# Low-temperature metallic state and superconductivity in quasi-one-dimensional organic conductors: pressure and irradiation investigations

Denis Jerome, M. Ribault, René Brusetti, K. Bechgaard, S. Bouffard

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Denis Jerome, M. Ribault, René Brusetti, K. Bechgaard, S. Bouffard. Low-temperature metallic state and superconductivity in quasi-one-dimensional organic conductors: pressure and irradiation investigations. Journal of Physics C: Solid State Physics, 1982. hal-04981979

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Low-temperature metallic state and superconductivity
in quasi-one-dimensional organic conductors: pressure
and irradiation investigations

S Bouffard†, M Ribault‡, R Brusetti‡, D Jérôme‡ and K Bechgaard§

† Section d'Etude des Solides Irradiés, Centre d'Etudes Nucléaires, BP 6, 92260 Fontenay-aux-Roses, France

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

§ HC Oersted Institute, Universitets-parken 5, DK-2100, Copenhagen, Denmark

Received 27 August 1981, in final form 7 December 1981

**Abstract.** The comparison between the disordered metallic state created by irradiation and the metallic regime stabilised by high pressure in TMTSF-DMTCNQ and TMTSF₂-PF₆ establishes the existence of a contribution from superconducting fluctuations to the conductivity below 50 K. A calculation using Ginzburg-Landau theory is in very good agreement with the experimental temperature dependence of the paraconductivity. We show that the metal-insulator transition in TMTSF₂-PF₆ is shifted by the disorder to a lower temperature. However, the effect is less for the spin-density-wave transition in TMTSF-PF₆ than for the charge-density-wave ordering in TMTSF-DMTCNQ. Finally we show that the superconductivity transition is strongly depressed by irradiation-induced defects.

**1. Introduction**

Over the past decade, most research in organic conductor physics has been devoted to low-temperature organic metals and organic superconductors. Investigations of the properties of TTF-TCNQ and analogous compounds have shown that minor changes in the structure packing or in the electronic structure of the molecules can produce new properties (see, for example, Bloch *et al* 1977). Extensive research has been focused on compounds derived from TTF-TCNQ by exchange of hetero-atoms in the donor and by attachment of small aliphatic substituents to both donor and acceptor molecules. In these investigations, high-pressure experiments play an important role: the metallic state of TMTSF-DMTCNQ has been stabilised under high pressure (Andrieux *et al* 1979). Another way to stabilise the metallic state is to introduce random disorder either by chemical substitution (Jacobsen *et al* 1978, Etemad *et al* 1978), by irradiation (Zuppiroli and Bouffard 1980) or by causing anion disorder like that in TMTSF₂-ClO₄ (Bechgaard *et al* 1981). The recent discovery of several organic superconductors also resulted from high-pressure experiments (Jerome *et al* 1980).

The present work focuses on the pressure dependence and on the defect concentra-
tion dependence of the conductivity of three systems: TMTSF-TCNQ, TMTSF-
DMTCNQ and TMTSF₂-PF₆. These three TMTSF salts represent the three main classes of organic conductors classified according to their transport properties. The first compound, TMTSF-TCNQ, belongs to the same class as the prototype TTF-TCNQ. This two-chain compound with a charge transfer of 0.57 ± 0.02 (Pouget 1981) has a well defined metallic range ($\sigma_{(300\text{K})} = 1000 (\Omega \text{ cm})^{-1)$) and a metal-insulator phase transition at 57 K. The second, TMTSF-DMTCNQ, crystallises in the same triclinic space group as TMTSF-TCNQ (there are differences in the lateral orientation of the stacks), and shows similar transport properties (Jacobsen et al 1978). The charge transfer of TMTSF-DMTCNQ is $\frac{1}{2}$ (Pouget 1981). That leads to a commensurate situation. Conductivity and thermopower data indicate (Jacobsen et al 1978) that the conductivity in the DMTCNQ chains is diffusive and low, while along the TMTSF chains there is a coherent and high conductivity. This is probably related to the narrow band width of the acceptor stacks (≈0.4 eV), whereas the band width of the donor stacks is larger (≈1 eV). However, we should not neglect the possibility of a localisation due to residual disorder in the DMTCNQ stacks which is present even in the so-called pure crystals (Hardebusch et al 1979, Zuppiroli et al 1982). TMTSF-DMTCNQ is an intermediate case between the two-chain and single-chain compounds. In this compound, the low-temperature Peierls state is suppressed by pressures above 10 kbar and the conductivity attains values of the order of $10^5 (\Omega \text{ cm})^{-1}$ below 15 K. It has been postulated that the huge magnetoresistance seen in this low-temperature high-pressure phase may be associated with a 1D fluctuation superconductivity along the high-conductivity axis for temperatures up to 40 K (Andrieux et al 1979).

