Table Of ContentConventional s-wave superconductivity in BiS -based NdO F BiS revealed by
2 0.71 0.29 2
thermal transport measurements
T. Yamashita1, Y. Tokiwa2, D. Terazawa1, M. Nagao3, S. Watauchi3, I. Tanaka3, T. Terashima2, and Y. Matsuda1
1Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
6 2Research Center for Low Temperature and Materials Science, Kyoto University, Kyoto 606-8501, Japan
1
3Center for Crystal Science and Technology, University of Yamanashi, Kofu 400-8511, Japan
0
(Dated: April11, 2016)
2
r To study the superconducting gap structure of BiS2-based layered compound NdO0.71F0.29BiS2
p (Tc = 5 K), we measured the thermal conductivity κ, which is a sensitive probe of low-energy
A quasiparticle spectrum. In theabsenceof a magnetic field, residual linear term in thethermal con-
ductivity κ0/T at T → 0 is vanishingly small, indicating that the residual normal fluid, which is
8
expected for nodal superconductors, is absent. Moreover, the applied magnetic field hardly affects
thermal conductivity in wide range of the vortex state, indicating the absence of Doppler shifted
]
n quasiparticles. These results provide evidence that NdO0.71F0.29BiS2 is a fully gapped supercon-
o ductor. Theobtainedgapstructure,alongwiththerobustnessofthesuperconductivityagainst the
c impurity,suggest a conventional s-wavesuperconductingstate in NdO0.71F0.29BiS2.
-
r
p
Recently a new family of layered superconductors gap), which is nearly five times larger than the BCS
u
s Bi4O4S3 andLnO1−xFxBiS2 (Lnisalanthanoid)1–6 has value14. Fully gapped superconductivity has been re-
. beenreported. Superconductivityemergesfromsemicon- portedby µSRmeasurementsofpolycrystallineBi O S
t 4 4 3
a ducting parent compound via electron doping by substi- andLaO F BiS 15. Tolook intothe superconducting
m 0.5 0.5 2
tuting O with F in the blocking layer. Up to now the state, the measurements on single crystals are more de-
- highest transition temperature T of 10.6 K is reported sirable. Ramanscattering experiments onsingle crystals
d c
n in LaO0.5F0.5BiS22. The crystal structure consists of al- ofNdO1−xFxBiS2 withx 0.5havesuggesteda possible
∼
o ternate stacking of BiS2 superconducting double layers phonon-mediated superconductivity16. Moreover, recent
c and LnO insulating blocking layers (inset of Fig.1(a)). measurementsofLondonpenetrationdepth λ(T)onsin-
[ Fermi surfaces consist of two-dimensional (2D) cylindri- glecrystalsforx=0.3and0.5havealsoreportedthefully
cal sheets. The band structure calculations suggest the gapped superconductivity17. However, the large Curie-
2
v presenceofstrongFermisurfacenestingatthewavevec- Weiss contribution at low temperature arising from lo-
2 tor (π,π)7–10. In particular, in the underdoped regime calized Nd3+ spins prevents the accurate determination
0 (x < 0.5), the Fermi surface consists of disconnected of superfluid density by the observed λ.
5 small electron pockets at the Brillouin Zone boundary
Here, to provide conclusive information on the super-
3
(inset of Fig.1(b)). Because of some common features
0 conductinggapstructureofBiS2-basedsuperconductors,
with Fe-based high temperature superconductors, BiS -
. 2 we performed thermal conductivity measurements on a
1 based superconductors have aroused great interest. On
high quality single crystal of NdO F BiS down to
0 0.71 0.29 2
the other hand, the conduction band in the 2D layer of
6 100mK.Itiswellestablishedthatlow-temperaturether-
BiS -based compounds is mainly of 6p and 6p orbits
1 2 x y malconductivityisapowerfulprobeforsuperconducting
of Bi7. The electron correlation effects, which play an
: gap structure, detecting low-energy quasiparticle excita-
v essential role for the superconductivity in Fe-based su-
tions sensitively18. Advantage of thermal conductivity
i
X perconductors, appear not to be important due to the is that it is insensitive to Nd magnetic moments. By
widely spread 6p orbitals. Thus a major outstanding
r thermalconductivitymeasurements,weprovideevidence
a question is whether the Cooper pairing is mediated by
thatNdO F BiS is a fully gappedsuperconductor.
