School of Material Science, University of Hyogo, Hyogo 650-004, Japan3
Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan
4
Center of Education and Research for Topological Science and Technology, Hokkaido University, Sapporo 060-8628, Japan
5
Graduate School of Pure and Applied Sciences, University of Tsukuba, Ibaraki 305-8577, Japan(Received 12 February 2012; revised manuscript received 29 May 2012; published 26 June 2012)2

We report magnetoresistance and magnetic torque measurements for the highly correlated 2D organic
superconductor κ-(BEDT-TTF)2 Cu(NCS)2 . Under magnetic ﬁeld parallel to the conducting layers, we obtainconvincing evidence of ﬂuctuating superconductivity in a wide temperature and ﬁeld range, where the magnetic
torque shows diamagnetism but the resistance shows no appreciable decrease.
DOI: 10.1103/PhysRevB.85.220506

PACS number(s): 74.40.−n, 74.25.Dw, 74.70.Kn, 75.30.Gw

In conventional superconductors, the superconducting transition is well characterized by zero resistance and diamagnetism due to exclusion of magnetic ﬂux (Meissner effect).1
Above the transition temperature (Tc ), the amplitude of theorder parameter ||, corresponding to density of Cooper pairs,
vanishes and the bulk phase coherence φ is lost. In strongly
correlated two-dimensional (2D) superconductors,2,3 however,vortex-Nernst effect measurements show that ﬂuctuating superconductivity (FSC), which has ﬁnite Cooper pair density
but no bulk phase coherence, appears substantially above Tc .
The FSC will be one of the most intriguing interpretations of
the pseudogap formation, which is likely an intrinsic property
in strongly correlated 2D superconductors.4
The FSC has been extensively studied with the vortexNernst effect in magnetic ﬁelds perpendicular to the conducting layers.2,3 In highly 2D superconductors, as the magnetic
ﬁeld is rotated from the perpendicular direction to the parallel
direction, the orbital effect, which is closely related to the
nucleation of vortices, is reduced and then the critical ﬁeld
increases signiﬁcantly. Because of the highly 2D nature of
the superconductivity, the FSC will be also ﬁeld-direction
dependent. However, the anisotropic properties of the FSC
have been rarely investigated so far.
The vortex-Nernst effect experiments under in-plane magnetic ﬁelds have been prevented for two reasons. First, underin-plane ﬁeld, the ﬂux lines penetrate only the insulating layers,
forming Josephson vortices, but not the superconducting layers. Because of the platelike shape of the samples, it is hard to
detect the Nernst effect of the Josephson vortices. Second, highmagnetic ﬁeld, which is not realized under normal laboratory
conditions, is required to destroy the superconductivity at
low temperatures especially for the high-Tc cuprates. Suchhigh critical ﬁeld makes it difﬁcult to obtain the global phase
diagram.
In this Rapid Communication, we report the magnetoresistance and magnetic torque measurements for a highly correlated 2D organic superconductor κ-(BEDT-TTF)2 Cu(NCS)2
with Tc of 10.4 K.5 Under magnetic ﬁeld parallel to the
conducting layers, we obtained convincing evidence of FSC ina wide temperature and ﬁeld range, where the magnetic torque1098-0121/2012/85(22)/220506(4)shows diamagnetism but the resistance shows no appreciable
decrease.
A charge transfer salt, κ-(BEDT-TTF)2 Cu(NCS)2 (hereafter κ-NCS) is one of the most studied highly correlatedorganic superconductors. The BEDT-TTF molecule layers
form the highly 2D electronic state separated by the Cu(NCS)2
anion (insulating) layers as shown in the inset of Fig. 1(a).
The dimerization of the BEDT-TTF donors gives rise toa half-ﬁlled energy band. The isostructural salt, κ-(BEDTTTF)2 Cu[N(CN)2 ]Br (hereafter κ-Br), with a slightly higher
Tc (∼12 K) has smaller t/U than κ-NCS, where t and U are
the transfer integral between the BEDT-TTF dimers and the
Coulomb repulsion on the dimer, respectively. Therefore, theelectronic state of κ-Br is closer to a Mott insulating phase thanκ-NCS in the T vs t/U phase diagram.6 Large Nernst signals
are clearly observed in perpendicular ﬁelds well above Tc for
κ-Br, but not for κ-NCS.3 With decreasing t/U, the number
uncertainty of the Cooper pairs N (=||2 ), which incurs a
Coulomb energy penalty, is reduced.7 From the uncertainty
relation between the Cooper pair number and the bulk phase,N φ > 1, the small t/U enhances the phase uncertainty,
leading to phase ﬂuctuation in the superconducting state.
A magnetic torque measurement is a powerful probe fordetecting FSC under in-plane ﬁeld. The magnetic torqueis quite sensitive to diamagnetism even in the ﬂuctuation
regime where supercurrent induces only local diamagnetism.8
The torque is given by τ = μ0 (M × H ) where H is theapplied magnetic ﬁeld and M the magnetization. For highly
2D superconductors, the torque under strong in-plane ﬁeld
is written as τ ≈ Hx Mz (Hz ) where the x(z) axis is parallel(perpendicular) to the conduction layers.9 Therefore, one canobtain the perpendicular magnetization curve Mz (Hz ) underlarge Hx by dividing the toque τ by Hx . In addition, we
can overcome the second difﬁculty for the highly 2D organic
superconductors since the in-plane upper critical ﬁeld is much
lower than that of high-Tc cuprates.
Single crystals of κ-NCS were grown electrochemically.10
The crystals have platelike shapes, whose typical sizes usedin the present experiments are 600 ×200 × 50 μm3 forthe resistance measurements and 200 × 100 × 20 μm3 for220506-1©2012 American Physical Society