The compound most studied recently, TMTSF₂-PF₆, is certainly the most exciting organic conductor: it was the first discovered to be a superconductor (Jerome et al 1980). since this first observation of superconductivity at 0.9 K under a hydrostatic pressure of 12 kbar, several crucial experiments have clarified our knowledge of the superconducting state in organic conductors. The existence of the bulk superconducting state has been confirmed by use of partial Meissner effects (Ribault et al 1980, Andres et al 1980). Similarly, in TMTSF-DMTCNQ, a huge magnetoresistance above the transition temperature has been interpreted as resulting from the conductivity caused by 1D superconductivity fluctuations (Schulz et al 1981). This hypothesis has been recently confirmed by a Schottky tunnelling experiment in TMTSF₂-PF₆ (More et al 1981), which has shown that the superconducting gap appears at about 15 K and that the gap energy is 40 K at 0.1 K under 11 kbar. At 40 K the superconductivity seems to be equal to the single-particle one. Furthermore, an important feature revealed by x-ray diffuse scattering is the absence of a low-temperature $2k_F$ Kohn anomaly in TMTSF₂-PF₆ (Pouget 1981); thus the superconductivity is not related to a soft mode at $2k_F$. Recent experiments involving NMR of the ⁷⁷Se and proton lines (Andrieux et al 1981) and magnetic susceptibility measurements (Mortensen et al 1981) have shown that the insulating regime in TMTSF₂-PF₆ is a spin-density-wave state and not the usual charge-density-wave state. Even at atmospheric pressure, TMTSF₂-PF₆ is characterised by exceptional transport properties. It exhibits a high conductivity, in excess of $10^5 (\Omega \text{ cm})^{-1}$, above the metal-insulator transition occurring at lower temperature than in previously investigated organic conductors (Bechgaard et al 1980).

The effects of disorder in the high-temperature metallic phase and in the low-temperature semiconducting regime are now well known. We have explored the effects of disorder in new phases in organic conductors: the low-temperature metallic phase stabilised by pressure, the superconducting regime and the spin-density-wave insulating regime.
## 2. Experimental details

The samples used in this study were prepared as described by Jacobsen *et al* (1978) and Bechgaard *et al* (1980). The four-contact resistance was measured by the usual low-frequency (≈70 Hz) technique. The applied current did not exceed 100 µA at high temperature; smaller current levels were used in the superconducting or semiconducting low-temperature regime. The unnested/nested voltage ratio (Schafer *et al* 1974) was always less than 10⁻³ for the two-chain compounds and typically a few per cent for TMTSF₂-PF₆. The resistance of the samples with independent circuits, placed within a teflon cell containing the pressure-transmitting medium, could be measured simultaneously. The experimental arrangement for measurement above 1.2 K was a Be–Cu pressure bomb. The temperature was measured with a copper–constantan thermocouple directly within the pressure cell and below 5 K with a germanium thermometer mounted on the outside wall of the vessel. For temperatures lower than 1.2 K, a Be–Cu pressure clamp cell was used cooled down in a ³He–⁴He dilution refrigerator. The temperature was measured with a platinum, carbon or germanium thermometer in good thermal contact with the pressure vessel. The irradiation was performed in mounted crystals, at room temperature, using a conventional x-ray generator with a copper tube (40 kR mn⁻¹). The crystals were directly placed in front of the window.

## 3. Experimental results

We have measured the temperature dependence of the longitudinal conductivity of pure TMTSF-TCNQ and TMTSF-DMTCNQ. The conductivity–temperature curves for TMTSF-TCNQ under three different pressures are shown in figure 1. Each pressure experiment was made on two different samples; the curves at 15 and 19 kbar are for the same crystal. At room temperature, the conductivity increases under pressure at a rate of 17 ± 4% kbar⁻¹. This rate is comparable to those for related compounds: 18 ± 1% kbar⁻¹ in TSF-TCNQ (Cooper *et al* 1977), 15 ± 5% kbar⁻¹ in HMTSF-TCNQ (Cooper *et al* 1976), 28% kbar⁻¹ in TMTSF-DMTCNQ (Andrieux *et al* 1979) and 20 ± 5% kbar⁻¹ in TMTSF₂-PF₆ (Parkin *et al* 1981 and this work). The phase transition occurring at 57 K under ambient pressure increases with pressure and reaches 70 K under 19 kbar (figure 2). This increase (δlg Tp/δp = 1.5% kbar⁻¹) is quite similar to those observed in TTF-TCNQ and TSF-TCNQ, namely 1.4 ± 0.4 and 6 ± 1% kbar⁻¹ respectively (Cooper *et al* 1977). Thus, TMTSF-TCNQ is a compound of the TTF-TCNQ class.

