ORGANIC SUPERCONDUCTIVITY

Denis Jerome

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Denis Jerome. ORGANIC SUPERCONDUCTIVITY. Physica B, 1982. hal-05011661

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# ORGANIC SUPERCONDUCTIVITY

D. JEROME*

Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France

Superconductivity is observed at low temperature in the conducting organic salts of the cation radicals tetramethyl-tetraselenafulvalene and tetramethyltetrathiofulvalene, $(TMSF)_2X$ and $(TMTTF)_2X$, with $T_c \le 1.2$ K and 3 K, respectively, where X is an inorganic anion. The superconducting properties are strongly influenced by the one-dimensional transport properties of these conductors.

The development of short-range superconducting order at temperatures much larger than the critical temperature manifests itself by a significant pseudo-gap in the quasi-particle density of states observed by electron tunneling spectroscopy up to 15 K. Moreover, paraconduction is the dominant conduction channel up to about 40 K.

Furthermore, preliminary junctions data indicate that the stabilization of superconduction at higher temperatures (i.e. 12 K in $(TMSF)_2PF_6$ under 11 kbar and possibly 26 K in $(TMSF)_2ClO_4$ under ambient pressure) is likely to arise from chain cross-linking.

The $(T,P)$ phase diagram of most organic superconductors displaying a phase transition line between a superconducting and a magnetic state, and the 1-D electron-gas theories suggest a dominant role of Coulomb interactions in the mechanism of Cooper pairs formation.

The discovery of superconductivity in condensed matter made of organic molecules is the outcome of a concerted work initiated by a suggestion of London [1] in 1950. According to London superconductivity need not be limited to the class of inorganic conductors but could possibly play an important role in certain large organic molecules of biochemical interest.

Following BCS's successful theory of superconductivity in metals based on the coherent motion of electron pairs held together by a phonon-mediated attractive interaction [2], Little [3] proposed an extension of that same pairing idea to electrons moving in media of high electrical polarizability.

In the model of Little, a large effective attraction between the electrons moving along an unsaturated carbon chain is provided by the virtual oscillation of charges on side-molecules attached to the chain. Moreover, this model of superconductivity with organic molecules suggested the possibility of critical temperatures as large as

ambient temperature and marked therefore the starting point of numerous researches in the field of conducting organic molecular solids.

It was not until the early seventies that organic conductors appeared in the guise of radical-cation salts [4] and charge transfer complexes [5]; both systems containing open shell planar molecules between which large intermolecular $\pi$-wave function overlaps are responsible for an electron delocalization. However, the stacked configuration of the planar molecules in the crystals confines the motion of the carriers to a single direction in space since the $\pi$-electrons' interaction is weak in the directions perpendicular to the stacking axis. It appeared therefore that the concepts of “physics in one dimension” fitted the description of the electronic properties of such unusually anisotropic conductors [6].

At an early stage Byschkov, Gorkov and Dzyaloshinskii [7] noticed that correlation functions of a different nature become equally divergent at low temperature for a one-dimensional (1-D) electron gas. More specifically, they showed that whenever the electron-electron interaction was approximated by two coupling

<footnote>* Work supported in part by DGRST, contract no. 80.7.0165, CNRS-ATP program 1981-1982 and a NATO grant 171.80.</footnote>
constants $g_1$ and $g_2$ for momentum transfer $2k_F$ and 0, respectively, both the Peierls (electron-hole) and the Cooper (electron-electron) pairings were equally divergent in the logarithmic approximation, and led to a phase transition at finite temperature. The degeneracy between superconducting and insulating ground states is however lifted by a more elaborate treatment of the 1-D problem. In the first-order renormalization theory [8], superconductivity is the most divergent instability at low temperature if $g_1 > 2g_2$; the triplet superconducting response function being more strongly divergent than the singlet response, for $g_1 > 0$. When $g_1 < 2g_2$, spin density wave (SDW) and charge density wave (CDW) responses both diverge for $g_1 > 0$, whereas the CDW state is the only divergent state at $g_1 < 0$.

Despite the absence of long-range order development at low temperature in 1-D conductors, it is possible for large size correlations to build up and to trigger the occurrence of a phase transition in real materials, this being due to various sources of interchain coupling.

