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Symmetry of the superconducting order parameter in Bechgaard salts
ELSEVIER
SyntheticMetals 103 1999)2030-2033
Symmetry
of the superconducting
order parameter in Bechgaard salts
K. Behnia, S. Belin and M. Ribault Laboratoire de Physique des SolidesiCNRS). UniversiG PCs-Sud, F-LJt305 Onay, Fwwc
I \\o ~lc~~t&s ;~I’tcl-the discovery of superconductivity in a Bechgaard salt. the pairing mechanism is not yc~ idcntiiiccl. ‘l’hc lirai 31cp icww~i~ such an identificatiori is to determine the symmetry of the superconducting order parameter. Results on heat transport in the ~lII”rcl,nilucting state of (TMTSF)$Z104 indicate a finite gap all over the Fermi surface. The magnitude of this-gap is contirmccl 174the i’irh[ CX~CI’II~~CI~~S clone on break junctions. A nodeless gap imposes a number of constraints on the symmetry ot’ the order pnramctcr. ,k’~~~nw~/.~: Supcrconductin~ transition, Organic superconductors 1.Introduction I II 1979, pressure-induced superconductivity was rcporretl in (TMTSF)?PF,[ I]. This organic compoundmember of a family which is now known as the Bechgaarrl salts- undergoes a Spin-Density-Wave (SDW) tlansition at ambient pressure. The occurence of the SDW transition is an understandable consequence of the extreme anisotropy of the system which has a quasi-onedimensional Fermi surface consisting of two warped \llCr’l\. l)tte to its nesting properties, such a Fermi ~LII.~;KY is inherently unstable towards a density-wave tranxltion. The application of pressure, by enhancing the tran5\erse coupling, reduces this instability. The rcmarkabie feature of the superconducting state discovered then was its emergence in the immediate ntli$borhtxx.i of the SDW transition. Since then, ~~~p~~cot~~l~~o~~vi~~~has been discovered in other members 01’thih thmily including in (TMTSF),CIO, which is the (1n1y~lmhient-Pressure superconductorof the group. Even bri’o~~ its birth. organic superconductivity was suspected to be unconventional; i.e. associated with a pairing mechanismdifferent from the one which is observed in ordinary metals. However. during the two past decades,the observation of ~ever;~lother remarkable features [the list includes fieldIllcll1Crtl-~l~iri-ilensity-w;lvetransitions[2], quantum Hall md etiwr /3 j commensurabilty effects in angular mngnetoresistance~4]~ in Bechgaard salts, led to a less inten.seexploration of superconductingstate. Meanwhile, the discovery of unexpected superconductivity in other syhternh-namely heavy fermions[5] and specially high-TT, cuprxeslhj- stimulated vast theoretical and experimental I L!w;ll‘uIl on t1w “unconventional superconductivity” prohlcmatic. In alI thesecompounds,the superconducting \t;Ity-which is observed in the proximity of a magnetic
instability- may be engendered by LI purely electronic pairing mechanismby contrast to the phonon-mediated Cooper pairs of the conventional superconductors. Experimental probesdo not couple directly to the pairing interaction and the identification of the latter has proved to be a very complicated task. On the other hand, during the last few years, another manif~tation of unconventional superconductivity, a non-trivial internal structure for the pair’s wave-filnctioll, has~- beenexperimentally investigated in cuprate ;und heavy fermions. There is now a general consensus that superconductivity in the cuprntes is associated with [Iwave pairing: Cooper pairs have a finite a~Gjh momentum and the superconducting order parameter is anisotropic enough to present nodes for scme spr?ific orientations[7]. Evidence for a complex structure of or& parameter has been also accumulated in heavy-fermion compoundsand notably in the casec~t’UPtx the choice of possiblesymmetries have been narrowed down in recenr years[S]. In the quasi-two-dimensionnl organic superconductors of the (BEDT-TTF)?X family, most recent investigations favor the presence of nodes in the order parameter[9]. Compared to all these fijmilies, the superconducting state of the (TMTSF),X salts has been poorly investigated and a vast arnrrunt of experimental data is still lacking. The aim of this paper is to pr
2. Possibie symmetries of the order parameter Possible types of superconductivity in a Qunsi-onedimensional system was classified by Hasegnwa :md Fukuyama in 198tl[ IO]. Thebe authors found that an attractive interaction working both- on-site and be&en nearest neighbors cari- lead tq singlet or triplcl
0379-6779/991$ - seefrontmatter0 1999Elsevier Science S.A. All rightsreserved. PII: so379-6779(98)0029 l-4
K. Behnia et al. I Synthetic
\Ill1Cl.t’olltl~li~Ii\‘if!’ on ;I Fermi Surface consisting of two ~l~p;~~~;~~t’ shtw,. Four possible order parameters- two \111glc1‘1nc1ILI’O triplet- can emerge in this context. Figure I gives ;I bchematic representation of the order parameter and the Fermi hurface in each case. Note that the two ,illglct hl;lte> are b:iaically different tiom each other. The ,I \tilte is ;lssoci;lted with s-wave superconductivity and thL%l.c,l.r~~l~o”‘iitl~ order parameter presents no nodes. By ~~,II~II;I\I. t/its 01dt31~ p;\r:lmeter osaociated with s2 presents ncxlt’r ;tnd the wave-function may have a tinite angulai I~~C~JI~IUI~. The two triplet states are also different. \I’hilc tlic 12 state is ;I p-wave supercondutor with nodes the tl state presents the remarkable Ill 01 Cli‘l’ ]xll’;lllletC’r, propi*~‘t> 01 changing sign without becoming zero ,III\ \\ 11~x1 jbon the Fermi surface. This is only possible due 10 iilL* OJIC~IIIIC~~ ol’the Fermi Surface.
