# A Survey of the Physics of Organic Conductors and Superconductors

Denis Jerome, Claude Bourbonnais, F. Creuzet

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Denis Jerome, Claude Bourbonnais, F. Creuzet. A Survey of the Physics of Organic Conductors and Superconductors. Physica Scripta, 1989. hal-05000082

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# A Survey of the Physics of Organic Conductors and Superconductors

D. Jérôme, F. Creuzet and C. Bourbonnais*

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

Received August 8, 1988; accepted September 8, 1988

## Abstract

Low dimensional organic conductors exhibit a wide variety of physical properties which is exemplified by the observation of ground states such as Peierls, spin-Peierls, SDW and Superconducting states. We survey the experimental situation with a special emphasis on the family of the one-chain conductors to which the famous (TMTCF)₂X series C = S, Se belongs.

Although the band picture seems to be a reasonable starting point for the understanding of these materials, interactions such as electron-phonon and electron-electron as well as the amplitude of the Umklapp scattering term and the size of the interchain tunneling coupling must all be taken into account. The amplitude of electron-electron interactions can be derived from a detailed analysis of the temperature dependence of the nuclear spin-lattice relaxation rate data. Coulomb interactions of the order of the bandwidth are found.

The interplay between magnetism and superconductivity is governed by the interchain overlap which can be varied under pressure. The possibility of a pairing mechanism based on the interchain exchange of 2k<sub>F</sub> spin fluctuations is strongly supported by experiments. In addition, a wealth of experimental features suggest the coexistence in the precursor (1-D) regime above long range ordering (magnetic or superconducting) of fluctuations simultaneously magnetic and superconducting.

The very fast increase of T<sub>c</sub> for organic superconductors which has been observed in the last eight years is very stimulating for the future development of this field.

## 1. Introduction

The history of superconductivity shows that the way to organic superconductors has not been fast and easy.

The suggestion of Little [1] in 1964 of an exciton mechanism based on the electron polarization of side-branched molecules on conducting spines has certainly boosted the search of organic conductors. However, seven years of research have been necessary between the publication of the first organic solid, (TTF-TCNQ), to possess a high and metal-like conductivity in a wide temperature domain [2, 3] and the discovery of superconductivity in (TMTSF)₂PF₆ under high pressure [4].

Superconductivity in these materials has been discovered in 1980, and soon after this finding the study of (TMTSF)₂PF₆ under pressure revealed the existence of a very remarkable phase diagram with a common border between superconductivity and magnetism. Hence, the likely existence of a non-conventional mechanism of superconductivity influenced by both the low dimensionality of the conductor and incipient antiferromagnetism was suggested [5].

Thus, a large fraction of the studies performed on organic conductors over the past decade has been devoted to the establishment of a theoretical framework for the various instabilities displayed by (TMTTF-TMTSF)₂X compounds

at low temperature and to the remarkable interplay between magnetism and superconductivity.

A survey of the effort is provided in this article.

## 2. Materials presentation

In conducting cation radical salts such as D₂⁺X⁻ the lattice periodicity along the stacking direction is determined by the anion spacing a. Consequently, the 3D unit cell accommodates two organic molecules (i.e., one hole per unit cell). The energy band formed by the overlap of the HOMO of these molecules is thus half-filled and the Fermi wave vector amounts to 2k<sub>F</sub> = π/a. Furthermore, the size of the gap separating the partially filled conduction band from the lower fully occupied band is related to the amplitude of the dimerization of the organic molecules along the a-axis. The amount of dimerization may vary from salts to salts, but it is usually more pronounced in (TMTTF)₂X compounds (Δd/d ≈ 2.8%) in (TMTTF)₂PF₆) than in the selenium analog series (Δd/d ≈ 0.8%) [6]. Furthermore, for two materials which will be discussed in some details in the present article (TMTSF)₂ClO₄ and (cyclo-penta perylene)₂PF₆, (CPP)₂PF₆ [7, 8], this dimerization is practically non-observable. The latter compound, exhibits a squel stacking of the organic molecules. This structure is thus different from the zig-zag stacking of the (TMTTF-TMTSF)₂X series, Fig. 1.