In an attempt to understand the phase transitions of quasi-one-dimensional (Q-1-D) conductors, two scales of temperatures are important. First, the temperature $T_3$ at which three-dimensional long-range order occurs and where a phase transition is detected as in 3-D materials. Secondly, the temperature $T_1$, such as $T_1 > T_3$, which characterizes the growth of the expectation value of the order parameter without any interchain coherence. As far as superconductivity is concerned the dimensionality of the order parameter is two (amplitude and phase). The treatment of the superconducting phase transition of a Q-1-D conductor is thus equivalent to the ordering of a Heisenberg two-dimensional ferromagnet and the transition temperature is given by [9]

$$T_3 \approx (\alpha_{\parallel} \alpha_{\perp})^{1/2}, \quad (1)$$

where $\alpha_{\parallel}$ and $\alpha_{\perp}$ are respectively the intra and

interchain superconducting coupling strengths. $\alpha_{\parallel}$ is related to the temperature $T_1$ (or the amplitude of the pseudo-gap at the Fermi level of the quasi-particle density of states) and $\alpha_{\perp}$ is given by the interchain Josephson coupling $t^2/t_1$ ($t_1$ and $t$ being respectively the intra and interchain overlap integrals). A weak interchain coupling can lead to a sizeable depression of the transition temperature by phase-fluctuations of the order parameter below $T_1$.

In 1979, Bechgaard et al. [10] found that the family of Q-1-D conducting salts based on the tetramethyltetraselenafulvalene (TMTSF) molecule, namely (TMTSF)₂X with X = (NO₃)₆ PF₆, AsF₆, SbF₆, ... ) exhibits unusually large values of the conductivity at low temperature. Around 15 K, conductivities of the order of $10^5 (\Omega cm)^{-1}$ have been reported [10] for (TMTSF)₂PF₆ or (TMTSF)₂NO₃. The increase of the conductivity at low temperature is however interrupted by the occurrence of a sharp transition towards an insulating ground state. As far as (TMTSF)₂PF₆ is concerned the metal-insulator transition occurs at $T_{M-1} \approx 12$ K under ambient pressure. A somewhat similar behaviour with high conductivity has been observed earlier in a charge transfer compound containing the TMTSF molecule. Under a pressure in excess of 10 kbar [11], the conductivity of TMTSF-DMTCNQ (dimethyl TCNQ) reaches $\approx 10^5 (\Omega cm)^{-1}$ at helium temperature. Moreover, the low resistance is extraordinarily sensitive to the presence of defects, since $\Delta\rho \approx 3000 \mu\Omega cm$ per % of impurities [12] and to the application of a magnetic field perpendicular of the stacking axis [11], fig. 1.

As an interpretation for the unusual transport properties of TMTSF-DMTCNQ, the author suggested [11] the existence of a gradual growth below 30 K of a fluctuating superconducting pairing between $+k_F$ and $-k_F$ electron states.

The determination by X-ray diffuse scattering experiments [13] of a band filling which is the lowest ever observed in highly conducting charge transfer complexes, namely a one-quarter filled
<figure><img src="image_2.png" /><figcaption>Fig. 1. Temperature dependence of the longitudinal resistivity of TMTSF-DMTCNQ at 13 kbar without applied magnetic field and under a magnetic field of 75 kOe applied along the transverse direction.</figcaption></figure>

band under ambient pressure, stimulated the elaboration of a series of organic conductors (TMTSF)₂X in which the charge transfer is fixed ($ρ = 0.5$) by the stoichiometry of the salt. (TMTSF)₂X salts are cation-radical salts of TMTSF with inorganic anions X = NO₃, BF₄, PF₆, AsF₆, SbF₆, TaF₆, ClO₄, ReO₄, etc. in which a positive charge is shared between two organic molecules. The three-dimensional structure consists of a triclinic columnar arrangement of TMTSF molecules in the form of sheets of donor stacks separated by anion sheets [14], fig. 2. Along the stacking direction the unit cell contains two TMTSF molecules. The two-dimensional side view of the structure, as shown in fig. 2, could imply that the potential created on the TMTSF molecules by the anions on the left and on the right of a given stack cancel each other. However, a consideration of the full three-dimensional triclinic structure indicates that no such cancellation occurs, and therefore the periodicity of the potential seen by the delo-

calized charges on the TMTSF stack is fixed by the distance between the anions, namely a. Consequently, the conduction band becomes half-filled (instead of one-quarter filled as suggested by the stoichiometry and fig. 2. The existence of a weak dimerization of the average intermolecular distance is a sign of the a lattice periodicity along the stacking direction.

At room temperature, under ambient pressure, the dimerization amounts to 0.08% and 0.027% in (TMTSF)₂PF₆ and (TMTSF)₂ClO₄, respectively [14, 15]. It is however interesting to notice that the sulfur analogue series of the (TMTSF)₂X family exhibits a dimerization which, crudely speaking, is one order of magnitude larger, since it amounts to 0.6% at 300 K in (TMTTF)₂Br [16] (the less dimerized salt of the sulfur series).