Metals
103 (1999) 2030-2033
203 1
(TMTSF)?CIO., coiisists of two pairs of sheets (Fig. 7-l. While qualitative features of the model presentetl 17) Hosegawa and Fukuyama (including nodeless hut \ignchanging order parmeter) survive in this context. the enumerated four types of superconductvity shall no mart compose an exhaustive list. However, in spite 01‘ thehc‘ in absence of a thorough theoretical shortcomings, investigation. we will refer to this model in the anoly\i\ of our data.
Fig. 2 Fermi surface of (TMTSF)~CIOJ before and al‘lcr minion ordering. 3.Thermal
Fig. I Schcni;ltic presentation of possible order parameters in a Ql D \YS~CIII.Upper lef‘t :sl : upper right tl ; lower left s2 and lower rlpiii Q. The cluhsitication summarized in Fig. 1 does not take into considcrntion the details of the crystal structure of t/it‘ Rcchg~u~I aaltlr. Working in the context of heavyfermion sul’erconductivity, Volovik and Gor’kov[ IO] ‘\howccI that for cubic, hexagonal and tetragonal crystal \ymmetrie5. there is a finite number of possible irrecluctible representations for the symmetry group of superconducting order parameter. A detailed the theoretical treatment of the possible symmetries in the Bcchgnard saltb should consider the consequences of the monoclinic crystal symmetry in these compounds. Moreover, in order to confront experimental data on (TMTSF,,CIO,, the model presented in Fig. 1 shall overcome a more serious insufficiency. The anionordering transition occuring at 24K in this salt leads to a ciimerization along the b direction which modifies the Fermi surfnce. The lnw-temperature Fermi surface in
conductivity
as a probe of gap structure
Thermal conductivity has been widely used during the present unconventional decade to probe superconductivity in cuprate and heavy-fermion superconductors. In an ordinary superconductor with a finite gap all over the Fermi surface, the condensation ot individual electrons due to the superconducting transition leads to an exponential decrease in the electronic component of thermal conductivity. By contrabt, the presence of nodes in the superconducting gap provide\ low-energy heat-carrying excitations which contribute significantly to heat conduction at low temperature. Such a residual electronic component of heat conductivity ha been observed notably in UPt.J[I’] ;1ml ill YBazCu300..,1[ 133 and is a compelling sign;lture 01‘ unconventional superconductvity in these systems.Since only delocalized quasi-particles can contribute to heat conduction, this probe is more conclusive than specific heat measurements which are sensitive to localized excitations associatedwith disorder in the system. Recently, we carried out a systematic study of lowtemperature heat conduction in (TMTSF),CIO, in order to check the presence of such a residual electronic contribution[l4]. Thermal conductivity was studied as a function of temperature below I .6K in the superconducting, metallic and insulating states of the samesample.The superconductingstate was obtained by slowly cooling the satnple through the 24K anionordering transition temperature. By putting a small tielcl (5 kOe) along the c-axis superconductivity was destroyed and the normal state could be studied down to 0. I SK. On the other hand, by heating the sample up to 1OK antI quenching it through the anion-ordering transition \\‘e
stabiliseda SDW stateat low temperature.Fig. 3 show\ the resultsfor the three states.
