Table Of ContentCharge fluctuations and superconductivity in organic conductors: the case of
β(cid:48)(cid:48)-(BEDT-TTF) SF CH CF SO
2 5 2 2 3
G. Koutroulakis,1 H. Ku¨hne,2 H.-H. Wang,3 J. A. Schlueter,4,5 J. Wosnitza,2,6 and S. E. Brown1
1Department of Physics & Astronomy, UCLA, Los Angeles, CA 90095, USA
2Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany
3Department of Materials Science and Engineering, UCLA, Los Angeles, CA 90095, USA
4Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
5Division of Materials Research, National Science Foundation, Arlington, VA 22230 USA
6Institut fu¨r Festko¨rperphysik, TU Dresden, D-01069 Dresden, Germany
6 A13CNMRstudyofthenormalandsuperconductingstatesoftheall-organiccharge-transfersalt
1 β(cid:48)(cid:48)-(BEDT-TTF)2SF5CH2CF2SO3 is presented. We find that the normal state is a charge-ordered
0 metal configured as vertical stripes, produced by a combination of 1/4-filling, correlations, and
2 a polar counterion sublattice. The NMR properties associated with the superconducting state are
consistentwithgapnodesandsingletpairing,andthereforesimilartootherorganicsuperconductors.
n
Quitedistinct,however,istheabsenceofevidenceforlow-energyantiferromagneticspinfluctuations
a
J forT >Tc =4.5K.Bothaspectsarediscussedinthecontextofaproposalthatthepairinginthis
compound is driven by charge fluctuations.
2
2
PACSnumbers: 74.70.Kn,74.25.nj,74.20.Rp,74.25.Dw
]
l
e
There are currently more than 50 known dis- bardmodelwhichincludesnearest-neighborrepulsivein-
-
r tinct superconducting charge transfer salts based on teractions V as well as on-site U and hopping parameter
t
s the bisethylenedithio-tetrathiafulvalene (BEDT-TTF, or t.
.
t ET) donor [1, 2]. In all of them, the ET molecules as-
a A natural question to ask is, does a superconduct-
sembleinsheetsseparatedbylayersofnegatively-charged
m ing state (SC) emerge from the collapsed CO insulat-
counterions, most commonly in the ratio of 2:1, so that
- ing state, and to what extent are charge fluctuations
d singly-charged counterions leave behind 1/2 delocalized (CF) relevant to pairing in that case? A variant of
n holeperdonor. Thecombinationofrelativelylowcharge-
this question has been raised recently in the context of
o carrier density and quasi-two dimensional (q2D) elec-
underdoped cuprates, where incommensurate CO leads
c
tronic structures enhance the influence of correlations.
[ to Fermi-surface reconstruction [13]. In relation to the
Thus, the superconductors are located proximate to cor-
1/4-filled molecular superconductors, calculations pro-
1 related insulating states, where tuning between insulat-
ducing superconductivity out of the collapsed CO state
v
ing and superconducting states is typically controlled by
7 are mostly limited to mean-field theory. For example, in
changing the lattice constants. Among the most familiar
0 Ref. [14], fluctuations remanent of the checkerboard CO
1 examplesaretheclosely-relatedq1D(TMTSF)2X (Bech- phaseareshown,inaslave-bosonapproach,tostabilizea
6 gaard) salts, and the q2D κ-(ET) X compounds [3, 4],
2 d superconductingstateonthesquarelattice. Though
0 where the insulators are also antiferromagnetic (AF) or xy
limitedinthatcasetoU/t→∞,d SCisalsoproduced
. xy
1 spinliquid[5]. Abroaderinterestinthesecompoundsde-
intherandomphaseapproximation(RPA)forfiniteU/t
0 rives from the proposition, as first articulated by Emery
proximate to both spin and charge density wave (SDW
6
[6]andmotivatedinpartbytheproximitytoAFground
1 and CDW) instabilities, also on the square lattice [15],
states,thatthesuperconductivityappearingonthehigh-
: which are stabilized in the large V and U limits, respec-
v pressure side of the metal-insulator transition involves
tively. Althoughapplicabilitytotherealmaterialsisun-
i
X magnetically mediated pairing. Taking the issue further clear, the RPA results indicate that to consider pairing
is the question of whether the magnetic mechanism not
r by pure CF is probably an oversimplification.