The (TMTSF)₂X family exhibits a wide spread of electronic properties, with the perrhenate (ReO₄) and the tetrafluoroborate (BF₄) becoming insulating at 180 K and 40 K, respectively [10, 17, 18], the hexafluorate salts (PF₆, AsF₆, TaF₆...) undergoing a metal to insulator transition at low temperature [10, 19] ($T_{M-1} \approx 12$ K) and the perchlorate (ClO₄) remaining in a highly conducting state, with $σ > 10^5 (Ωcm)^{-1}$ down to helium temperature [20].

The salient feature of the conductivity of a salt such as (TMTSF)₂PF₆ remaining highly conducting below 20 K is the discrepancy existing between the temperature dependence of the d.c. conductivity, increasing by ×100 between ambient and 20 K, and the optical conductivity increasing by no more than a factor 3.5 in the same temperature interval [21].

Contrasting with all other studied charge transfer Q-1-D molecular conductors, X-ray diffuse scattering investigations have failed to detect any appreciable precursor scattering with wave vector $2k_F$ at T larger than $T_{M-1}$ [22] as expected if the insulating state observed below $T_{M-1}$ in (TMTSF)₂PF₆ were of a Peierls nature [23]. Instead, several magnetic measurements performed on the insulating state of (TMTSF)₂
<figure><img src="image_3.png" /><figcaption>Fig. 2. Two molecules, TMTSF and TMTTF, leading to superconducting cation-radical salts. A side view of the (TMTSF)₂PF₆ crystalline structure. The high conduction direction is along the stacking axis.</figcaption></figure>

PF₆ or AsF₆ have provided some clear-cut information as to the driving force of the insulating state in these salts. The ⁷⁷Se ($I = \frac{1}{2}$) NMR line of (TMTSF)₂PF₆ broadens inhomogeneously at 12 K, and becomes too broad to be detected below 11 K [24]. A similar line broadening is also observed for the methyl-group protons [24, 25]. Since both sets of nuclei have spin ½, NMR shows the existence of strong local magnetic fields below $T_{M-I}$ (fig. 3).

The ESR line disappears abruptly in the insulating state below $T_{M-I}$ [26], whereas hardly any change of the powder susceptibility is noticed with a Farady susceptibility technique [27].

<figure><img src="image_4.png" /><figcaption>Fig. 3. ⁷⁷Se NMR signal amplitude vanishing below 12 K at the onset of the SDW state in (TMTSF)₂PF₆. The dashed curve shows the Curie law temperature dependence which is expected in the absence of magnetic ordering.</figcaption></figure>
These results point out that unlike TTF-TCNQ and similar compounds exhibiting a Peirls insulating ground state, magnetism remains present in the insulating state of $(TMTSF)_2PF_6$, $(AsF_6)$.

Moreover, single crystal susceptibility measurements [28] have revealed a behaviour of the susceptibility of the insulating state analogous to that of an antiferromagnet. Below $T_{M-1}$, the easy axis of the magnetization [29] lies close to the *b*-axis of the crystal structure, whereas the *a* and *c*-axes are the intermediate and hard axes, respectively. Field dependence studies of the magnetization show the existence of a spin-flop transition along *b** exceeding ≈4.5 kOe (fig. 4).

The possibility for the occurrence of magnetic ordering, i.e. spin density waves (SDW) in low-dimensional conductors, has been suggested by

Slater [30]. Quite generally the stabilization of a SDW state implies the predominance of the repulsive electron-electron over the electron-phonon interactions. Therefore, in a SDW state the exchange part of the electron potential couples the states at +$k_F$ and -$k_F$ and opens an exchange gap at the Fermi level which transforms the Q-1-D conductor at high temperature into an insulator below $T_{M-1}$.

At $T < T_{M-1}$, on the one hand SDW modes couple to the nuclear spins enhancing the nuclear spin lattice relaxation [24], while on the other hand they shift the ESR far away from the nearly free ESR line position observed in the conducting regime [31]. An activation energy of ≈30 K is derived from the temperature dependence of the susceptibility with $H\|b^*$ in $(TMTSF)_2AsF_6$ [29], in fair agreement with the band gap of ≈66 K observed in electron tunneling experiments with $(TMTSF)_2PF_6$ under ambient pressure [32]. No such activated regime is however detected in the temperature dependence of the conductivity at low temperature in the absence of a magnetic field [33]. An increase of the helium temperature conductivity at high frequency above ≈10⁹ Hz has been interpreted in terms of the response of a collective pinned SDW mode to a high-frequency excitation [34].