2032
K, Behnia
et al, / Synthetic
Metals
IO3 (1999)
203~2033
T, and no residual electronic contibution survives at temperatures as high as one third 01’ T,.. Thib behavior,indicative of the abbence of’ low-t’n~fy excitations, is very different from what is seen in :I superconductor such as UPt, where low-cncrpy excitations associatedwith nodes in the gap contri hurt> signiiioantly to heat conduction at TLJ3. It c:m IX reproduced using the standard BRT theory! IS] t’<~:;m isotropic nodelessgap with a moderately stl.onf-ctlul~iil~~ value (&JkBT, = 2.3). It is important to note thnt ;I finite electron-phonon coupling doesnot affect this concIu’;ion. Indeed, such a coupling can only enhance latticct conductivity in the superconducting state and woultl yield a sharper decrease in the electronic thermal conductivity and a more pronounced difference 6th what is expected for a behavior associatedwith nods\ in the gap.
Fig. 3 Thermal conductivity of (TMTSF)&ZlO., in metallic, superconducting and insulating states.
Access to the three states allowed us to overcome a major (ohhtacte in using thermal conductivity data in (TMTSQCQ to probe the electronic excitations. Indeed, at the onset of superconductivity, the electronic component is just a fraction of total lattice-dominated bent conduction. This relative weight of phononic and electronic contribitions can be estimated using the Wieilmann-FI-anz(WF)law at T,. According to this law, in absence of inelastic scattering the ratio of thermal and electrical conductivities of a Fermi liquid is a universal constant(L,,) multiplied by temperature. Using WF, we found that electrons count for 15% of thermal conductivity at T,. We attempted to extract the electronic thermal conductivity by comparing the data on the superconducting and normal states. If the lattice crmponrnt were not affected by the superconducting tranxition, the difference between the two K(T) would represenr the difference between the electronic thermal crmductivities of the normal and superconducting states. Obviously, this hypothesis is not true in the case of strong electron-phonon coupling which would lead to an enh;incement of lattice contribution in the superconducting state due to the disappearance of electronic scatterers. Evidence for the weakness of electron-photon coupling in this system is provided by the thermal conductivity of the insulating (TMTSF)?CIOJ. Here, heat conduction is only due to the lnttice and there is no electronic scattering of phonons. The large reduction in phonon thermal conductivity indicntes that phononsare much more sensitive to anion disorder than to presenceof electrons. Neglecting electron-phonon coupling, we present in Fig. 1. the extracted electronic thermal conductivity of the superconducting state. In order to compare it with other superconductors,the magnitude of thermal conductivity is normalized to its value at T,. The important outcome of our study is seen in the figure. The electronic contribution to heat conduction decreasesrapidly below
1.2 ,
0~8 0.6 0.4
-0,21 0.0
(TMTSF),CIO,
I
, 0.2
I
, 0.4
, 0.6
I
, 0.8
.
, I .o
,
, 1.2
I
.i
TKc
Fig.
4 Normalised electronic thermal conductivity 01 (TMTSF)&104 (open circles) compared with UPt3 (solid squares)and theoreticalpredictionsfor nn isotropic gap [Tull line)(sectext).
Thus, our study of heat conduction provides strong evidence for the absenceof nodes in the superconducting gap. We note that this result contradicts the intel.pl.et~I[ioll of early NMR data[ltij. However, fie symmetry ot the order parameter as well as the possibly tmconvention;ll nature of superconductivity rem&l open questiCons. While we can rule out order parameterssuch as s2 and t?. which present nodes, an order parameter such as t I can not be excluded. As mentioned above, due to thr openness of Fermi surface, the order parameter can change s~ignwithout presenting a node. P-wave (triplet) superconductivity in Bechgaard sal_tsis an appealing option to explain the fascinating behavior of the upper critial field which exceeds the Pauli limit at low temperatures[171.However, there is n-otyet any evidence for ferromagnetic fluctuations which-would favor triplet pairing.