0.71 0.29 2
unconventional (non-phononic) interactions, such as an-
Basedontheseresults,togetherwiththeimpurityeffect,
tiferromagnetic fluctuations. To elucidate this issue, the
we discuss the mechanism of superconductivity.
identification of superconducting gap structure is of pri-
mary importance, because it is intimately related to the NdO0.71F0.29BiS2 single crystals were grown by the
pairing interaction. high-temperaturefluxmethodwithCsCl/KClasaflux19.
The onsetofsuperconductivityisT onset 5.2K,which
c
Severalsuperconductinggapstructures,includingcon- is in agreement with the previous report1∼9. The super-
ventionals-,signreversings-,spintripletp-,andd-wave conducting volume fraction determined by the magnetic
symmetries have been proposed for BiS -based super- susceptibility measurements is close to 100 %. The X-
2
conductors theoretically7–13. A possible unconventional ray diffraction shows no impurity phase. Thermal con-
superconductivity has been reported by an extremely ductivity κ was measured along the tetragonal a axis
large ratio of 2∆/k T 17 (∆ is the superconducting (heatcurrentq a)onasamplewitharectangularshape
B c
∼ k
2
(a)
25
500
S Bi H = 0 0 T H
0.05 T
400 Nd 20 0.1 T
)
m O 0.2 T
cΩ 300 ) 0.6 T
(ρ µ 200 2mK 15 25 TT
c W/
100 b m
a T ( 10
0 /κ 15
0 10 20 30 40 50
T (K) 10
5
(b) 5 0 T
H = 0 0
0.06 0 0.04 0.08 0.12
0
0 0.04 0.08 0.12
)
m
2 T 1.3 (K1.3)
K 0.04 π
/
W
T
( c FIG.2: (Coloronline)Thermalconductivitydividedbytem-
T/ κ 0.02 ky peratureκ/T ofNdO0.71F0.29BiS2plottedagainstT1.3insev-
eral magnetic fieldsapplied parallel tothec-axis. Inset: κ/T
−π vsT1.3inzerofield. Solidlinerepresentslinearfittothedata
−π kx π below 0.3K.
0
0 1 2 3 4 5 6
T (K) scattering regime at low temperature is expressed as
1
FIG. 1: (Color online) Temperature dependence of (a) elec- κ = β v ℓ T3, (1)
ph s ph
trical resistivity ρ and (b) thermal conductivity divided by 3 h i
temperature κ/T of NdO0.71F0.29BiS2 at zero field. Dashed
whereβ isthephononspecificheatcoefficient, v isthe
line indicates the electronic contribution estimated from the s
h i
Wiedemann-Franzlaw. Insetof(a)displaysthecrystalstruc- mean acoustic phonon velocity, and ℓph is the phonon
ture of NdO1−xFxBiS2. Inset of (b) shows Fermi surface of mean free path. For diffuse scattering limit, ℓph be-
NdO1−xFxBiS2 for x∼0.37,8. comes T-independent, resulting in κph T3. On the
∝
other hand, in case of specular reflection, ℓ follows
ph
T−1-dependence, leading to κ T2. In real systems,
ph
( 2.6 1.16 0.015 mm3) by the standard steady state κph Tα with α of intermediat∝e value between 2 and
∝
m∼etho×d in a×3He-4He dilution refrigerator. 3. In fact, α =2.74, 2.4 and 2.77 has been reported in
V Si20, YBa Cu O 20 and Al O 21, respectively.