RAPID COMMUNICATIONSSATOSHI TSUCHIYA et al.

12K
11K
10K
9K
8K
7K

4

10

2

7 .5 T
I // aθ

bc plane
BEDT-TTF
Cu(NCS)2

20

8

27T
26T
25T
24T
23T

6

22T
21T

-20

-1 0

50

0

5K

25

0

5K
I // a
-2 0

0

20

20

19T

-20

θ (degrees)

10

20

200

-25

-50

0

θ (degrees)

20T
21T
22T
23T
24T
25T
26T
27T

(d)

19T

8K

θ (degrees)

20T
4

7K

-2 0

τ/μ Hx (N m T )0θ (degrees)(c)
R (a rb . units)

800

H

-20

τ/μ0Hx (N m T-1)

0
-20

0

τ/μ Hx (N m T )

6

7.5 T

20

τ/μ0Hx (N m T-1)

13K

-2 0

-1 0

0

0

θ (degrees)10θ (degrees)

20

20

FIG. 1. (Color online) (a), (b): Angular dependence of theinterlayer resistance R and magnetic torque τ at 7.5 T for various
temperatures in κ-(BEDT-TTF)2 Cu(NCS)2 . (c), (d): Angular dependence of the interlayer resistance and magnetic torque at 5 K forvarious magnetic ﬁelds. The inset of (a) shows a schematic of thecrystal structure and the deﬁnition of the ﬁeld angle θ . Each datum
above 8 K in (a) and 20 T in (c) is shifted by a 0.5  step for clarity.
The insets of (b) and (d) show the overall views of the torque curves.
The changes of the torque curves near θ = 0◦ show diamagnetism(negative Mz ) of the sample.