4. An experiment
with break junctions
K. Belmia
et al. I Synthetic
Metals
103 (1999)
2030-2033
2033
of three distinct peaks. This is reminiscent 01’ what is reported in weak links created in mechanically controlled break junctions of niobium[ 191.It is tempting to attribute the features observed here to a subharmonic gap structure expected in the case of multiple Antlreev scattering. The value obtained for the superconducting gap in this case (0.3 meV) is compatible once again with a moderately strong-coupling value (AtJkUT, =~ 2.6). While, in absence of a systematic study, the precihc determination of the gap amplitude is subject to caution, it is noteworthy that this is the first spectroscopic evaluation of the superconducting gap in this system. The only available study is an early tunneling experiment [ 201 which reported an unreasonablyhigh value for the gap. consisting
7’11~itlentitication of the symmetry of the order parameter (l~,pcnd\ on the use of powerful experimental probes in~luciirlg those which couple directly with the phase of Ill? orders parameter. It was this class of experiments \\hich iixccl the issue of the debate in the case of high-T, i111)1~;ne\lI Sl. The study of Josephson current between a I~c~ch;a:~rtl sitIt and ;I conventional superconductor, fat ~~\;~n~l-~lc.c;111bc instructive on the eventual sign changes 01' iIlL> Ol.(lt'l. ~lxmlrtel'. For the moment, technical l~ohlr~t~~ implied in making such junctions are not yet \ol\‘t‘cl.
5. Conclusion Until now, the symmetry of the order parameter in the Bechgaard salts has been barely explored. The absence of low-energy electronic heat carriers points to a nodeless gap. A p-wave nodelessgap would naturally explain the insensitivity of the upper critical field to the Pauli limit. This appealing option shall be tested in the future by experimental probes which couple to the phaseof ortlet parameter.
I I.8
-0.6
a
11
,a
IS
I(,
-0.4
-0.2
0.0
0.2
3 0.4
I
0.6
* 0.8
v0-w Fig. 5: Upper panel: I-V characteristicsof a (TMTSF)f2104 break-lunction at T=O.O7K. Lower pannel: Dynamical Rcsixti\4!) ;IS a function of bias voltage for different tcmpcrnture.The vertical scale correspondsto the T=0.07 curve. For 111~ sake01’clarity. all othercurveshave beenshifted dmvnwlril.
Here we present the preliminary results of a study of the dynamical conductance of a (TMTSF)zC104 break junction. It shows that the spectroscopic observation of gap-like features is a relatively easy task in this system. The resistivity was measuredalong the c-axis with small point-like contacts and the broken junction was produced merely by rapidly cooling the sample. As shown in Fig. 5, within the entry of the system in the superconducting state, the junction presentsa non-linear conductivity. By lowering temperature, one can resolve a clear structure
[ 11D. Jerome ,A. Mazaud, M. Ribault and K. Bechgaard, J. Phys. (Paris) Lett. 56, L-95 (1980). [2] M. Ribault et al., J. Phys. Lett. 44, L-953 (1983). [3] J. R. Cooper et al., Phys. Rev. Lett. 63, I984 ( 1989) ; S. T. Hannahset al., Phys. Rev. Lett. 63, 1988(1989). [4] T. Osadaet al ., Phys. Rev. Lett. 66, 1525( I99 I ) : W. Kang et al., Phys. Rev. Lett. 69, 2827 (1992). [S] F. Steglich et al., Phys. Rev. Lett. 43, I892 (I 979). [6] J. G. Bednorz and K. A. Muller, Z. Phys. B 64, I89 (1986): [7] D. Scalapino, Phys. Rep. 250, 329 (1995). [8] J. A. Sauls,Adv . phys. 43, I I3 (1994). [9]K. Kanoda, Hyp. Interact. 104, 235 (1997). [IO] Y. Hasegawaand H. Fukuyama, J. Phys. Sot. Jpn. 55, 3978 (1986). [I 11G. E. Volovik and L. Gorkov, JETP 61, 843 ( 19X5). [ 121 H. Suderow et al., J. Low Temp. Phys. 108, I I (I 997). 1131L. Taillefer et al., Phys. Rev. Lett. 79, 483 (1997). [ I41 S. Belin and K. Behnia, Phys. Rev. Lett. 79, 2125 (1997). [15] J. Bardeen, G. Rickaysen and L. Tewordt, Phps. Rev. 113,982 (1959). [ l6J M. Takigawa, H. Yasuoka and G. Saito, J. Phys. Sot. Jpn. 56, 873 (I 987). [ 171I. J. Lee et al., Phys. Rev. Lett. 78, 3555 (I 997). [I81 D. A. Wollman et al., Phys. Rev. Lett. 71, 2134 (I 993); C. C. Tseui et al., Phys. Rev. Lett. 73, 593 ( 1994). [I91 C. J. MulIer, J. M. van Ruitenbeek and L. J. de Jongh, Physica C 191,385 (1992). [20] C. More et al., J. Phys. (Paris) Lett. 42, L-3 I3 ( IX I ).