Band parameters derived from optical reflectance measurements are respectively 4t<sub>||</sub> = 0.8, 1 and 0.8 eV in (TMTTF)₂PF₆, ClO₄ and (BEDT-TTF)₂I₃. Apparently the band is larger for arene compounds since 4t<sub>||</sub> ≈ 2 eV has been reported in (fluoranthene)₂PF₆ [9]. The band structure anisotropy is small (≈ 3) for (BEDT-TTF)₂I₃ [10], intermediate (≈ 10) in (TMTSF)₂X [11] and presumably larger in the more 1-D arene salts.

## 3. One dimensional physics

A major problem arising in the interpretation of the physical properties of 1-D conductors is the determination of the actual dimensionality of the electronic properties. As we shall see in the following, the band structure anisotropy may seriously underestimate the 1-D character when electrons are interacting.

A well established characteristic feature of 1-D electrons is the mixture between Peierls and Cooper channels [12]. The diagrammatic expansion of the Cooper pair response for a 1-D interacting electron gas contains contributions coming from density fluctuations (Peierls or SDW) and vice-versa. At low temperature both channels diverge at the same rate and the coupling between them cannot be neglected. In a purely 1-D

<footnote>* Also at University of Sherbrooke, Sherbrooke Québec, Canada.</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. Side view of the structure of organic conductors, zig-zag stacking in (TMTSF)₂X (left), uniform stacking in (CPP)₂PF₆ (right).</figcaption></figure>

system, the diagram showing the most divergent correlations for given values of the electron-electron interactions is obtained from renormalization group theory. This is the well-known g-ology diagram, Fig. 2. In this diagram, interactions are parametrized by three constants $g_1, g_2, g_3$. They represent respectively e-e interactions with momentum transfer $2k_F$, 0 and $4k_F$. The latter process involves the transfer of two electrons from one side of the flat Fermi surface to the other side at a distance $2k_F$. Such a scattering is allowed only if $4k_F$ is a reciprocal lattice vector (Umklapp scattering for a half-filled band). It is the anionic environment which is responsible for the dimerization. The amplitude of the Umklapp scattering term $g_3$ is thus related to the size of the dimerization gap $\Delta(4k_F)$. According to Barisic and Brazovskii [13] the following relation between $g_3$ and $g_1$ holds: $g_3 = g_1 \Delta(4k_F)/E_F$.

Once the mixture between channels is properly taken into account the 1-D divergence of the various correlation functions follows a power law at low temperature with non-universal exponents which depend on the coupling constants [14]. Pair correlations and density fluctuations are more divergent when $g_1 > 2g_2 + g_3$ and $g_1 < 2g_2 + g_3$ respectively. The existence of a power law divergence of the 1-D response functions in a wide temperature domain is a signature of 1-D physics.

In real 1-D conductors the theoretical 1-D situation of flat Fermi surfaces is never truly justified at low temperatures below a certain cross-over region (characterized by the cross-over temperature $T_{x1}$ which is related to the non-zero transverse overlap $t_\perp$). $T_{x1}$ is thus the temperature below which 1-D physics is no longer applicable. Hence, the Fermi surface curvature recovers its entire meaning below $T_{x1}$ with a concomitant decoupling of pairing and density correlations [15].

If long range SDW's order at a temperature $T_{SDW} < T_{x1}$ the situation is reminiscent of the well known Overhauser mechanism in which the wave vector $Q$ of the spin modulation corresponds to the vector providing the best nesting of the

$3$-D surface. For this situation, 1-D physics and the accompanying power law divergences are no longer followed below $T_{x1}$ and a 2D(3D) Fermi liquid model prevails between $T_{x1}$ and $T_{SDW}$. It is an important question for a given 1D conductor to derive the value of $T_{x1}$ from experiments.

On the basis of band structure parameters [6] $T_{x1}$ should amount to $\approx 100$ K for the (TMTSF)₂X series. For such a situation 1-D physics (in particular power law divergences) should not be observable below 100 K. However, as we shall see in the rest of this review, power laws are observed experimentally down to about 10 K. This means that the derivation of $T_{x1}$ from a model of non-interacting quasi-1-D electrons can be misleading. The question of the width of the 1-D regime is more complex and requires taking into account electron-electron interactions [16].