The $(TMTSF)_2ClO_4$ salt is the only salt of the $(TMTSF)_2X$ family in which an insulating state does not take place at low temperature under ambient pressure. The resistance of $(TMTSF)_2ClO_4$ exhibits a continuous fall by about two orders of magnitude between room temperature and 5 K [20]. Below 5 K a slight upturn of the resistance is however observed in good-quality (low-resistance) crystals [19]. The resistance at 1.2 K can become two or four times larger than the value at 5 K. It is the result of high pressure work which stimulated to a large extent the interest in conducting charge transfer compounds. As far as TTF-TCNQ is concerned, high pressure has revealed commensurability effects in the vicinity of 19 kbar [35] when the wave length of the CDW becomes commensurate with

<figure><img src="image_5.png" /><figcaption>Fig. 4. Spin susceptibility of $(TMTSF)_2AsF_6$ as deduced from static measurements with field parallel to *a*, *b*\* and *c*\*. The magnetic field $H = 3$ kOe is less than the critical spin-flop field. (After ref. 29 and K. Mortensen, private communication.)</figcaption></figure>
the underlying lattice with concomitant con-
sequences on the pinning of the conductivity of
Fröhlich fluctuating origin [35]. In the
(TMTSF)₂X family, high pressure suppresses the
insulating state, fig. 5. Above 6 kbar or so, the
SDW state of (TMTSF)₂PF₆ or (TMTSF)₂AsF₆ is
very quickly removed by the hydrostatic pres-
sure. The plot of the logarithm of the transition
versus the applied pressure shows (fig. 6) that a
law such as

$$
T_{\text{SDW}} \approx A \exp \left( - \frac{B}{\sqrt{P_c - P}} \right)
$$

would apply (with P_c = 11.5 kbar) between 1 atm.
and 8 kbar. Above 8.5 kbar the ground state of
(TMTSF)₂PF₆ is superconducting [36]. The resis-
tivity under 12 kbar drops to zero below 0.9 K (fig.
7), whereas above 0.9 K the constant rate increase
observed as from helium temperature is in striking
contrast with the behaviour of the resistance
limited by impurities and lattice defects in ordinary
metals. In the pressure regime where SDW and
superconductivity coexist with a common phase
transition line, the phase diagram is rather com-
plex [37]. In fact, a detailed pressure investigation
performed on the (TMTSF)₂AsF₆ phase diagram
shows that superconductivity is re-entrant under

<figure><img src="image_6.png" /><figcaption>Fig. 5. Temperature dependence of the resistance of (TMTSF)₂PF₆ under ambient pressure (showing a metal semiconductor transition at 12 K) and under 12 kbar with a highly conducting state stable down to very low temperature.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. The phase diagram (temperature versus pressure) of (TMTSF)₂PF₆. The various points on the superconducting transition line come from the data obtained at Orsay ▲, Bell Labs. ● and IBM □.</figcaption></figure>

the SDW state at low temperature in that pressure
regime [38].

As shown in fig. 6, the critical temperature for
superconduction is strongly pressure dependent:
∂ ln T_c/∂P ≈ -7% kbar⁻¹ at P = 11 kbar [39].
However, the pressure dependences of the band
parameters cannot explain this large pressure
coefficient. The ambient temperature Seebeck
coefficient which does not vary significantly be-
tween 1 atm and 12 kbar and the measurement of
the 300 K conductivity anisotropy σ∥/σ⊥ ≈ (t∥/t⊥)²
which has been successful without sample break-
ing in (TMTSF)₂NO₃ up to 12 kbar [40] show that
neither t∥ nor t⊥ increase by more than 10% or so
under a pressure of 12 kbar.

The superconducting state of (TMTSF)₂X salts is characterized by a diamagnetic state [41] and magnetic flux expulsion [42], with a field dependence of the magnetization which reveals a type-II behaviour.