SyntheticMetals 103 1999)2030-2033
Symmetry
of the superconducting
order parameter in Bechgaard salts
K. Behnia, S. Belin and M. Ribault Laboratoire de Physique des SolidesiCNRS). UniversiG PCs-Sud, F-LJt305 Onay, Fwwc
I \\o ~lc~~t&s ;~I’tcl-the discovery of superconductivity in a Bechgaard salt. the pairing mechanism is not yc~ idcntiiiccl. ‘l’hc lirai 31cp icww~i~ such an identificatiori is to determine the symmetry of the superconducting order parameter. Results on heat transport in the ~lII”rcl,nilucting state of (TMTSF)$Z104 indicate a finite gap all over the Fermi surface. The magnitude of this-gap is contirmccl 174the i’irh[ CX~CI’II~~CI~~S clone on break junctions. A nodeless gap imposes a number of constraints on the symmetry ot’ the order pnramctcr. ,k’~~~nw~/.~: Supcrconductin~ transition, Organic superconductors 1.Introduction I II 1979, pressure-induced superconductivity was rcporretl in (TMTSF)?PF,[ I]. This organic compoundmember of a family which is now known as the Bechgaarrl salts- undergoes a Spin-Density-Wave (SDW) tlansition at ambient pressure. The occurence of the SDW transition is an understandable consequence of the extreme anisotropy of the system which has a quasi-onedimensional Fermi surface consisting of two warped \llCr’l\. l)tte to its nesting properties, such a Fermi ~LII.~;KY is inherently unstable towards a density-wave tranxltion. The application of pressure, by enhancing the tran5\erse coupling, reduces this instability. The rcmarkabie feature of the superconducting state discovered then was its emergence in the immediate ntli$borhtxx.i of the SDW transition. Since then, ~~~p~~cot~~l~~o~~vi~~~has been discovered in other members 01’thih thmily including in (TMTSF),CIO, which is the (1n1y~lmhient-Pressure superconductorof the group. Even bri’o~~ its birth. organic superconductivity was suspected to be unconventional; i.e. associated with a pairing mechanismdifferent from the one which is observed in ordinary metals. However. during the two past decades,the observation of ~ever;~lother remarkable features [the list includes fieldIllcll1Crtl-~l~iri-ilensity-w;lvetransitions[2], quantum Hall md etiwr /3 j commensurabilty effects in angular mngnetoresistance~4]~ in Bechgaard salts, led to a less inten.seexploration of superconductingstate. Meanwhile, the discovery of unexpected superconductivity in other syhternh-namely heavy fermions[5] and specially high-TT, cuprxeslhj- stimulated vast theoretical and experimental I L!w;ll‘uIl on t1w “unconventional superconductivity” prohlcmatic. In alI thesecompounds,the superconducting \t;Ity-which is observed in the proximity of a magnetic
instability- may be engendered by LI purely electronic pairing mechanismby contrast to the phonon-mediated Cooper pairs of the conventional superconductors. Experimental probesdo not couple directly to the pairing interaction and the identification of the latter has proved to be a very complicated task. On the other hand, during the last few years, another manif~tation of unconventional superconductivity, a non-trivial internal structure for the pair’s wave-filnctioll, has~- beenexperimentally investigated in cuprate ;und heavy fermions. There is now a general consensus that superconductivity in the cuprntes is associated with [Iwave pairing: Cooper pairs have a finite a~Gjh momentum and the superconducting order parameter is anisotropic enough to present nodes for scme spr?ific orientations[7]. Evidence for a complex structure of or& parameter has been also accumulated in heavy-fermion compoundsand notably in the casec~t’UPtx the choice of possiblesymmetries have been narrowed down in recenr years[S]. In the quasi-two-dimensionnl organic superconductors of the (BEDT-TTF)?X family, most recent investigations favor the presence of nodes in the order parameter[9]. Compared to all these fijmilies, the superconducting state of the (TMTSF),X salts has been poorly investigated and a vast arnrrunt of experimental data is still lacking. The aim of this paper is to pr
2. Possibie symmetries of the order parameter Possible types of superconductivity in a Qunsi-onedimensional system was classified by Hasegnwa :md Fukuyama in 198tl[ IO]. Thebe authors found that an attractive interaction working both- on-site and be&en nearest neighbors cari- lead tq singlet or triplcl
0379-6779/991$ - seefrontmatter0 1999Elsevier Science S.A. All rightsreserved. PII: so379-6779(98)0029 l-4
K. Behnia et al. I Synthetic
\Ill1Cl.t’olltl~li~Ii\‘if!’ on ;I Fermi Surface consisting of two ~l~p;~~~;~~t’ shtw,. Four possible order parameters- two \111glc1‘1nc1ILI’O triplet- can emerge in this context. Figure I gives ;I bchematic representation of the order parameter and the Fermi hurface in each case. Note that the two ,illglct hl;lte> are b:iaically different tiom each other. The ,I \tilte is ;lssoci;lted with s-wave superconductivity and thL%l.c,l.r~~l~o”‘iitl~ order parameter presents no nodes. By ~~,II~II;I\I. t/its 01dt31~ p;\r:lmeter osaociated with s2 presents ncxlt’r ;tnd the wave-function may have a tinite angulai I~~C~JI~IUI~. The two triplet states are also different. \I’hilc tlic 12 state is ;I p-wave supercondutor with nodes the tl state presents the remarkable Ill 01 Cli‘l’ ]xll’;lllletC’r, propi*~‘t> 01 changing sign without becoming zero ,III\ \\ 11~x1 jbon the Fermi surface. This is only possible due 10 iilL* OJIC~IIIIC~~ ol’the Fermi Surface.