a onlyapplies, butisubiquitousamongstmolecularsuper-
The so-called θ as well as the β(cid:48)(cid:48) [16] compounds are
conductors.
cited in Ref. [14] as good candidates for testing the idea
ThepredominanceoftheMottstateintheκmaterials of CF-mediated superconductivity. In both cases, the
follows from the dimerized intralayer arrangement of the molecular layers are comprised of side-by-side stacks of
ET molecules [7], such that the system is effectively 1/2- ET molecules (see Fig. 1). The unit cell of β(cid:48)(cid:48) is com-
filled[8]. Whereas,inpracticeifnotpreciselybysymme- prisedof4ET’sdonatingtwoelectronstothecounterion
try,theθ andβ(cid:48)(cid:48) configurationsareconsidered1/4-filled. sublattice. However, with near-neighbor repulsive inter-
Nevertheless,astrongtendencyforchargeordering(CO) actions intrastack and interstack, the systems are pre-
[9, 10] produces insulating ground states far more com- sumed unstable to insulating CO states. (This is the
monly than superconducting ground states [11, 12], in case for most of the θ compounds as well, for exam-
accordance with the applicability of an extended Hub- ple θ-(ET) X, X =RbZn(SCN) , CsZn(SCN) , though
2 4 4
2
θ β ’’ for spin-fluctuation-mediated organic superconductivity,
(TMTSF) X [21], the κ-phase ET superconductors [22]
2
(which exhibit the highest T ’s amongst ET supercon-
c
ductors), or other correlated superconductors such as
cuprate [23], heavy-fermion [24], or iron-based supercon-
ductors [25]. The expected absence of normal state SF
was proposed as a test for CF-mediated superconductiv-
ity [14].
FIG. 1. Representation of the planar molecular donor ar-
rangements of the θ and β(cid:48)(cid:48) salts. The long axis of the ET
molecules are into the page. b
inner
a
X=I is superconducting [11, 17].) For the β(cid:48)(cid:48) com-
3
O
poundconsideredhere,differentgroundstatesresultwith c
small changes to the counterion which we abbreviate as
X=SF RSO [16, 18]. For example, R=CHFCF un-
5 3 2
dergoes a metal-insulator transition (presumed at about
0.8 B=8.453T , T=78K
170 K, and R=CHF is an insulator already at ambient
s)
temperature. To make more concrete the idea that the nit
u0.6
collapse of charge order leads to fluctuations and super- b.
conductivity,ageneralphasediagramhasbeenproposed, ar
whereby the insulators could be tuned with application sity (0.4
of pressure so as to produce superconductivity [16]. The n
superconducting R=CH2CF2 salt is placed adjacent to Inte0.2
theCOphaseboundarybecause,forexample,astrongly a b c d a b c d
0.0
temperature-dependent oscillator strength in the mid-
90.500 90.505 90.510 90.515 90.520 90.525
infraredconductivity[19]wasinterpretedasevidencefor
frequency (MHz)
CF.
Here, we describe 13C NMR spectroscopy and relax- FIG.2. Top: Crystalstructureofβ(cid:48)(cid:48)-(ET)2SF5CH2CF2SO3,
ation of the β(cid:48)(cid:48) superconductor (R=CH CF ), and com- viewed along the stack direction a (left), and along the b-
2 2 axis (right). The ET molecules are spin-labelled with 13C
pare those results to expectations for pairing mediated
on the bridging sites for the NMR measurements; these are
by CF associated with the “nearby” insulating phase of
distinguished here by the red and orange colors, which also
R=CHFCF . The results reveal two independent and
2 highlightsthecrystallographicinequivalenceofthetwostacks.