Figure 1(a) shows the temperature dependence of the 3We found2that3 κ6(.T99) is well fi2tte3d as κ T2.2−2.5 in
in-plane electrical resistivity ρ(T) of NdO0.71F0.29BiS2. the widest temperature range of T < 300m∝K. In the in-
Below50K,ρ(T)exhibitsFermiliquidbehaviorwithT2-
set of Fig.2, κ/T in zero field is plotted as a function of
dependence downto T . Figure 1(b) showsthe T depen-
c T1.3. As shown with the red line, κ/T is extrapolated
dence of κ/T in zero field. At T , κ/T shows no dis-
c to zero at T 0, i.e. the absence of a residual term.
cernible anomaly. The electronic contribution estimated →
The vanishingly small residual term is obtained in the
by assuming the Wiedemann-Franz law, κ/T = L /ρ,
0 range of α between 2.2 and 2.5. We note that for α=3,
where L0 = π32 (cid:0)keB(cid:1)2 is the Lorenz number, is about 11 thereisafiniteresidualtermbutwellfittedrangeislim-
% of the total thermal conductivity at Tc. In the super- ited to T < 150mK and for α = 2, the residual term
conducting state, κ/T decreases with decreasing T after becomes negative. It is well known that finite residual
showing a broadmaximum at around1.5K. We will dis- termindicatesexistenceofaresidualnormalfluid,which
cuss this behavior later. is expected for an unconventional superconductor with
We first discuss the low temperature behavior of κ/T line nodes in the energy gap. This residual normal fluid
in zero field. Thermal conductivity can be written as a isaconsequenceofimpurityscattering,evenforlowcon-
sum of the quasiparticle and phonon contributions, κ = centrationsofnonmagneticimpurities. Thereforetheab-
κ +κ . Thephononconductivityinboundary-limited senceofresidualtermsuggeststhatthereisnolinenodes
qp ph
3
in the field dependence of the thermal conductivity be-
tween fully gapped and nodal superconductors18. In the
former, all the quasiparticles states are bound to vortex
cores and, therefore, the applied magnetic field hardly
5 18 affects the thermal conduction except for the vicinity of
m) 6 upper critical field. By contrast, in the latter, the heat
2K transport is dominated by delocalized quasiparticles. In
4 / 17
W 4 the presence of a supercurrentwith a velocity v around
) m Hc s
2mmW/K 3 T (/κ0200 c12 2 3 16κWm( /T ttphhaeertsviucolpreteiwrcceiotsnhidnmudcuotmcienedgnbtcuoymnmdepangisnsaetDteiocbpfiypeElledr(,pse)hni→efrtgeEdy(orpef)laa−tqivvusea·stpio-.
T/ (κ02 µ0H (TH) * 15)mK/2 Tofofhrκep(HoDion)p/tTpnloe∝rde√ssh.Hiftfgoirvleisnerinseodteosaanndinκit(iHal)s/tTee∝p iHnclroegaHse
H
1 14 Since H∗ is much larger than the lower critical
∗
field, H H , which is estimated to be µ H =
c1 0 c1
≫
0 13 4πλΦ(00)2 ln(λξ(a0b)) ≈ 3mT, the field-independent κ0/T is
notduetotheabsenceoffluxpenetration. Here,Φ isthe
0 0.05 0.10 0.15 0.20 0.25 0
flux quantum, λ(0) 447nm is the zerotemperature in-
µ H (T) ≈
0 planepenetrationlength17 andξab =pΦ0/(2πµ0Hcc2)=
18nmisthein-planecoherencelength. Thereforetheob-
FIG.3: (Coloronline)Fielddependenceoftheresiduallinear
served field-insensitive thermal conductivity at low field
cteirrcmlesκ)0f/oTr H(rekdc.diTamheonredssi)duaanldteκr/mTκa0t(HT)/=T1i7s0demteKrm(ibnleude icnitdeidcabtyesmthagantetthicefideelldocaatlilzeeadstquupestiopaHrticleHs∗are 0n.o2tHecx-.