Metals
103 (1999) 2030-2033
203 1
(TMTSF)?CIO., coiisists of two pairs of sheets (Fig. 7-l. While qualitative features of the model presentetl 17) Hosegawa and Fukuyama (including nodeless hut \ignchanging order parmeter) survive in this context. the enumerated four types of superconductvity shall no mart compose an exhaustive list. However, in spite 01‘ thehc‘ in absence of a thorough theoretical shortcomings, investigation. we will refer to this model in the anoly\i\ of our data.
Fig. 2 Fermi surface of (TMTSF)~CIOJ before and al‘lcr minion ordering. 3.Thermal
Fig. I Schcni;ltic presentation of possible order parameters in a Ql D \YS~CIII.Upper lef‘t :sl : upper right tl ; lower left s2 and lower rlpiii Q. The cluhsitication summarized in Fig. 1 does not take into considcrntion the details of the crystal structure of t/it‘ Rcchg~u~I aaltlr. Working in the context of heavyfermion sul’erconductivity, Volovik and Gor’kov[ IO] ‘\howccI that for cubic, hexagonal and tetragonal crystal \ymmetrie5. there is a finite number of possible irrecluctible representations for the symmetry group of superconducting order parameter. A detailed the theoretical treatment of the possible symmetries in the Bcchgnard saltb should consider the consequences of the monoclinic crystal symmetry in these compounds. Moreover, in order to confront experimental data on (TMTSF,,CIO,, the model presented in Fig. 1 shall overcome a more serious insufficiency. The anionordering transition occuring at 24K in this salt leads to a ciimerization along the b direction which modifies the Fermi surfnce. The lnw-temperature Fermi surface in
conductivity
as a probe of gap structure
Thermal conductivity has been widely used during the present unconventional decade to probe superconductivity in cuprate and heavy-fermion superconductors. In an ordinary superconductor with a finite gap all over the Fermi surface, the condensation ot individual electrons due to the superconducting transition leads to an exponential decrease in the electronic component of thermal conductivity. By contrabt, the presence of nodes in the superconducting gap provide\ low-energy heat-carrying excitations which contribute significantly to heat conduction at low temperature. Such a residual electronic component of heat conductivity ha been observed notably in UPt.J[I’] ;1ml ill YBazCu300..,1[ 133 and is a compelling sign;lture 01‘ unconventional superconductvity in these systems.Since only delocalized quasi-particles can contribute to heat conduction, this probe is more conclusive than specific heat measurements which are sensitive to localized excitations associatedwith disorder in the system. Recently, we carried out a systematic study of lowtemperature heat conduction in (TMTSF),CIO, in order to check the presence of such a residual electronic contribution[l4]. Thermal conductivity was studied as a function of temperature below I .6K in the superconducting, metallic and insulating states of the samesample.The superconductingstate was obtained by slowly cooling the satnple through the 24K anionordering transition temperature. By putting a small tielcl (5 kOe) along the c-axis superconductivity was destroyed and the normal state could be studied down to 0. I SK. On the other hand, by heating the sample up to 1OK antI quenching it through the anion-ordering transition \\‘e
stabiliseda SDW stateat low temperature.Fig. 3 show\ the resultsfor the three states.