The next important problem is the evaluation of the parameters characterizing the interaction of electrons among themselves and with the lattice.

### 4. Electron-phonon versus coulombic interactions

The determination of the respective role of electron-phonon and electron-electron interactions in 1-D conductors is a key issue for the understanding of the physical properties of these materials. This is of particular importance since what has made 1-D conductors so popular is the discovery of the Peierls transition in the linear platinum chain compound (KCP) [17] due a joint effect of low dimensionality and el-ph interaction. Moverover, it is important to determine whether superconductivity of materials such as (TMTSF)₂X involves a phonon mediated interaction or an other kind of interaction possibly non-phonon mediated.

In the (TMTTF-TMTSF)₂X series $2k_F$ CDW scattering is rarely observed. Only in (TMTTF)₂PF₆, $2k_F$ scattering develops below 75 K with a temperature dependence $\chi_{CDW}(2k_F, T) \approx T^{-1}$ [17]. This is the precursor regime above the onset of a spin-Peierls long range order at 20 K. In the selenium family, the weak $2k_F$ CDW response which becomes visible below 200 K levels off and vanishes below 50 K when $2k_F$ SDW correlations start to grow [18] (vide-infra).

Quite a different situation is encountered in the 1-D conductor (CPP)₂PF₆ in which electron-phonon interactions play a major role. In this material diffuse scattering at $2k_F$ is observed below room temperature and a 3-D condensation occurs at 150 K [8]. This behaviour is very much what is observed for the Peierls transition observed in KCP or NbSe₃ when the electron-phonon coupling constant is larger than electron-electron couplings ($\lambda > g_t$) [19].

As a matter of facts the large bandwidth of arene salts provides a favourable situation for the predominance of $\lambda$ over $g_t$ since $\lambda \approx t_\parallel$ whereas $g_t \approx t_\parallel^{-1}$ in the tight binding approximation [19].

Umklapp scattering is likely to be unimportant in (CPP)₂PF₆ materials as the regular squel stacking of the organic molecules shows no sign of dimerization. The conduction band is thus effectively 1/4-filled instead of 1/2-filled in strongly dimerized systems. The quarter band filling of (CPP)₂PF₆ no longer inhibits the development of the coupled $2k_F$ CDW-PLD at low temperature.

The precursor regime is clearly observable above $T_P$ on the temperature dependence of the resistivity Fig. 3. Under pressure both $T_P$ (identified by the maximum of $d \log \rho/d(1/T)$)

<figure><img src="image_4.png" /><figcaption>Fig. 2. g-ology phase diagram.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Temperature dependence of the resistivity of two 1-D conductors under pressure ($TMTTF_2PF_6$), left, the spin-Peierls ground state becomes SDW above ~10 kbar. ($CPP_2PF_6$), right, the Peierls ground state is hardly affected under pressure (various curves correspond to different pressures from 1 bar to 12 kbar (from right to left)).</figcaption></figure>

and the width of the precursor regime decrease. This may be attributed to an increase in the 3-D character. Unlike TTF-TCNQ, no fluctuating contribution to the conductivity is observed in the 1-D precursor regime since the wave vector of the fluctuating CDW's is commensurate (×2) with the underlying lattice. The upturn of the resistivity between 300 and 150 K is the result of the Peierls pseudo-gap opening. As shown on Fig. 3. The ($TMTTF-TMTSF_2X$) series behaves quite differently from the arene materials. High pressure can induce a change in the nature of the ground state Fig. 4. A transition from a spin-Peierls to a SDW ground state has been detected around 10 kbar in ($TMTTF_2PF_6$) via NMR experiments [20]. Superconductivity is stabilized by a pressure

of 9 kbar in the compound ($TMTSF_2PF_6$) which exhibits a SDW ground state under ambient pressure. In addition, signs of superconductivity have also been reported in ($TMTTF_2Br$) below 4 K under 25 kbar [21]. An interesting experimental feature displayed by ($TMTTF_2X$)-like salts is the loss in the charge degree of freedom which is observed below $T_c$ and which is not accompanied by any loss of the spin degree of freedom as shown by the lack of activation for the spin susceptibility and the temperature dependence of the relaxation rate, Fig. 5.