the torque measurements. The samples 01-02 and 03-04 areused in the interlayer and in-plane resistance measurements,
respectively, and samples 02, 05, and 06 are used in the torquemeasurements. The torque measurement for sample 02 is
carried out after the resistance measurement. The magnetic
torque was measured by a microcantilever technique.11 The
interlayer and in-plane resistances are measured with thestandard four-terminal method with lock-in ampliﬁers withac current of about 10 μA along the a axis and bc plane,
respectively. Four gold wires of 10 μm in diameter are attachedto the samples by carbon paste. These experiments were
performed by a 20 T superconducting magnet with a 3 He
cryostat or by a 30 T resistive magnet with a 4 He cryostat at
Tsukuba magnet laboratories, NIMS.
Figure 1(a) shows the angular dependence of the interlayer
resistance of κ-NCS at 7.5 T for various temperatures.
We observe the resistance drops at zero degrees due tosuperconductivity below 8 K but there is no sign of thesuperconductivity above 9 K. In Fig. 1(b), the torque curves
are presented. The torque steeply increases as the ﬁeld is tilted
from zero degrees (in-plane ﬁeld) below 9 K. This linear
increase shows large diamagnetism [Mz (Hz ) < 0]: A large
number of the magnetic ﬂuxes remain between the superconducting layers and are excluded from the superconducting
layers. As the magnetic ﬁeld is further tilted, the torquehas a sharp peak and then rapidly decreases, showing thatmost of vortices start penetrating the superconducting layers.
This behavior is interpreted in terms of a lock-in transitionof ﬂux lines, a transition from parallel ﬂux lines to tilted
ﬂux lines.12 At higher angles, the diamagnetism is gradually
reduced and then the superconductivity is completely broken.
As temperature increases, the diamagnetism is considerably
reduced: The magnetic ﬂuxes are only partially excluded evenfor small Hz , and the lock-in transition is smeared out. The
quite unusual behavior is that the diamagnetic signal is evident
at high temperatures up to 12 K whereas the resistance shows
no appreciable decrease above 9 K. This diamagnetism above
9 K can be ascribed to FSC. Although the interpretation of thevortex-Nernst effect due to FSC seems still controversial,13–17
the observation of the diamagnetism in κ-NCS provides
convincing evidence of FSC. No appreciable hysteresis of thetorque curve with ﬁeld angle in the FSC region shows very
weak pinning of the vortices, consistent with the picture of
FSC. Figures 1(c) and 1(d) show the interlayer resistance andthe torque at 5 K under ﬁelds from 19 to 27 T, respectively. No
sign of superconductivity in the resistance is seen above 22 T.
However, the diamagnetic signal is obviously observed evenat 27 T in the torque curves, showing the signiﬁcantly large
FSC in the wide ﬁeld range.
We can obtain the absolute values of the perpendicular magnetization from the magnetic toque. The inset of
Fig. 2 shows the perpendicular magnetization vs the internal

3T
4T
5T
7.5T
12.5T
15T
17T

-3

10

-4

10

-5

10

1.4
-4
x10

-6

10

μ0 Mz (T )

14K

9K
10K
11K
12K
13K
14K
15K

-dM z/dHz

(b)

15K

(a)

a axisR (arb. units)

8

PHYSICAL REVIEW B 85, 220506(R) (2012)

-7

10

0
0.0

-8

10

4

7K
7.5
8
8.2
8.4
8.6
8.8

7.5T

9
9 .5
10
1 0 .511
1 1 .512
1 2 .51314
15

μ0Hi,z (T )

2.0

6

8

10

12

14

T (K )

FIG. 2. (Color online) Temperature dependence of the diamagnetic susceptibility −dMz /dHz for Hz → 0. The perpendicularcomponent of the magnetization Mz (Hz ) is derived from the relation
Mz (Hz ) = τ/(μ0 Hx ). The inset shows Mz (Hz ) curves as a function of
Hz for sample 05 at 7.5 T. Thick and thin arrows indicate the starting
points of the upward curvatures and the saturation temperatures of−dMz /dHz (Tcsat ), respectively.

220506-2

RAPID COMMUNICATIONSFLUCTUATING SUPERCONDUCTIVITY IN THE STRONGLY . . .

35
30

R esista nce#01 (T , I // a)#02 (T , I // a )#03 (T , I // b c)
#04 (T , I // b c)
T o rqu e# 0 2 (T *)# 0 5 (T *)# 0 6 (T *)# 0 7 (T *)# 0 5 (T sat)
S pe cific h ea t
Ref. 21κ-(B E D T -T T F ) 2C u(N C S ) 2
H // bc plane

μ0H// (T)

25
20

FSC

15
10
Bulk SC

Normal

5
0

0

2

4

6

8

10

12

14

T (K )
FIG. 3. (Color online) Phase diagram of κ-(BEDT-TTF)2 Cu(NCS)2 under the in-plane magnetic ﬁeld. Circles and squares indicate
Tc (H) determined from the interlayer resistance (I a) and thein-plane resistance (I bc plane), respectively. Triangles represent
Tc∗ (H) determined from the magnetic torque measurements. Diamonds indicate Tc (H) determined from the speciﬁc heat measurement(Ref. 21). Bulk SC and FSC indicate bulk superconductivity andﬂuctuating superconductivity, respectively.