2032
K, Behnia
et al, / Synthetic
Metals
IO3 (1999)
203~2033
T, and no residual electronic contibution survives at temperatures as high as one third 01’ T,.. Thib behavior,indicative of the abbence of’ low-t’n~fy excitations, is very different from what is seen in :I superconductor such as UPt, where low-cncrpy excitations associatedwith nodes in the gap contri hurt> signiiioantly to heat conduction at TLJ3. It c:m IX reproduced using the standard BRT theory! IS] t’<~:;m isotropic nodelessgap with a moderately stl.onf-ctlul~iil~~ value (&JkBT, = 2.3). It is important to note thnt ;I finite electron-phonon coupling doesnot affect this concIu’;ion. Indeed, such a coupling can only enhance latticct conductivity in the superconducting state and woultl yield a sharper decrease in the electronic thermal conductivity and a more pronounced difference 6th what is expected for a behavior associatedwith nods\ in the gap.
Fig. 3 Thermal conductivity of (TMTSF)&ZlO., in metallic, superconducting and insulating states.
Access to the three states allowed us to overcome a major (ohhtacte in using thermal conductivity data in (TMTSQCQ to probe the electronic excitations. Indeed, at the onset of superconductivity, the electronic component is just a fraction of total lattice-dominated bent conduction. This relative weight of phononic and electronic contribitions can be estimated using the Wieilmann-FI-anz(WF)law at T,. According to this law, in absence of inelastic scattering the ratio of thermal and electrical conductivities of a Fermi liquid is a universal constant(L,,) multiplied by temperature. Using WF, we found that electrons count for 15% of thermal conductivity at T,. We attempted to extract the electronic thermal conductivity by comparing the data on the superconducting and normal states. If the lattice crmponrnt were not affected by the superconducting tranxition, the difference between the two K(T) would represenr the difference between the electronic thermal crmductivities of the normal and superconducting states. Obviously, this hypothesis is not true in the case of strong electron-phonon coupling which would lead to an enh;incement of lattice contribution in the superconducting state due to the disappearance of electronic scatterers. Evidence for the weakness of electron-photon coupling in this system is provided by the thermal conductivity of the insulating (TMTSF)?CIOJ. Here, heat conduction is only due to the lnttice and there is no electronic scattering of phonons. The large reduction in phonon thermal conductivity indicntes that phononsare much more sensitive to anion disorder than to presenceof electrons. Neglecting electron-phonon coupling, we present in Fig. 1. the extracted electronic thermal conductivity of the superconducting state. In order to compare it with other superconductors,the magnitude of thermal conductivity is normalized to its value at T,. The important outcome of our study is seen in the figure. The electronic contribution to heat conduction decreasesrapidly below
1.2 ,
0~8 0.6 0.4
-0,21 0.0
(TMTSF),CIO,
I
, 0.2
I
, 0.4
, 0.6
I
, 0.8
.
, I .o
,
, 1.2
I
.i
TKc
Fig.
4 Normalised electronic thermal conductivity 01 (TMTSF)&104 (open circles) compared with UPt3 (solid squares)and theoreticalpredictionsfor nn isotropic gap [Tull line)(sectext).
Thus, our study of heat conduction provides strong evidence for the absenceof nodes in the superconducting gap. We note that this result contradicts the intel.pl.et~I[ioll of early NMR data[ltij. However, fie symmetry ot the order parameter as well as the possibly tmconvention;ll nature of superconductivity rem&l open questiCons. While we can rule out order parameterssuch as s2 and t?. which present nodes, an order parameter such as t I can not be excluded. As mentioned above, due to thr openness of Fermi surface, the order parameter can change s~ignwithout presenting a node. P-wave (triplet) superconductivity in Bechgaard sal_tsis an appealing option to explain the fascinating behavior of the upper critial field which exceeds the Pauli limit at low temperatures[171.However, there is n-otyet any evidence for ferromagnetic fluctuations which-would favor triplet pairing.