This charge localization has been attributed by Emery et al. [23] to the development of a $4k_F$ localization enhanced by $g_3$ terms with no breaking of the symmetry. The $g_3$ scattering (i.e., dimerization) plays an essential role for the determination of the nature of the ground state. Large values of $g_3$ enhance the occurrence of a strong $4k_F$ localization with a subsequent spin Peierls ordering at low temperature. For intermediate values of $g_3$, the $4k_F$ localization does not develop and SDW becomes the stable ground state (e.g., ($TMTSF_2PF_6$) at 1 atm). In agreement with the role of $g_3$ in the theory, structural studies performed under pressure have clearly shown a pressure induced decrease of the dimerization (or of $g_3$) [6].

For materials which undergo a superconducting transition at low temperature the absence of diffuse scattering at $2k_F$ suggests that $\lambda$ is not pertinent, namely $\lambda < g_1$. In addition, the absence of $4k_F$ localization means that $g_3 \ll g_1$, $g_2$.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Generalized phase diagram P-T for the ($TMTTF-TMTSF_2X$) series.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. Temperature dependence of $T_1^{-1}(^{13}C)$ and conductivity of ($TMTTF_2PF_6$) at 1 bar.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 6. Temperature dependence of the spin susceptibility and of $[T_1 T_s^2]^{-1}$ in (TMTSF)₂ClO₄.</figcaption></figure>

Therefore an important task is the derivation of the coupling constants $g_1$ and $g_2$ from susceptibility and NMR data.

<figure><img src="image_9.png" /><figcaption>Fig. 7. Temperature dependence of $T_1^{-1}$ ($^{77}$Se) in (TMTSF)₂ClO₄. The agreement between the theory and experiments (full dots) is considerably improved by taking into account the effect of thermal dilation above 80 K (see Ref. [32]).</figcaption></figure>

## 5. Coulombic coupling constants

The temperature dependence of the susceptibility of (TMTSF)₂ClO₄ and related materials in the (TMTTF-TMTSF)₂X series implies a positive value of $g_1$ since within the g-ology model $\chi_s(T)$ reads [24]:

$$\chi_s(T) = \chi_s(0)(1 + g_1(T)/2\pi v_F^*)$$

where $\chi_s(0) = \chi_{band}/(1 - g_1/2\pi v_F)$ and $v_F(v_F^*)$ are the bare (renormalized) spin excitation velocities.

The renormalized $g_1(T)$ becomes:

$$g_1(T) = g_1/(1 + g_1/\pi v_F^* \ln E_F/T)$$

The experimental value of the ratio $\chi_s(0)/\chi_{band} = 2$ [25] leads to $g_1/2\pi v_F \approx 0.5$.

The interpretation of the temperature dependence of the nuclear spin-lattice relaxation induced by the modulation of the hyperfine interaction allows an other derivation of the coupling constants [26].

$T_1^{-1}$ involves a summation of the imaginary part of the SDW response over all $q$-vectors [27]. For a 1D conductor, the summation over $q$ is restricted to the dominant contributions at $q \approx 0, 2k_F$ [28]. Hence the relaxation rate reads:

$$(TT_1)^{-1} = A\chi_{SDW}(2k_F, T) + B\chi_s^2(T). \quad (1)$$

Equation (1) shows that a violation of the law $T_1 T_s^2 = \text{const}$ (the Korringa law) is expected whenever the $2k_F$ SDW response function is divergent. Such a situation occurs at low temperature in the upper right part of the g-ology diagram, Fig. 6.