inequivalentmoleculesovertheentiretemperaturerange Withineachmoleculeareinequivalentsites“inner”(sitesa,b)
of the measurements, 1.5−300 K. We associate the two and “outer” (c,d). From the spin-lattice relaxation (below),
species to the ET molecules in the two structurally in- we estimate the charge-carrier imbalance between the two
dependent stacks [18, 20]. Specifically, our sensitivity stacks is ρred/ρorange ∼1.9 at T =78 K. Bottom: 13C spec-
trum, which resolves the contributions from red (4 highest-
derives fromthe hole-density imbalance betweenthe two
frequency peaks) and orange sites (see text). Dashed lines
stacks, which is reminiscent of a vertical-stripe CO con-
aresimulatedpeaksperEq. 1,appropriatelybroadened,and
figuration [9] though the symmetry between stacks is al-
black solid line is the sum.
ready broken in the crystal (Fig. 2). The increase of
the relative difference of the paramagnetic shifts and re- The crystals were grown by the standard electrolysis
laxation of the two species upon cooling is evidence that method using ET molecules with 13C spin-labelled on
the disproportionation is not trivially determined by the thecentralcarbons. X-raydiffractionmeasurementscon-
polarity of the counterion sublattice, and for that reason firmed the known unit-cell parameters of the β(cid:48)(cid:48) phase.
we interpret it as a charge-ordered metallic state. The Superconductivity was observed at temperatures below
superconductivity emerging from the CO metal is a spin T = 4.5 K by dc-susceptibility methods (zero-field
c
singlet, since it exhibits a diminishing Knight shift for cooled) as well as by NMR spin-lattice relaxation and
T < T . This is accompanied by a sharp decrease in tank-circuit impedance measurements. For the NMR
c
therelaxationratewhichcloselyfollowstheoft-observed measurements, the strongly anisotropic superconducting
T−1∼T3,andwithoutanydiscernibleHebel-Slichteren- properties allowed for orientation in the ab plane [20] to
1
hancement below T , even for applied fields B <1 T. within±0.1◦ bymeansofapiezoelectricrotator, andor-
c
Most notable, however, is the absence of evidence for thogonal to the most highly conducting b-axis to within
antiferromagnetic spin fluctuations (SF) in the normal ∼ 5◦. The sample mass was 0.9 mg, with dimensions
state, especially when compared to the standard-bearer 0.8mm×4.3mm×0.1mm. Asecondcrystalgavesimilar
3
results. to the average of all sites. [T T]−1, which is expected
1
In recounting the NMR measurements, we begin at T-independent for a Fermi liquid, is plotted in the inset.
the intermediate temperatures. The spectrum at T =78 Both shifts and [T T]−1 increase with higher tempera-
1
K is shown in the lower panel of Fig. 2. Eight peaks tures. The shifts are anomalous, in the sense that the
are visible, originating from four inequivalent shifts, and temperaturedependenceofthesusceptibilityistooweak
the splitting of each associated with the 13C-13C dipo- to account for the variation and therefore the hyperfine
lar coupling of the spin-labelled ET bridging sites. The coupling appears temperature dependent [29].