4. An experiment
with break junctions
K. Belmia
et al. I Synthetic
Metals
103 (1999)
2030-2033
2033
of three distinct peaks. This is reminiscent 01’ what is reported in weak links created in mechanically controlled break junctions of niobium[ 191.It is tempting to attribute the features observed here to a subharmonic gap structure expected in the case of multiple Antlreev scattering. The value obtained for the superconducting gap in this case (0.3 meV) is compatible once again with a moderately strong-coupling value (AtJkUT, =~ 2.6). While, in absence of a systematic study, the precihc determination of the gap amplitude is subject to caution, it is noteworthy that this is the first spectroscopic evaluation of the superconducting gap in this system. The only available study is an early tunneling experiment [ 201 which reported an unreasonablyhigh value for the gap. consisting
7’11~itlentitication of the symmetry of the order parameter (l~,pcnd\ on the use of powerful experimental probes in~luciirlg those which couple directly with the phase of Ill? orders parameter. It was this class of experiments \\hich iixccl the issue of the debate in the case of high-T, i111)1~;ne\lI Sl. The study of Josephson current between a I~c~ch;a:~rtl sitIt and ;I conventional superconductor, fat ~~\;~n~l-~lc.c;111bc instructive on the eventual sign changes 01' iIlL> Ol.(lt'l. ~lxmlrtel'. For the moment, technical l~ohlr~t~~ implied in making such junctions are not yet \ol\‘t‘cl.
5. Conclusion Until now, the symmetry of the order parameter in the Bechgaard salts has been barely explored. The absence of low-energy electronic heat carriers points to a nodeless gap. A p-wave nodelessgap would naturally explain the insensitivity of the upper critical field to the Pauli limit. This appealing option shall be tested in the future by experimental probes which couple to the phaseof ortlet parameter.
I I.8
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a
11
,a
IS
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-0.4
-0.2
0.0
0.2
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v0-w Fig. 5: Upper panel: I-V characteristicsof a (TMTSF)f2104 break-lunction at T=O.O7K. Lower pannel: Dynamical Rcsixti\4!) ;IS a function of bias voltage for different tcmpcrnture.The vertical scale correspondsto the T=0.07 curve. For 111~ sake01’clarity. all othercurveshave beenshifted dmvnwlril.
Here we present the preliminary results of a study of the dynamical conductance of a (TMTSF)zC104 break junction. It shows that the spectroscopic observation of gap-like features is a relatively easy task in this system. The resistivity was measuredalong the c-axis with small point-like contacts and the broken junction was produced merely by rapidly cooling the sample. As shown in Fig. 5, within the entry of the system in the superconducting state, the junction presentsa non-linear conductivity. By lowering temperature, one can resolve a clear structure
[ 11D. Jerome ,A. Mazaud, M. Ribault and K. Bechgaard, J. Phys. (Paris) Lett. 56, L-95 (1980). [2] M. Ribault et al., J. Phys. Lett. 44, L-953 (1983). [3] J. R. Cooper et al., Phys. Rev. Lett. 63, I984 ( 1989) ; S. T. Hannahset al., Phys. Rev. Lett. 63, 1988(1989). [4] T. Osadaet al ., Phys. Rev. Lett. 66, 1525( I99 I ) : W. Kang et al., Phys. Rev. Lett. 69, 2827 (1992). [S] F. Steglich et al., Phys. Rev. Lett. 43, I892 (I 979). [6] J. G. Bednorz and K. A. Muller, Z. Phys. B 64, I89 (1986): [7] D. Scalapino, Phys. Rep. 250, 329 (1995). [8] J. A. Sauls,Adv . phys. 43, I I3 (1994). [9]K. Kanoda, Hyp. Interact. 104, 235 (1997). [IO] Y. Hasegawaand H. Fukuyama, J. Phys. Sot. Jpn. 55, 3978 (1986). [I 11G. E. Volovik and L. Gorkov, JETP 61, 843 ( 19X5). [ 121 H. Suderow et al., J. Low Temp. Phys. 108, I I (I 997). 1131L. Taillefer et al., Phys. Rev. Lett. 79, 483 (1997). [ I41 S. Belin and K. Behnia, Phys. Rev. Lett. 79, 2125 (1997). [15] J. Bardeen, G. Rickaysen and L. Tewordt, Phps. Rev. 113,982 (1959). [ l6J M. Takigawa, H. Yasuoka and G. Saito, J. Phys. Sot. Jpn. 56, 873 (I 987). [ 171I. J. Lee et al., Phys. Rev. Lett. 78, 3555 (I 997). [I81 D. A. Wollman et al., Phys. Rev. Lett. 71, 2134 (I 993); C. C. Tseui et al., Phys. Rev. Lett. 73, 593 ( 1994). [I91 C. J. MulIer, J. M. van Ruitenbeek and L. J. de Jongh, Physica C 191,385 (1992). [20] C. More et al., J. Phys. (Paris) Lett. 42, L-3 I3 ( IX I ).