The experimental data of $^{77}$Se relaxation in (TMTSF)₂ClO₄ reveal a clear-cut violation of the Korringa law below 50 K, Fig. 6. Below 30 K, $T_1^{-1}$ becomes temperature independent down to ≈ 6 K. A "Korringa regime" is recovered at lower temperatures. The temperature dependence of $T_1^{-1}$ at low temperature allows to rule out relaxation induced by paramagnetic impurities. So, it becomes clear that the violation of the Korringa law is due to the divergence of the SDW response function. An inspection of the $T_1^{-1}$ data below 30 K shows that a power law $T^{-\gamma}$ with $\gamma \approx 0.80$ provides a reasonable fit.

The experimental finding of a power law dependence for

$\chi_{SDW}(2k_F, T)$ at low temperature is a serious argument in favour of the 1-D character of the spin excitations.

The divergence of $\chi_{SDW}(2k_F, T)$ is frozen in below 8 K. A 2D(3D) Fermi liquid regime is achieved and a Korringa-like regime is recovered (see the behaviour of $T_1^{-1}$ below 6 K in the insert of Fig. 7. The temperature region around 8 K marks the cross-over between 1-D and 2-D behaviours.

The relation between the power law exponent and the coupling constant $g_1, g_2$ and $g_3$ is model dependent. Within the weak coupling limit the power law exponent of the $2k_F$ spin susceptibility becomes $\gamma_{1D} = 2g_2 - g_1/2\pi v_F^*$, assuming $g_3$ to be negligible. A very good fit to the data is obtained at low temperature when $\chi_{SDW}(2k_F, T)$ is dominant (see the insert of Fig. 7) with $\gamma_{1D} = 0.80, g_1/2\pi v_F^* = 0.9, g_2/2\pi v_F^* = 0.85, E_F^* = 500$ K and a bare transverse coupling $t_\perp/E_F = 1/15$. The values derived for the coupling constants are admittedly rather large; they correspond to an intermediate coupling regime ($U \approx 4t_\perp$). Although the weak coupling approximation may not be entirely justified we feel that the above derivation provides a qualitative indication for the strength of the coupling parameters.

The dashed and dashed-dotted lines display respectively the temperature dependence of the $q = 2k_F$ and $q = 0$ contributions. At 300 K the $q = 2k_F$ contribution is quite small compared to $T_1^{-1}(q = 0)$ and there exists very little hope to be able to measure it directly via very high-field relaxation measurements.

The deviation between the fit and the experimental data above 100 K can be considerably reduced once it is realised that the model provides a temperature dependence at constant volume whereas the data are taken under constant pressure. This point has been emphasized for the transport properties [29, 30] and the susceptibility [31] of TTF-TCNQ. The susceptibility of (TMTSF)₂X (and thus $T_1^{-1}$) is also pressure (volume) dependent with a pressure coefficient $\delta \log \chi_s/\delta P = -3\%$ kbar⁻¹ at 300 K [25]. The effect of the thermal contraction on the a-axis between 300 and 100 K is equivalent to the application of a pressure of 4–5 kbar at 300 K. Consequently, the experimental temperature dependence of $\chi_s^2(T)$ (or $T_1^{-1}$) at constant volume (that of 100 K) should be than the one measured under constant pressure.
The correction of $T_1^{-1}$ data from constant pressure to constant volume amounts to a decrease of 25-30% at room temperature. Taking this effect into account improves remarkably the quality of the fit in the high temperature domain [32].

Stronger power law divergences have also been detected in $(TMTTF)_2PF_6$ when the holes are localized by $g_3$-enhanced correlations below 100 K ($\gamma_{1D} \approx 1$) [32]. On the other hand smaller exponents ($\gamma_{1D} \approx 0.7$) are found in the two-chain conductor TTF-[Ni(dmit)$_2$]$_2$ [33].