by fitting κ(T)/T data at different fields below 0.3K with ≈ ≈ c2
κ0/T+aT1.3,whereκ0/T andaarefittingparameters. Both These results lead us to conclude the absence of any
κ0/T and κ/T at T = 170 mK are independent of magnetic kind of nodes in the gap function of NdO0.71F0.29BiS2.
field up to H∗. Inset shows κ0/T in an extended field range. In typical s-wave superconductors, such as Nb, κ(H)/T
c
Hc2 is thesuperconducting uppercritical field along c-axis. increases steeply only in the vicinity of upper critical
field22. Therefore the increase of κ (H)/T above H∗
0
well below H suggests large modulation of the super-
c2
in NdO F BiS . Since the presence of point node is conducting gap along the 2D Fermi surface.
0.71 0.29 2
unlikely in the 2D Fermi surface, the zero field thermal Finally we discuss the mechanism of the superconduc-
conductivity suggest a fully gapped superconductivity. tivityinNdO F BiS . AsshowninFig.1(b),nodis-
0.71 0.29 2
This conclusion is strongly supported by thermal con- cernible anomaly is observedin κ/T at T . In the super-
c
ductivity in magnetic field applied perpendicular to the conductorswithstrongelectroncorrelationeffect,includ-
2D plane (H c). Figure3 shows the H-dependence ingcuprates23,iron-pnictides24 andheavyfermions25–27,
k
of κ (H)/T, which is obtained by the extrapolation to the striking enhancement of the thermal conductivity
0
T 0 at each field value shown in Fig.2. We fitted the just below T is often observed. This enhancement is
c
→
datainfinitemagneticfieldsbyusingα=2.3inthesame caused by the strong suppression of the quasiparticle in-
temperature range as H =0 (T <300mK). As shown in elastic scattering rate due to the formation of supercon-
Fig.3, κ (H)/T is field independent at low field up to ducting gap,which overcomesreduction of the quasipar-
0
∗
µ H 0.12T. In Fig.3, κ(H)/T at T = 170mK is also ticle density of states. Therefore the electroncorrelation
0
≈
shown. We stress that since κ(H)/T at T = 170 mK effect in the present compound is not strong. Moreover,
∗
is also field independent up to H , the field indepen- when electron-phonon coupling is strong, the enhance-
∼
dence of κ (H)/T at low-H is not caused by the choice ment of the thermal conductivity below T is also often
0 c
∗
of α. Above H , κ (H)/T increases and becomes field observed by the enhancement of the phonon mean free
0
independentinthenormalstateaboveµ Hc 0.8T.In path due to the gap formation. Thus electron-phonon
thenormalstate,κ (H)/T is0.0055W/K02mc2,≈whichisin coupling is also not strong.
0
agreementwiththevalueexpectedfromtheWiedemann- Until now, severalsuperconducting gap structures,in-
Franzlaw. Here wecommentonthe influence ofNdions cluding conventional s-, sign-reversings-, spin triplet p-,
onthethermalconduction. SinceNdionsareinthepara- andd-wavesymmetrieshavebeenproposedtheoretically
magnetic state in the present temperature range, mag- for the BiS -based superconductors 7–12. Since there is
2
neticexcitationsdonotcarrytheheat. Moreoverthefact noholepocketaroundtheΓ-pointasshownintheinsetof
thatκ/T isindependentofmagneticfieldinthelow-field Fig.1(b),wedonotdiscusssign-reversings-wavesymme-
regime of the superconducting state and in the normal try. Among d-wave symmetries, we can rule out d-wave
state above Hc2 indicate that the heat conduction is not with accidental nodes proposed in Ref.[7] and dxy sym-
influenced by magnetic excitations. metry. The remaining possibilities ofthe unconventional
Itiswellestablishedthatthereisanessentialdifference symmetries are p and dx2−y2, which has no node in the
4
presentFermisurface. However,theseunconventionalsu- rities, is absent. The magnetic field hardly affects the
perconductivity is unlikely because of the following rea- thermal conductivity up to 0.2Hc , indicating the ab-
∼ c2
son. The in-plane mean free path ℓ is comparable to the sence of Doppler shifted quasiparticles. These results
in-plane coherence length ξab = pΦ0/(2πHcc2) = 18nm. provideevidencethatNdO0.71F0.29BiS2 isafullygapped
In fact, ℓ is estimated to be 30 50nm by using the superconductor. Notably, the estimated mean free path
relation ℓ = (µ λ(0)2v )/ρ ,∼where−Fermi velocity v is is comparable to the superconducting coherence length,
0 F 0 F
reported to be v = 0.95 106m/s by angle resolved indicating that the superconductivity is robust against
F
photoemissionspectroscopy×28 andρ =500 800µΩcmof impurity. Based on these results, we conclude a conven-
0
∼
this study and the previous reports14,19. This robust- tionals-wavesuperconductingstateinNdO F BiS .