R (Ω)

2 .0

(a)

2T
5K

5 .2 K

4 .8 K
1 .5

2T

(b)

5 .4 K 5 .5 K 6 K

3

τ /μ0H x (N m T-1)

-2

2 .5 x1 0

2

4 .5 K
6K

1

5 .5 K
4 .8 K
5K

0-1

5 .2 K5 .4 K

1 .0-2

4 .5 K-2 0 -1 0

0

10

20

θ (d e g re e s)-2

2 .5 x1 0(c) 4 K

-2 0

8

7T 6T

-1 0

0

10

20

θ (d e g re e s)

(d)

4K
2T

6

4T
1 .5
3T

τ/μ0H x (N m T-1)

5T

2 .0

R (Ω)

perpendicular magnetic ﬁeld Hi,z = Hz − nMz . The demagnetization factor of the sample, n = 0.7, is obtained from theellipsoid approximation.18 Figure 2 shows the temperaturedependence of the slope of the τ /Hx curve as a function of
Hz at zero degrees under various ﬁelds, corresponding to
the diamagnetic susceptibility −dMz /dHz for Hz → 0. All
the curves have qualitatively similar temperature dependence.
At 3 T, for instance, −dMz /dHz shows a steep increaseat 11 K and tends to saturate below 9 K with decreasing
temperature. The steep increase will correspond to the rapid
growth of the phase coherence. We tentatively deﬁne Tc
as the starting point of the upward curvature (thick arrows
in Fig. 2). Different deﬁnitions of Tc will be acceptable,
but our conclusions will not be affected by them. As ﬁeld
increases, the −dMz /dHz curves shift to low temperatures:
Tc is reduced with increasing ﬁeld. At low temperatures,dMz /dHz tends to saturate, suggesting that the bulk phasecoherence is almost achieved. The susceptibility −dMz /dHz =1 corresponds to 100% diamagnetism (full Meissner effectalong the z direction). As shown in Fig. 2, only a few percent of
the Meissner volume fraction is obtained at low temperatures at
3 T. This small diamagnetism will be attributed to the fact thatthe perpendicular Hc1 is too small to detect the full Meissner
effect under large in-plane ﬁelds in the torque measurements.
The lower critical ﬁeld μ0 Hc1 in the perpendicular direction is
only ∼10 G at 7 K19 and it corresponds to 0.006 degrees forμ0 H = 10 T. This value is smaller than the resolution of therotation angle (∼0.02 degrees).
The phase diagram of κ-NCS under the in-plane ﬁeld isshown in Fig. 3, where Tc and Tc are the critical temperature
determined by the torque and resistance measurements, respectively. The Tc values are deﬁned as the temperatures where theresistances drop by 10%, which are in good agreement with

PHYSICAL REVIEW B 85, 220506(R) (2012)

4

6T

3T

7T

2

4T

0

5T

-2
-4

1 .0

2T
-6

-2 0 -1 0 0

10θ (d e g re e s)

20

-2 0

-1 0

0

10

θ (d e g re e s)

20

FIG. 4. (Color online) (a), (b): Angular dependence of the interlayer resistance and magnetic torque at 2 T for various temperaturesin a typical anisotropic superconductor NbSe2 . (c), (d): Angulardependence of the interlayer resistance and magnetic torque at 4 K
for various magnetic ﬁelds in NbSe2 . The wavy torque curves areprobably caused by unknown pinning effects of the vortices.

the previous reports.20 The Tc values are apparently higher
than Tc , showing that FSC appears in the wide temperatureand ﬁeld region.
Recently, heat capacity measurements have been done
under in-plane ﬁeld up to 23 T, whose Tc values are alsoplotted in Fig. 3 for comparison.21 We note that our Tc
values well agree with those determined by the heat capacity
measurements for μ0 H > 8 T. At zero ﬁeld, our Tc (about
10.8 K) is higher than the reported value Tc = 9.1 K. Thisdifference, however, will give no profound inﬂuence on ourconclusion. The saturation temperatures of dMz /dHz , Tcsat ,showing the bulk phase coherence, are also plotted. The
Tcsat values are in good agreement with Tc . This agreement
will provide further evidence showing that the bulk phasecoherence is achieved at Tc .
For comparison, we have performed the same experiments
for a typical anisotropic superconductor NbSe2 with Tc =7.2 K.22 Figures 4(a) and 4(b) show the angular dependenciesof the resistance and the torque, respectively, at various temperatures. We note that reductions of resistance and diamagnetic
signal due to superconductivity near zero degrees (in-planeﬁeld) disappear simultaneously above 5 K. As shown in
Figs. 4(c) and 4(d), both the resistance drop and diamagnetismat 4 K also disappear above 5 T. At Tc (4.9 K) for 2 T, for220506-3

RAPID COMMUNICATIONSSATOSHI TSUCHIYA et al.