## 6. The cross-over regime around 8 K

In the previous section we have mentioned that $T_{x1}$ is about 8 K. How can we reconcile such a low value with the estimate of $\approx 100$ K based on band structure parameters? Bourbonnais et al. [16] have remarked that 1-D antiferromagnetic correlations (which have been observed experimentally) weaken the hopping of carriers between chain as they tend to form fluctuating e-e and e-h pairs on each chains. This effect can be viewed as a reduction (renormalization) of the interchain tunneling coupling $t_\perp$. The free-electron cross-over temperature $T_{x1}^0$ which is of the order of $t_\perp/\pi$ is thus renormalized down to:

$$T_{x1} = T_{x1}^0(t_\perp/E_F)^{\theta/1-\theta}$$

where $\theta$ is an exponent which depends on the 1-D power law divergence. Given $T_{x1} \approx 8$ K and $t_\perp/E_F \approx 0.1$ we derive $\theta \approx 1/4$ which is compatible with the size of the interactions $g_1$ and $g_2$. Clearly the SDW transition of $(TMTSF)_2PF_6$ between 12 and 8 K for the low pressure regime ($P < 5$ kbar) satisfies the condition $T_{SDW} > T_{x1}$. Thus, the 2D or 3D Overhauser mechanism which requires the existence of a well established 2D(3D) Fermi surface is not appropriate for this situation. Instead, Bourbonnais and Caron [34] have proposed that when $T_N$ is higher than $T_{x1}$ the necessary transverse interaction for the establishment of long range order comes from an interchain exchange (IEX) interaction in the 1-D regime which originates in the tunneling of an electron-hole pair between neighbouring chains.

In this case the 3-D susceptibility becomes:

$$\chi_{3D}(q, T) = \chi_{1D}(2k_F, T)/1 - J(q_\perp)\chi_{1D}(2k_F, T) \quad (2)$$

where $q_\perp = (2k_F, \pi/d, \pi/d)$ for an orthorombic lattice and $q_\perp = (\pi/d, \pi/d)$. $J(q_\perp)$ in eq. (2) is the interchain exchange (IEX) interaction.

It has been pointed out that the wave vector of the spin modulation does not allow to discriminate between the two models (Overhauser or IEX) [35]. As the IEX interaction amounts to a virtual interchain electron hop it is again the curvature of the hypothetical Fermi surface which is probed in this process. NMR analysis of the spin modulation of $(TMTSF)_2PF_6$ has indeed provided a modulation vector which is similar to the calculated best nesting vector of the free-electron Fermi surface. The behaviour of $T_1^{-1}$ corresponding to both situations for the onset of an SDW state ($T_{SDW} >$ or $< T_{x1}$) is displayed on Fig. 8.

For the field-induced stabilization of a SDW state [11] (a typical 2D effect) we clearly observe two regimes near $T_{SDW}$ where $T_1^{-1}$ experiences (i) a square root divergence in a narrow temperature domain and (ii) a broad temperature regime above $T_{x1} \approx 8$ K in which $T_1^{-1}$ is enhanced above the

<figure><img src="image_10.png" /><figcaption>Fig. 8. Behaviour of $T_1^{-1}$ for two different approaches to a SDW state. Left: the SDW state stabilized under a high magnetic field ($T_{SDW} < T_{x1}$). Right: the SDW state of $(TMTSF)_2PF_6$ in the low pressure regime ($T_{x1} > T_{SDW}$).</figcaption></figure>

Korringa value. This example provides a good illustration of the difference between a critical divergence which is restricted to the very vicinity of the transition and the large enhancement of $T_1^{-1}$ which results from the non-critical divergence of 1D antiferromagnetic correlations below 40 K.

The other situation $T_{SDW} > T_{x1}$ is exemplified by the behaviour of $(TMTSF)_2PF_6$ at $P = 5.5$ kbar where the enhancement of $T_1^{-1}$ observed above $T_{SDW}$ up to 30 K extends in a temperature regime too broad to be caused by 2D or 3D critical fluctuations. It can be attributed to the development of 1D-AF correlations.

## 7. Discussion and conclusion

In summary, NMR has provided a remarkable probe for the $2k_F$ spin susceptibility of low dimensional conductors. The observation of a power law divergence of $\chi(2k_F, T)$ below 40 K has been related to the growth of intra-chain AF correlations in a 1-D regime. The $T_1^{-1}$ temperature dependence suggests an extension of the 1-D character of the correlations down to a fairly low temperature ($T_{x1} \approx 6-8$ K). Below this cross-over domain when the material is conducting a 2D or 3D Fermi liquid description is recovered. A fit of the NMR data with a theory of nuclear relaxation leads to sizeable repulsive interactions for all members of the $(TMTTF-TMTSF)_2X$ family. In $(TMTSF)_2ClO_4$ for example they amount to $g_1/2\pi v_F^*, g_2/2\pi v_F^* \approx 0.8-0.9$.