spectrum resolves easily the contributions from the two
molecules: at the high-frequency end is the 4-peak con- 300
B=6.87T
tribution from one of the inequivalent molecules, and at 500
250
low frequency is the other. Within a molecule, the fre-
quency shift of the four contributions (a−d) are given m) 400 200)m
by pp pp
K ( 300 150K(
δ
ωa−d =ω¯ ±(cid:2)δω2+d2(cid:3)1/2±d+ωorb, (1) 200 100
with ω¯ ≡(1/2)(ω +ω ), δω ≡(ω −ω ), d the in- 100 50
out in out in
ternuclear dipolar coupling, and ωorb the orbital (chemi- 0 50 100 150 200 250 300
cal) part of the frequency shift. Then the two hyperfine T (K)
parts of the shift are K =(ω¯)/ω ±(1/2)δω/ω . In
out,in 0 0 0.1 )K
contrasting the shifts from the two molecules, we assign c
e
the greater to the “red”, since adjacent to it are the SO3 s/1
ligandsofthecounterions,wherethenegativechargepre- 0.01T(
T1
dominantly resides. Note that details of charge dispro- /1
portionationinotherorganicsystemsareofteninfluenced 1 10 100
by coupling to the counterion sublattice [26–28]. How- ec)
s
etovepr,rondeuarc-enaeigChOboervreenpuinlsitvheeinctaesreaoctfioanhsi(gVhe)rw-soyumldmteetnrdy T (1/1 0.1 ~T
counterion. In the ET compounds, the exhibited CO 1/ ~T 3 B=6.87T
orange mol.
patterns are stripes; the direction along which they are 0.01 red mol.
aligned should depend on parameter details: overlap in- Whole line
tegrals within and between stacks and strength of the 2 3 4 567 2 3 4 567 2 3
1 10 100
corresponding intrastack (vertical in Fig. 1) and inter- T (K)
stack repulsive interactions, as well as coupling to the
lattice. The disproportionation seen in the ET salts is FIG. 3. Top: Normal-state shifts vs. temperature, av-
commonly associated with a broken symmetry and an eraged for each of the two molecules (left), and difference
δK ≡ K −K vs. temperature (right). The color desig-
insulating state. Here, there is no symmetry breaking out in
nation applies to the “red” and “orange” molecules defined
and the system is metallic throughout, and both near-
in Fig. 2. K is the shift for the 13C site centered closest to
in
neighborrepulsionandcounterioninteractionareimpor-
midwaybetweenthecounterionlayers(alsoFig. 2). Bottom:
tant. Note also that in 2D, there are generally at least InthemainpanelisT−1vs. T,with[T T]−1vs. T appearing
1 1
two critical V in the extended Hubbard model, with the in the inset.
CO onset occurring at a smaller value for V than the
metal-insulator transition. [9]. Since the hole densities are proportional to the hyper-
Thetemperaturedependenceofthenormal-stateshifts fine fields on the two molecules, the disproportionation
andrelaxationratesforthedifferentsitesappearsinFig. can be extracted from the ratio of averaged relaxation
3, where the external field is oriented in the conducting rates on the red and orange sites [30, 31],
plane and orthogonal to the high-conducting b direction. Torange (cid:20) ρred (cid:21)2
The data points originating with the two molecules are 1 = , (2)
Tred ρorange
denoted by the same color scheme as above, red and or- 1
ange. InthetoppanelisplottedtheaveragetotalshiftK where the average hole density is < ρ >= (1/2)(ρ +
red
(left) and difference δK (right) for each molecule. Note ρ ). The result is shown in Fig. 4, which shows
orange
that the chemical part has not been subtracted out from a considerable monotonic increase of the disproportiona-
thetotal,whichistypicallyoforderK ∼100-150ppmfor tion upon cooling, from ∼1.4 at 300 K to ∼ 2.0 at 5 K.
c
ET salts. In the bottom panel appears the spin-lattice The strong and non-trivial T dependence suggests the
relaxation rate T−1; the colors refer to the average for disproportionation does not result simply from the po-
1
the two sites on each molecule, and the blue points refer lar counterions, but rather should be interpreted as a
4
vertical-striped metallic CO state, associated also with
intralayer correlations. B=6.87T
400
)
m T
p c
2.2 )ces8 K (p 300
T( 14
1/2 2.0
redT)11.8 0 200
orangeT / 111..64 0 1 2 T3 (K) 4 5 6
(
1.2 FIG. 5. K vs. T for 13C in β(cid:48)(cid:48)-(ET) SF CH CF SO , mea-
2 5 2 2 3
0 50 100 150 200 250 300
sured at low temperature and entering the superconducting
T (K)
state. The average shift for each of the two inequivalent
molecules is indicated by the colors, as before.