Magnetization curves in very low fields in-
dicate that field penetration into the supercon-
ducting state occurs already at a very low am-
plitude of the perpendicular applied field. In
(TMTSF)₂ClO₄, the only salt of the (TMTSF)₂X
<figure><img src="image_8.png" /><figcaption>Fig. 7. Supraconductive transition in (TMTSF)₂PF₆ under a pressure of 12 kbar, detected by resistance measurements (left) and a.c.-susceptibility with a comparison with a Niobium marker sample.</figcaption></figure>

<figure><img src="image_9.png" /></figure>

series in which the superconducting ground state is stable under ambient pressure, the lower critical field $H_{c1}^{\perp}$ is likely to be smaller than 50 mGs at 50 mK [43], fig. 8. Easy field penetration is however expected for loosely coupled chains. The upper critical field $H_{c2}$ is measured by the field at which the resistivity recovers its value just above $T_c$. The angular dependence reveals a very pronounced anisotropy of the critical field in the plane perpendicular to the stacking axis. For example, in (TMTSF)₂AsF₆ the ratio $H_{c2}^{\parallel b^*}/H_{c2}^{\parallel c^*}$ is equal to $15 \pm 2$ under 9.5 and 11 kbar [38], fig. 9. This anisotropy of $H_{c2}^{\perp}$ reveals a band parameter anisotropy along the transverse directions. Within the framework of the Landau-Ginzburg theory for the superconducting state below $T_c$ with open Fermi surfaces, the anisotropy of the coherence length and band parameter are equal [44]. Therefore, as far as (TMTSF)₂AsF₆ is concerned $t_{\perp}^{b^*}/t_{\perp}^{c^*} = 15 \pm 2$. The accurate measure of the anisotropy between the stacking axis direction and the transverse direc-

tions is hard to reach via critical fields experiments, since it requires an alignment of the sample with the external field which is very difficult to achieve with small crystals. Optical reflectance experiments have been probably more reliable. The anisotropy of the plasma edge leads to $t_{\perp}^{\parallel}/t_{\perp}^{\perp*} = 30$ in (TMTSF)₂PF₆ at 25 K under ambient pressure [21]. Consequently, the band parameters of the (TMTSF)₂PF₆ and (TMTSF)₂AsF₆ structures are within the ratios $t_{\perp}^{\parallel}:t_{\perp}^{\perp*}:t_{\perp}^{c^*} = 1, 1/30, 1/450$, respectively, with an anisotropy independent of pressure [40].

Superconductivity has been found in several other members of the (TMTSF)₂X family, namely X = TaF₆, SbF₆, ReO₄ [19, 18]. In addition, recent experiments show that superconductivity can be found in the sulfur analogue series, (TMTTF)₂X, with X = Br [45].

At 22 kbar, (TMTTF)₂Br undergoes a metal to insulator transition at 5 K, with a resistance ratio $R(300 \text{ K})/R(5 \text{ K}) = 16$, but below 25 kbar a transition towards a superconducting state is observed.
<figure><img src="image_10.png" /><figcaption>Fig. 8. Field dependence of the magnetization in (TMTSF)₂ClO₄ at various temperatures as measured by a SQUID technique (after ref. 43). The dashed line represents the variation of the diamagnetic shielding versus magnetic field at T = 0.2 K.</figcaption></figure>

ved at 3 K, as shown by a sharp drop of the resistance and the effect of the magnetic field, fig. 10. Therefore, superconductivity of organic molecules is not restricted to a single family of molecules containing selenium heteroatoms. It is likely to be a very general property which can be observed in most 2 to 1 cation radical salts. The superconductivity of organic conductors has also been studied via tunneling spectroscopy, a technique which has been widely used to derive quantities such as the gap in the quasi-particle density of states in metallic superconductors.

As far as (TMTSF)₂PF₆ is concerned the Schottky barrier technique has been used with some success [46]. Schottky junctions are pre-

<figure><img src="image_11.png" /><figcaption>Fig. 9. Temperature dependence of the Hc₂ critical field of (TMTSF)₂AsF₆ under 11 kbar derived from resistive measurements (after ref. 38) with H along *b*\* or *c*\*.</figcaption></figure>

pared by evaporating tellurium doped GaSb ($N_d > 3 \times 10^{18} \text{cm}^{-3}$) on a natural face of a (TMTSF)₂PF₆ single crystal.

After pressurization and cooling, the differential resistance of the junction is studied versus

<figure><img src="image_12.png" /><figcaption>Fig. 10. Superconductivity in (TMTTF)₂Br under a pressure of 25 kbar. The magnetic field is applied along the transverse direction. The finite resistance in the superconducting state is due to non-superconducting breaks in the sample (after ref. 45).</figcaption></figure>
the bias voltage. The large resistance maximum at zero bias, together with the two minima observed on each side of the characteristics, point out the existence of a gap in the quasi-particle density of states, fig. 11. The recording on fig. 11 has been performed under 11 kbar, at $T = 50$ mK. Following the traditional interpretation of the tunneling data [47] the pairing energy $2\Delta$ in fig. 11 amounts to 3.6 mV (40 K), i.e. about 40 times the critical temperature for $(TMTSF)_2PF_6$ at 11 kbar.