In the low pressure regime of $(TMTSF)_2PF_6$ the SDW transition occurs above the Fermi surface cross-over temperature (i.e., in the 1-D regime). For such a situation the necessary transverse coupling is not related to the nesting of the 2D Fermi surface (which is not relevant at $T > T_{x1}$) but rather to an effective interchain exchange coupling originating in the transverse delocalization of the intrachain correlations via the finite value of $t_\perp$. The existence of a IEX coupling was well established for the case of intrachain localization due to a large $4k_F$ localization. Then, $J \approx (t_\perp/\Delta)^2$, where $\Delta$ is the localization gap due to strong in-chain repulsions. Bourbonnais [34] has shown that the exchange coupling remains finite even in the absence of localization (namely $\Delta < T$), thus $J \approx g_1^2(T_{x1}/T)^2$.

A side effect of this exchange interaction is the generation in the 1-D regime of an attractive pairing between electrons on different chains with opposite spins. Below $T_{x1}$ this attractive interaction could compete against the intrachain repulsion
<figure><img src="image_11.png" /><figcaption>Fig. 9. Time dependence of $T_c$ in superconducting oxides and organic superconductors.</figcaption></figure>

and is likely to become the driving force for superconductivity [35].

The present pairing mechanism relies strongly on the exchange of a $2k_F$ spin fluctuations between electrons on neighbouring chains. It is thus natural to suppose that the pairing efficiency is enhanced by the vicinity of a magnetically ordered state. In several respects, this mechanism supports the proposal made in 1981 of a pairing interaction boosted by SDW fluctuations [5].

We finally comment about some experimental consequences of the model:

(i) The superconducting gap is anisotropic $\Delta(k) = \Delta_0 \cos k_\perp d$ with lines of zeros at $k_\perp d = \pi/2$. The existing data of $^1$H relaxation in the superconducting state of (TMTSF)$_2$ClO$_4$ showing a power law dependence of $1/T_1$ and an anomaly at $T_c$ support the possibility for an anisotropic gap and a singlet pairing [36].

(ii) Scattering from non-magnetic impurities are likely to mix electron states at $k_\perp = 0$ with those around $k_\perp \approx \pi/2d$ with a concomitant decrease of the mean superconducting gap (and $T_c$) [37]. Indeed, organic superconductivity is known for its remarkable sensitivity to non-magnetic impurities [38].

(iii) Superconducting fluctuations are likely to coexist with AF correlations in the low temperature regime since the attractive pairing is generated in the 1-D regime. The growth of such fluctuations could explain first the emergence below 20 K of a zero frequency collective mode in the far-infrared reflectance spectra [39], secondly the anomalously large value of magnetoresistance observed up to $\approx 30$ K and the decrease of conductivity anisotropy below 40–50 K [40].

Summarizing; our understanding of organic superconductivity in the TMTSF series has been considerably improved over the past few years.

Crucial data such as NMR relaxation rate measurements have pointed towards the existence of 1-D correlations coexisting in the same temperature domain with superconducting fluctuations.

The possibility of an attractive pairing interaction mediated by the interchain exchange of AF fluctuations in quasi-1D organic conductors must be seriously taken into consideration.

In other materials such as the salts of the radical cation BEDT-TTF with enhanced 2-D character organic supercon-

ductivity has been stabilized above 8 K [41] at ambient pressure and even above 10 K in (BEDT-TTF)$_2$Cu(SCN)$_2$ [42]. One order of magnitude in $T_c$ has been gained in less than ten years of work Fig. 9. A future task will be the evaluation of the pertinent parameters (intra-chain interactions, dimerization, transverse coupling, etc...) which govern $T_c$ and the potentiality for such a coupling to give rise to superconductivity at higher temperatures ($T_c > 15$ K).

## Acknowledgement

We thank P. Wzietek for his contribution in NMR measurements.

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