FIG. 4. Overlaid onto the spectrum in the inset are data
(black squares) representing the relaxation time for each of
the components. The measurement conditions were B=6.87
T, T=30 K. The red diamond is the average for the entire Inthatcontext,severalquestionsregardingthepairing
spectrum. In the main panel is the temperature variation of in β(cid:48)(cid:48) remain open. To summarize the observations, we
[Torange/Tred]1/2, which we take to be proportional to the haveanexampleofacorrelated,metallicCOstatewhich
1 1
ratio of hole density between red and orange molecules. then gives way to superconductivity at low temperature.
TheSC,atleastfromtheperspectiveoftheNMRresults,
Theveryweaktemperaturedependenceof[T T]−1 be- is consistent with a spin-singlet ground state with nodes
1
low 100 K persists down to T =4.5 K. Below that, the on the Fermi surface, but stabilized without evidence for
c
relaxation rate drops abruptly and without exhibiting low-energy SF. Prior to this work, there were sugges-
a Hebel-Slichter peak. The results are compared to a tions that the β(cid:48)(cid:48) materials are an example of SC pair-
T3 variation in Fig. 3, which is commonly observed in ing mediated by CF, first from mean-field calculations
correlated superconductors such as the κ-phase organic on the square lattice and recently as an interpretation of
superconductors [22, 32], (TMTSF) X [33], as well as results of IR-conductivity experiments [14, 16, 19], and
2
cuprate[34]andheavy-fermionsuperconductors[24,35]. further that a test for the hypothesis would be [T1T]−1
Usually, this is taken as a signature of line nodes and unenhancedbySF.TheproximitytoanearbyCOphase
changeinsignoforderparameterovertheFermisurface, was inferred, in part, from a diversity of ground states
even though there is no specific reason within mean-field observed in other β(cid:48)(cid:48) salts with related counterions. A
theory to find the T3 variation in nodal superconductors pertinent example is the salt with counterion SF5RSO3
except when T (cid:28) Tc [36]. What is also unlike these (R=CHFCF2), which undergoes a metal-insulator tran-
other superconductors is the absence for enhancement sition at ∼170 K, but which is accompanied by a drop
of the normal-state [T T]−1 due to low-energy AF SF, in spin susceptibility [18]. Given that the system is in-
1
which tend to dominate the relaxation. In the specific sulating, thetransitionislikelyaccompaniedbyalattice
example of (TMTSF) PF , a greater than five-fold en- distortion to a valence bond solid with singlet ground
2 6
hancement is observed at temperatures below 20 K [21]. state. While it is natural to consider that SC is emerg-
We contrast that to the case of the β(cid:48)(cid:48) superconductor, ing from fluctuations around this state [37], the [T1T]−1
inwhichtheenhancementisnegligible(Fig. 3). Further, resultsreportedhereposeachallengeforthisinterpreta-
given that the results here closely resemble other nodal tionbecausethereisnodropin[T1T]−1 attemperatures
superconductors, such an observation opens the door to approaching Tc.
whether the physics of pairing in the β(cid:48)(cid:48) superconduc- Clearly, direct evidence for charge fluctuations would
tor would include correlation physics other than, or at be beneficial and toward that end two approaches war-
leastbeyond,AFSF.Complementingtherelaxation-rate rantmentioning. First, theavailablenuclearprobes, 13C
measurements are the low temperature shift data upon 1H, 19F, are all spin I=1/2, and thus absent an electric
entering the SC state, as shown in Fig. 5. The drop in quadrupolemomentthatcouplestothelocalelectricfield
shift is consistent with a decrease in spin susceptibility gradient (EFG). Samples spin-labelled with 2H (I=1)
as for a spin-singlet superconductor. Note that the de- might correct that deficiency. However, to our knowl-
crease is much larger for the red molecule than it is for edge I > 1/2 nuclei were not previously applied in in-
orange, consistent with the interpretation of larger hy- vestigationsofCOfluctuations. Ontheotherhand,slow
perfine fields and spin (carrier) density on the former. collective charge fluctuations are known to enhance the
homogeneouslinebroadening(1/T )arisingfromtempo-
2
5
ral variations in the paramagnetic shift, in for example Whangbo, R. W. Winter, J. Mohtasham, and G. L.