At higher temperatures, namely $T > T_3$, the amplitude of the zero bias resistance maximum decreases steadily, but remains clearly visible up to about 15 K. A large magnetic field applied in a direction perpendicular to the stacking axis removes the large zero-bias resistance peak, fig. 12.

Results such as those displayed in fig. 11 have

<figure><img src="image_13.png" /><figcaption>Fig. 11. The tunneling characteristics of the $(TMTSF)_2PF_6$-N/GaSb Schottky barrier at $T = 50$ mK under $P = 11$ kbar.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 12. Temperature dependence of the zero-bias tunnel resistance with a modulation current of $10^{-7}$ A and magnetic field dependence at $T = 50$ mK with a modulation current of $5 \times 10^{-9}$ A.</figcaption></figure>

been interpreted by the opening of a gap in the quasi-particle density of states due to the formation of superconducting pairs in $(TMTSF)_2PF_6$. Electron tunneling data suggest that the gap of $2\Delta = 40$ K is not related to the establishment of a 3-D superconducting state below $T_3$, but rather to the onset of very large intrachain pairing up to $T_1$.

Since between $T_1$ and $T_3$ only the expectation value of the amplitude of the order parameter is large but the phase itself is still fluctuating, it is probably more appropriate to speak of a pseudo-gap of amplitude $2\Delta$ rather than of a real gap [48].

Schottky junctions performed with $(TMTSF)_2ClO_4$ [49] exhibit a $dV/dI$ characteristic with a pseudo-gap $2\Delta \approx 4$ mV (45 K).
In a large number of junctions the tunneling data display a behaviour different from that shown in fig. 11. Instead of a zero-bias resistance maximum with two resistance minima separated by 2Δ, typical of electron tunneling between a superconductor and a conductor in the normal state, i.e. S-I-N tunneling, a minimum of resistance at zero bias is observed quite often with two sets of resistance anomalies separated by 2Δ and 4Δ [50]. This is illustrated by the state 2 of a junction in fig. 13. State 2 can be understood in terms of a junction exhibiting S-I-S quasi-particle tunneling between two superconducting domains of the organic superconductor, separated by a weak insulating barrier. The resistance minimum at V=0 shows that a superconducting current is able to flow between two superconducting domains. The application of a magnetic field of a few kOe suppresses the superconducting current and decreases the amplitude of the anomalies at ±2Δ.

In one junction of relatively low resistance

<figure><img src="image_15.png" /></figure>

Fig. 13. The two states observed with (TMTSF)₂PF₆-GaSb junctions. State 1 corresponds to the tunneling of electrons through a S-I-N contact. The distance 2Δ between resistance minima provides approximately the amplitude of the pseudogap of the 1-D fluctuating superconductor. State 2 shows resistance extrema at ±Δ and ±2Δ corresponding to S-I-N and S-I-S tunneling occurring in parallel at the junction. The large resistance dip at zero bias is the sign of a Josephson current flowing through the junction. This resistance dip is suppressed by the application of a magnetic field.

($\approx 10\Omega$) at high temperature, the zero voltage contact resistance dropped to zero below 12 K. fig. 14. This result seems to indicate that a superconducting short circuit sets in at the barrier. As a matter of fact, the strong tendency of (TMTSF)₂PF₆ towards superconductivity can be stabilized by allowing electron pairs to jump from one chain to its neighbour through local interchain bridges.

The theory of the superconductivity in 1-D conductors in the presence of randomly distributed interchain cross-links [51] shows that a concentration of 4% per molecule of cross-links (with $t_1$ (local) = $t_\parallel$) is large enough to raise $T_c$, given by eq. (1), up to the neighbourhood of $T_1$.

The temperature of 12 K, below which the (TMTSF)₂PF₆-GaSb contact becomes superconducting, is very close to the 1-D mean-field temperature derived from the weak coupling limit BCS relation, namely $2Δ/kT_c = 3.5$. This agreement is probably not very significant, but order of magnitude wise these tunneling data show that the onset of superconducting pairing along each chain occurs in a temperature domain which is at least ten times larger than the temperature where 3-D ordering takes place in the bulk of a crystal.