0.71 0.29 2
ness of the superconductivity against the impurity ap- This puts a strong constraint on the theory of the su-
pearstobeatoddswiththeunconventionalpairingsym- perconductivity of BiS -based layered compound, whose
2
metries. These considerations lead us to conclude that electronic and crystal structures bear some resemblance
NdO F BiS is likely to be a conventional s-wave to Fe-based superconductors.
0.71 0.29 2
superconductor. We thank S. Kasahara, Y. Kasahara, Y. Mizuguchi,
In summary, to clarify the superconducting gap struc- Y. Ota, T. Shibauchi and S. Shin for useful discussions.
tureofNdO F BiS ,weperformedthermalconduc- This work was supported by Grants-in-Aid for Scientific
0.71 0.29 2
tivity measurements down to 100mK. Thermal conduc- Research (KAKENHI) from Japan Society for the Pro-
tivityshowsnodiscernibleanomalyatT ,suggestingthat motionofScience(JSPS),andbythe‘TopologicalQuan-
c
bothoftheelectroncorrelationandelectron-phononcou- tum Phenomena’ (No. 25103713) Grant-in-Aid for Sci-
plingeffectsarenotstrong. Theabsenceofresidualther- entific Research on Innovative Areas from the Ministry
mal conductivity indicates that a residual normal fluid, of Education, Culture, Sports, Science and Technology
which is expected for nodal superconductors with impu- (MEXT) of Japan.
1 Y. Mizuguchi, H. Fujihisa, Y. Gotoh, K. Suzuki, H. Usui, 17 L. Jiao, Z. Weng, J. Liu, J. Zhang, G. Pang, C. Guo, F.
K.Kuroki,S.Demura,Y.Takano,H.IzawaandO.Miura, Gao, X.Zhu,H.-H.WenandH.Q.Yuan,J.Phys.: Cond.
Phys. Rev.B 86, 220510 (2012). Mat. 27, 225701 (2015).
2 Y.Mizuguchi,S.Demura,K.Deguchi,Y.Takano,H.Fuji- 18 Y. Matsuda, K. Izawa and I. Vekhter, J. Phys.: Cond.
hisa,Y.Gotoh,H.IzawaandO.Miura,J.Phys.Soc.Jpn. Matt. 18, R705 (2006).
81, 114725 (2012). 19 M.Nagao,S.Demura,K.Deguchi,A.Miura,S.Watauchi,
3 J. Xing, S. Li, X. Ding, H. Yang, and H.-H. Wen, Phys. T. Takei, Y. Takano, N. Kumada and I. Tanaka, J. Phys.
Rev.B 86, 214518 (2012). Soc. Jpn. 82, 113701 (2013).
4 D. Yazici, K. Huang, B. D. White, A. H. Chang, A. J. 20 M.Sutherland,D.G.Hawthorn,R.W.Hill,F.Ronning,S.
Friedman, and M. B. Maple, Philos. Mag. 93, 673 (2013). Wakimoto,H.Zhang,C.Proust,E.Boaknin,C.Lupien,L.