θ-(ET) RbZn(SCN) , at temperatures greater than the Gard, J. Mater. Chem. 11, 2008 (2001).
2 4
transition to a CO insulator [38]. Similar measurements [19] S.Kaiser,M.Dressel,Y.Sun,A.Greco,J.A.Schlueter,
G. L. Gard, and N. Drichko, Phys. Rev. Lett. 105,
are currently planned.
206402 (2010).
TheauthorsacknowledgehelpfuldiscussionswithMar-
[20] G.Koutroulakis,H.Ku¨hne,J.A.Schlueter,J.Wosnitza,
tin Dressel, Steve Kivelson, and Hitoshi Seo. Apprecia-
and S. E. Brown, (arXiv 1511:03578).
tion is extended to R. Kato and H. Yamamoto for con-
[21] S. E. Brown, M. J. Naughton, and P. M. Chaikin,
tributing 13C spin-labelled ET molecules for the crystal “The physics of organic superconductors and conduc-
growth. TheworkwassupportedinpartbytheNational tors,” (Springer, Heidelberg, 2008) Chap. La tour des
Science Foundation grant number DMR-1410343 (sb). sels Bechgaard, pp. 49–87.
J.W. and H.K. acknowledge the support of the HLD at [22] S. M. De Soto, C. P. Slichter, A. M. Kini, H. H. Wang,
U. Geiser, and J. M. Williams, Phys. Rev. B 52, 10364
HZDR,amemberoftheEuropeanMagneticFieldLabo-
(1995).
ratory (EMFL). JAS acknowledges support from the In-
[23] M.Takigawa,A.P.Reyes,P.C.Hammel,J.D.Thomp-
dependentResearch/Developmentprogramwhileserving
son, R. H. Heffner, Z. Fisk, and K. C. Ott, Phys. Rev.
at the National Science Foundation. B 43, 247 (1991).
[24] G.-q. Zheng, K. Tanabe, T. Mito, S. Kawasaki, Y. Ki-
taoka, D. Aoki, Y. Haga, and Y. Onuki, Phys. Rev.
Lett. 86, 4664 (2001).
[25] F. Ning, K. Ahilan, T. Imai, A. S. Sefat, R. Jin, M. A.
[1] T. Ishiguro, K. Yamaji, and G. Saito, McGuire, B. C. Sales, and D. Mandrus, J. Phys. Soc.
Organic Superconductors, Springer Series in Solid- Jpn. 78, 013711 (2009).
State Sciences, Vol. 88 (Springer-Verlag, Berlin, 1998). [26] P. Monceau, F. Y. Nad, and S. Brazovskii, Phys. Rev.
[2] A.G.Lebed,ed.,Organic superconductors and conductors, Lett. 86, 4080 (2001).
Springer Series in Materials Science, Vol. 110 (Springer- [27] W. Yu, F. Zhang, F. Zamborszky, B. Alavi, A. Baur,
Verlag, Berlin, 2008). C.A.Merlic, andS.E.Brown,Phys.Rev.B70,121101
[3] A. Ardavan, S. E. Brown, S. Kagoshima, K. Kanoda, (2004).
K.Kuroki, H.Mori, M.Ogata, S. Uji, andJ.Wosnitza, [28] L. Zorina, S. Simonov, C. M´ezi´ere, E. Canadell, S. Suh,
J. Phys. Soc. Jpn. 81, 011004 (2012). S.E.Brown,P.Foury-Leylekian,P.Fertey,J.P.Pouget,
[4] S. E. Brown, Physica C 514, 279 (2015). and P. Batail, J. Mater. Chem. 19, 6980 (2009).