Cross-linking can be achieved by the diffusion of foreign atoms (for example antimony) between organic stacks at the interface between the

<figure><img src="image_16.png" /></figure>

Fig. 14. The zero-bias resistance of a (TMTSF)₂PF₆-GaSb contact (resistance at the centre of the dip in the state 2 of fig. 13) going to zero below 12 K which is interpreted by the three-dimensional stabilization of a superconducting state via chain cross-linking in the vicinity of the barrier.
(TMTSF)₂PF₆ crystal and the evaporated Ga-Sb layer [50]. Point contact junctions with (TMTSF)₂ClO₄ display similar effects [49]. The large zero-bias resistance dip is strongly affected by microwave irradiation, as shown in fig. 15, at T = 3.9 K, i.e. a temperature which is three times bigger than the critical temperature of the bulk of sample. Data in fig. 15 provide serious indications in favour of the existence of a Josephson effect. Several studies show that (TMTSF)₂ClO₄ junction characteristics are drastically affected by radio-frequency or microwave irradiations up to about 26 K or so [49]. Moreover, a TTF-TCNQ test junction with similar characteristics does not exhibit any sensitivity to a microwave irradiation up to a power level as large as 10 mW, at temperatures between 53 and 35 K.

<figure><img src="image_17.png" /><figcaption>Fig. 15. Differential resistance of a (TMTSF)₂ClO₄-chrysocal point contact junction located in an EPR microwave cavity (ν = 9.6 GHz), irradiation at 3.9 K (a) and at 25 K (b).</figcaption></figure>

Thermal conductivity experiments performed on (TMTSF)₂PF₆ at 12 kbar [52] show a significant drop in the conductance, beginning around 40 K. The electronic contribution to the thermal conductivity predominates over the phonon contribution since the Wiedeman-Franz law is fairly well obeyed, both σ and κ increasing with the same rate under pressure at high temperature. The behaviour of the thermal conductivity at low temperature is thus an additional argument in favour of a pseudo-gap opening below 40 K. In the presence of a gap (or pseudo-gap) at the Fermi level, the density of particles able to contribute to the conduction is likely to decrease with decreasing temperatures. This is, however, in striking contrast with the huge enhancement of the conduction observed experimentally at low temperature either in (TMTSF)₂PF₆ under pressure [44] or even in (TMTSF)₂ClO₄ at ambient pressure [20]. As was suggested following the study of TMTSF-DMTCNQ, the formation of fluctuating pairs can contribute to the conduction even at temperatures much larger than T₃ in Q-1-D conductors [11, 44].

The excess conduction (or paraconduction) is proportional to ⟨|Δ|²⟩, i.e. it becomes negligible above T_c in most 3-D superconductors. But the problem is quite different whenever the volume of a fluctuating domain is reduced by a factor (d⊥/ξ‖)², as in the 1-D fluctuation regime (ξ⊥ < d⊥) of a Q-1-D superconductor [44].

The paraconductivity of a Q-1-D superconductor worked out by Schulz [53] gives the following result:

$$ \sigma'_{\parallel} = \frac{\pi e^2}{16 d_{\perp}^2} \xi_{\parallel}(0) e^{-3/2}, \quad (2) $$

where ε = (T - T₁)/T₁ and ξₗ(0) is the zero temperature Landau-Ginzburg coherence length. Besides supercurrents along the chains in the fluctuating regime, transverse supercurrents are likely to occur between adjacent chains with well-developed order parameters. As the likeli-
hood of this occurrence decreases with increasing temperature, $\sigma'_\perp$ decreases in temperature faster than $\sigma'_\parallel$, i.e. $\sigma'_\perp \approx \epsilon^{-5/2}$. Consequently, the anisotropy of paraconductivity varies linearly with temperature above $T_1$. With $\xi_\parallel(0)/d_\perp \ge 50$, $\sigma'_\parallel$ can easily exceed $10^4 (\Omega cm)^{-1}$ at temperatures as large as 25 K.

Following the previous estimate, the paraconductivity is largely dominant at helium temperature and consequently is likely to be suppressed by (i) the application of a magnetic field along a transverse direction, and (ii) a low concentration of magnetic defects created by irradiation [12].

In these concluding paragraphs we summarize the most significant experimental results of organic superconductivity and attempt to suggest some guidelines towards an interpretation of the phenomena.