PHYSICAL REVIEW B 85, 220506(R) (2012)

instance, we obtain −dMz /dHz (Hz → 0) ∼ 2 × 10−5 , whichis two orders of magnitude smaller than that for κ-NCS.
These results lead us to conclude that FSC is not observed
under the in-plane ﬁeld for NbSe2 . There will be two possible
reasons for the absence of the FSC: The electronic state is nothighly 2D and/or the electron correlation is not sufﬁciently
strong. To clarify this point, further investigation will benecessary.
In conventional BCS superconductors, the amplitude ﬂuctuation is considered to be dominant: Phase ﬂuctuation is
negligible. As discussed in the literature,23 there are two typesof phase ﬂuctuation, classical (thermal) and quantum ﬂuctuations. For the classical phase ﬂuctuation, “phase stiffness” ofthe order parameter is generally determined by the superﬂuid
density ns (0): The smaller the density, the more the phaseﬂuctuation. The density is given by ns (0) ∼ m /λ(0)2 , wherem and λ(0) are the effective mass and penetration depth,
respectively. Since λ(0) ∼ 8000 Å for κ-NCS and λ(0) ∼200 Å for NbSe2 ,24 ns (0) is about three orders of magnitude
smaller for κ-NCS. The quantum ﬂuctuation arises from thenumber-phase uncertainty relation, N φ > 1. For layered
structures, the charge ﬂuctuation between the neighboringlayers will be suppressed (because of the charge neutrality),
which will enhance the quantum phase ﬂuctuation. In this way,
the phase will be much more ﬂuctuated for κ-NCS than for
NbSe2 . Therefore, the large FSC for κ-NCS is likely dominatedby the phase (not by amplitude) ﬂuctuation.
Surprisingly the vortex-Nernst effect measurements of
κ-NCS show almost no FSC above Tc under perpendicularﬁelds.3 The fact suggests that the orbital effect of the in-plane
ﬁeld plays a crucial role in the emergence of FSC: The phaseﬂuctuation is enhanced by the in-plane ﬁeld. In Fig. 3, we
actually note that the FSC region seems wider at higher ﬁelds

although the measurements are limited in a relatively low ﬁeld
region at present.
Because of the layered structure, the interlayer transport isdescribed as a quantum tunneling for κ-NCS. The interlayer
tunneling conductance of layered structures under in-plane
ﬁeld has been studied theoretically25 and experimentally.26
Under in-plane ﬁeld (H  y), the interlayer tunneling, which
requires the momentum and energy conservation, is suppressedsince the ﬁeld (H  y) causes a momentum shift for thetunneling carriers, kx = eH d/ h, where d is the layer spacing.
Therefore, for layered superconductors such as κ-NCS, theinterlayer tunneling of the Cooper pairs is suppressed by
the in-plane ﬁeld: The Cooper pairs are conﬁned in eachsuperconducting layer. The conﬁnement will reduce the number uncertainty N, and consequently, enhance φ. It may
explain why the FSC is evident only under the in-plane ﬁeld.
In conclusion, we performed systematic measurement of
the angular dependence of the magnetoresistance and magnetic
torque for a highly correlated 2D organic superconductor κNCS. Our work provides clear evidence of the diamagnetism
due to the FSC in a wide temperature and ﬁeld range under thein-plane ﬁelds. Since the vortex-Nernst effect measurementsof κ-NCS show almost no FSC above Tc under perpendicularﬁelds, the orbital effect of the in-plane ﬁeld plays a crucial rolein the emergence of the FSC. Moreover, no appreciable FSC
in NbSe2 gives an important insight into the origin of the FSC;
strong electron correlation and/or high two dimensionality willbe crucial for the FSC.

*

14

TSUCHIYA.Satoshi@nims.go.jp
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We would like to thank H. Aoki for valuable discussions.
This work is partially supported by a Grant-in-Aid for
Scientiﬁc Research on Innovative Areas (No. 20110004) from
the Ministry of Education, Science, Sports, and Culture.

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