[5] Y.Kurosaki,Y.Shimizu,K.Miyagawa,K.Kanoda, and [29] M. Dressel, private communication.
G. Saito, Phys. Rev. Lett. 95, 177001 (2005). [30] D. S. Chow, F. Zamborszky, B. Alavi, D. J. Tantillo,
[6] V. J. Emery, J. Phys. 44, 977 (1983). A. Baur, C. A. Merlic, and S. E. Brown, Phys. Rev.
[7] K. Oshima, H. Urayama, H. Yamochi, and G. Saito, J. Lett. 85, 1698 (2000).
Phys. Soc. Jpn. 57, 730 (1988). [31] F.Zamborszky,W.Yu,W.Raas,S.E.Brown,B.Alavi,
[8] H. Kino and H. Fukuyama, J. Phys. Soc. Jpn. 65, 2158 C. A. Merlic, and A. Baur, Phys. Rev. B 66, 081103
(1996). (2002).
[9] H.Seo,J.Merino,H.Yoshioka, andM.Ogata,J.Phys. [32] K. Kanoda, K. Miyagawa, A. Kawamoto, and
Soc. Jpn. 75, 051009 (2006). Y. Nakazawa, Phys. Rev. B 54, 76 (1996).
[10] T.Takahashi,Y.Nogami, andK.Yakushi,J.Phys.Soc. [33] M. Takigawa, H. Yasuoka, and G. Saito, J. Phys. Soc.
Jpn. 75, 051008 (2006). Jpn. 56, 873 (1987).
[11] H.Mori,S.Tanaka, andT.Mori,Phys.Rev.B57,12023 [34] T. Imai, T. Shimizu, H. Yasuoka, Y. Ueda, and K. Ko-
(1998). suge, J. Phys. Soc. Jpn. 57, 2280 (1988).
[12] T. Mori, Bull. Chem. Soc. Jpn. 71, 2509 (1998). [35] D. E. MacLaughlin, C. Tien, W. G. Clark, M. D. Lan,
[13] S. E. Sebastian, N. Harrison, F. F. Balakirev, M. M. Z. Fisk, J. L. Smith, and H. R. Ott, Phys. Rev. Lett.
Altarawneh,P.A.Goddard,R.Liang,D.A.Bonn,W.N. 53, 1833 (1984).
Hardy, and G. G. Lonzarich, Nature 511, 61 (2014). [36] Wenotethatthespecific-heatdatagiveevidenceforcom-
[14] J. Merino and R. H. McKenzie, Phys. Rev. Lett. 87, pletegapsinorganicsuperconductors.See,e.g.,R.Beyer,
237002 (2001). et al., J. Low Temp. Phys. 39, 293 (2013), H. Elsinger,
[15] A.Kobayashi,Y.Tanaka,M.Ogata, andY.Suzumura, et al., Phys. Rev. Lett. 84, 6098 (2000). Optics exper-
J. Phys. Soc. Jpn. 73, 1115 (2004). iments were interpreted similarly, see S. Kaiser, et al.,
[16] A. Girlando, M. Masino, J. A. Schlueter, N. Drichko, Phys. Status Solidi B 249, 985 (2012).
S. Kaiser, and M. Dressel, Phys. Rev. B 89, 174503 [37] S. Dayal, R. T. Clay, H. Li, and S. Mazumdar, Phys.
(2014). Rev. B 83, 245106 (2011).
[17] T.Mori,H.Mori, andS.Tanaka,Bull.Chem.Soc.Jpn. [38] R. Chiba, K. Hiraki, T. Takahashi, H. M. Yamamoto,
72, 179 (1999). and T. Nakamura, Phys. Rev. Lett. 93, 216405 (2004).
[18] J. A. Schlueter, B. H. Ward, U. Geiser, H. H. Wang,
A. M. Kini, J. Parakka, E. Morales, H.-J. Koo, M.-H.