The properties of the superconductivity which occurs in the conducting cation-radical salts $(TMTSF)_2X$ and $(TMTTF)_2X$ is strongly influenced by low dimensionality. In this respect the tunneling data have answered crucial key questions. Short-range superconducting pairing takes place along the chains (without interchain coherence) at temperatures as high as 15 K. The impact of this short-range pairing manifests itself on the quasi-particle density of states by the observation of a pseudo-gap at the Fermi level below 15 K or so in $(TMTSF)_2PF_6$ under pressure. Moreover, the ratio $2\Delta/kT_c$ of about 40 for $(TMTSF)_2PF_6$ under 11 kbar and $(TMTSF)_2ClO_4$ under ambient pressure indicates that the actual critical temperature $T_c$, below which both a zero resistance state and magnetic flux expulsion are observed, is not determined solely by the strength of the superconducting pairing within each chain. The superconducting phase transition occurs when coherence is established between the phases of the order parameters on adjacent chains. As far as superconductivity is concerned, the transverse couplings which matter most are on the one hand the so-called transverse tunneling coupling $t_\perp$ which

allows an electron to travel from one chain to its neighbour, and on the other hand the Josephson coupling $t_\perp^2/t_\parallel$ which can transfer an electron pair between the chains.

Admittedly the transverse coupling in the $(TMTSF)_2X$ structure is stronger along the $b^*$ direction which corresponds to short Se-Se interchain distances than along $c^*$. However, the anisotropy of the plasma frequency edge between the $a$ and $b^*$ axes leads to a longitudinal coupling $t_\parallel$ about 30 times bigger than $t_\perp^{b*}$ [21].

Several experiments have shown that one may be able to take advantage of the existence of strong superconducting fluctuations at high temperature. The observation of a contact between $(TMTSF)_2PF_6$ and an evaporated Ga-Sb film becoming superconducting below 12 K has been interpreted as a local increase of the 3-D ordering temperature at the interface through randomly diffused interchain cross-links. The response of $(TMTSF)_2ClO_4$-GaSb junctions to a weak 10 GHz irradiation suggests that the stabilization of a superconducting state via enhanced interchain coupling is potentially feasible up to 26 K, or even to higher temperatures!

The high-temperature 1-D superconducting ordering controls the behaviour of the transport properties below 40 K:

(i) the conduction of pairing origin which becomes dominant over the single particle conductivity below about 40 K, can be suppressed by the application of a magnetic field or by irradiation; and

(ii) the thermal conduction coming from the electrons starts to drop significantly below 40 K.

The guide towards an interpretation is therefore the pronounced 1-D behaviour accompanied by a large fluctuation temperature regime observed between $T_c$ and $\approx 10T_c$. A major experimental piece of information is the existence of a SDW state at low temperature next to superconductivity. It is very likely that the stability of the dielectric SDW state is favoured by the presence of Umklapp scattering of two electrons from one side of the Fermi surface to
the other. All theories seem to agree on the important role played by Umklapp scattering on the nature of the ground state [54, 55].

Under ambient pressure the dimerization along the *a*-axis (and consequently the amplitude of the Umklapp scattering) appears to be smaller in $(TMTSF)_2ClO_4$, where superconductivity is observed, than in $(TMTSF)_2PF_6$, where a dielectric SDW state is the stable ground state. However, it is only with a structure determination of $(TMTSF)_2PF_6$ under pressure that the role of Umklapp scattering will be more firmly established. Is the interaction between the electrons leading to the superconducting pairing mediated by the phonons or not? We tend to favour a non-phonon mediated interaction for the following reasons: (i) the interplay between superconductivity and a magnetic state which suggests the presence of dominant Coulomb interactions; (ii) the enhancement of the spin susceptibility at high temperature and its non-activated temperature dependence which agrees with a positive $g_1$; and (iii) the observation of (weak) 1-D $4k_F$ X-ray diffuse scattering at high temperature in $(TMTSF)_2PF_6$, $(TMTSF)_2ClO_4$ and $ReO_4$ [56].

However, the role played by the retarded electron-phonon interactions versus the non-retarded electron-electron interactions awaits further investigations. Finally, the superconductivity of organic conductors appears as a new opening in condensed matter physics. The discovery of superconductivity in sulfur-based organic molecules shows that this phenomenon is probably not restricted to a small number of molecules.

The existence of high-temperature fluctuations and the possibility of $T_c$ enhancement via chain cross-linking open up vast domains of investigation for the near future.

## Acknowledgments

I wish to acknowledge the very fruitful cooperation which I have had (and still have)

with many of my colleagues: K. Bechgaard at Copenhagen, J.M. Fabre and L. Giral at Montpellier as well as the members of experimental groups at Orsay working on organic conductors. I am very grateful to J. Friedel, S. Barišić and H.J. Schulz who have strongly influenced the development of the theory in the field of one-dimensional conductors and superconductors.

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