5 S. Demura, Y. Mizuguchi, K. Deguchi, H. Okazaki, H. Taillefer, R.Liang,D.A.Bonn,W.N.Hardy,R.Gagnon,
Hara,T.Watanabe,S.J.Denholme,M.Fujioka,T.Ozaki, N.E.Hussey,T.Kimura,M.NoharaandH.Takagi,Phys.
H. Fujihisa, et al., J. Phys.Soc. Jpn. 82, 033708 (2013). Rev.B 67, 174520 (2003).
6 R. Jha, A. Kumar, S. Kumar Singh, and V. P. S. Awana, 21 R.O.PohlandB.Stritzker,Phys.Rev.B25,3608(1982).
J. Supercond.Nov.Magn. 26, 499 (2013). 22 J.LowellandJ.B.Sousa,J.LowTemp.Phys.3,65(1970).
7 H.Usui,K.SuzukiandK.Kuroki,Phys.Rev.B86,220501 23 R. C. Yu,M. B. Salamon, J. P. Lu, and W. C. Lee, Phys.
(2012). Rev.Lett. 69, 1431 (1992).
8 T. AgatsumaandT.Hotta,J. Magn.Magn. Matter.400, 24 S. Kasahara, T. Watashige, T. Hanaguri, Y. Kohsaka, T.
73 (2016). Yamashita, Y. Shimoyama, Y. Mizukami, R. Endo, H.
9 X.Wan,H.-C.Ding,S.Y.SavrasovandC.-G.Duan,Phys. Ikeda, K. Aoyama, T. Terashima, S. Uji, T. Wolf, H. v.
Rev.B 87, 115124 (2013). Loehneysen, T. Shibauchi, and Y. Matsuda, Proc. Natl.
10 T. Yildirim, Phys. Rev.B 87, 020506 (2013). Acad. Sci. USA111, 16309-16313 (2014).
11 Y. Liang, X. Wu, W.-F. Tsai and J. Hu, Front. Phys. 9, 25 K.Izawa,H.Yamaguchi,Y.Matsuda,H.Shishido,R.Set-
194 (2014). tai and Y.Onuki,Phys.Rev.Lett. 87, 057002 (2001).
12 Y. Yang, W.-S. Wang, Y.-Y. Xiang, Z.-Z. Li and Q.-H. 26 R. Movshovich, M. Jaime, J. D. Thompson, C. Petrovic,
Wang, Phys. Rev.B 88, 094519 (2013). Z. Fisk, P. G. Pagliuso and J. L. Sarrao, Phys. Rev. Lett.
13 G. B. Martins, A. Moreo, and E. Dagotto, Phys. Rev. B 86, 5152 (2001).
87, 081102(R) (2013). 27 M.A.Tanatar,J.Paglione,S.Nakatsuji,D.G.Hawthorn,
14 J.Liu,D.Fang,Z.Wang,J.Xing,Z.Du,S.Li,X.Zhu,H. E. Boaknin, R. W. Hill, F. Ronning, M. Sutherland, L.
Yangand H.-H.Wen,Europhys.Lett. 106, 67002 (2014). Taillefer, C. Petrovic, et al., Phys. Rev. Lett. 95, 067002
15 G.Lamura,T.Shiroka,P.Bonf`a,S.Sanna,R.DeRenzi,C. (2005).
Baines, H.Luetkens,J.Kajitani, Y.Mizuguchi,O.Miura, 28 Z. R. Ye, H. F. Yang, D. W. Shen, J. Jiang, X. H. Niu,
et al., Phys.Rev. B 88, 180509 (2013). D. L. Feng, Y. P. Du, X. G. Wan, J. Z. Liu, X. Y. Zhu,
16 S. F. Wu, P. Richard, X. B. Wang, C. S. Lian, S. M. Nie, et al., Phys.Rev.B 90, 045116 (2014).
J. T. Wang, N. L. Wang, and H. Ding, Phys. Rev. B 90,
054519 (2014).