In contrast, previous experiments made by one of us on TMTSF-DMTCNQ have shown that under pressure this compound shows completely different behaviour: above 10 kbar the conductivity of TMTSF-DMTCNQ presents a metallic range down to 1.2 K and a saturation below 6 K. We have made the same experiment at temperatures as low as 90 mK. Figure 3 shows the temperature dependence of the resistivity normalised at room temperature under 12 kbar of TMTSF-DMTCNQ, and demonstrates the saturation below 5 K. This experiment has failed to show any superconducting transition down to 90 mK. The same figure shows the unusually large magnetoresistance in this compound (the magnetic field is perpendicular to the conducting chains). The magnetic field seems to restore a semiconducting transition. In spite of these similar structure and transport properties at atmospheric pressure TMTSF-TCNQ and TMTSF-DMTCNQ present contrasting behaviour under pressure.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Temperature dependence of the longitudinal conductivity in TMTSF-TCNQ under 6(A), 15(B) and 19(C) kbar.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Phase diagram of TMTSF-TCNQ showing the increase of $T_c$ with pressure. The zero-pressure point is taken from Jacobsen *et al* (1978).</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Temperature dependence down to 90 mK, of the longitudinal resistivity of TMTSF-DMTCNQ at 12 kbar and under magnetic fields (*H* ⊥ *b*) of (kOe) 0 (A), 2 (B), 4 (C), 6 (D), 8 (E), 10 (F), 12 (G), 30 (H), and 75 (I). Curve I is taken from Andrieux *et al* (1979).</figcaption></figure>

It is well known that TMTSF₂-PF₆ is an organic conductor in which pressure smears the insulating transition. Several irradiation experiments on low-dimensional organic conductors have shown that the metal-insulator transition is temperature-depressed and smeared out by defects (Chiang *et al* 1977). It was interesting to compare the metallic state stabilised by pressure with those created by irradiation-induced defects. Furthermore, the previous radiation experiments were made on compounds in which the ground state is a charge-density-wave regime. Since TMTSF₂-PF₆ possesses a spin-density-wave state, it was considered interesting to study the effect of disorder in this new phase.

Thus we have irradiated several crystals of TMTSF₂-PF₆ with Cu α x-rays for five hours, which corresponds to an absorbed energy of 56.6 Mrad. Extensive experiments on x-ray-damaged crystals have shown that in organic conductors the defect concentration is directly proportional to the absorbed energy. One needs an absorbed energy of 7.1 keV to damage a molecules unit of TMTSF-DMTCNQ, 13.5 keV for a molecular unit of TTF-TCNQ and 147 keV for a molecules unit of TTT₂-I₃ (Mihaly and Zuppiroli 1981). Preliminary results on TMTSF₂-PF₆ and TMTSF₂-ClO₄ strongly suggest that the absorbed energy needed to damage a molecular unit of TMTSF₂-PF₆ is of the same order as that in TMTSF-DMTCNQ. Thus an absorbed energy of 1000 Mrad produces a molecular defect concentration of about 1%.
Figure 4 shows the temperature dependence of the resistivity normalised at 50 K in irradiated TMTSF₂-PF₆ under 4 and 6.5 kbar. The two curves are for the same crystal in which the molecular defect concentration is about 6 × 10⁻⁴. The arrows indicate the transition temperature seen for the same pressure in the pure crystal. The transition temperature, defined as the maximum slope of the conductivity curve, is lower in the damaged crystals than in the pure samples: 5 ± 0.5 K at 4 kbar and 5 ± 1 K at 6.5 kbar (respectively 9 ± 0.5 K and 7 ± 0.5 K in the pure samples). These results are qualitatively similar to those found in the charge-density-wave compounds. However, the effects of irradiation-induced defects on the metal-insulation transition seem to be less important for the spin-density-wave state (about −50 K per %) than for the charge-density-wave state (−150 K per % in TTF-TCNQ (Chiang et al 1977, Bouffard et al 1981) and −110 K per % in TMTSF-DMTCNQ (Forro et al 1981)). Due to small anomalies above the freezing temperature of the pressure-transmitting medium, we cannot compare the absolute value of the resistivity below the phase transition. However, to within the experimental resolution, we can say that the resistivity seems to decrease in the semiconductor state when the disorder increases.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Temperature dependence of the resistivity of irradiated TMTSF₂-PF₆ under 4 (A) and 6.5(B) kbar, showing the low-temperature shift of the transition temperature. The arrows show the transition temperature in TMTSF₂-PF₆ from Jerome *et al* (1980).</figcaption></figure>

At ambient pressure, in the high-temperature metallic range and in the low-temperature disordered metallic state, the exponential increase of the resistivity with the defect concentration is related to the strong potentials of the defects which divide the conducting chains into decoupled segments (Zuppiroli *et al* 1980). In this investigation we consider the effects of defects on the low-temperature metallic state stabilised by pressure. Irradiation was carried out as described above, although the defect concentrations are better known in TMTSF-DMTCNQ than in TMTSF₂-PF₆: an absorbed energy of 1000 Mrad produces a molecular defect concentration of 0.97%. We have
measured the temperature dependence under 15 kbar of the resistivity of pure and irradiated TMTSF-DMTCNQ (in a concentration range of 0.01 to 0.52%). Note that in this conductor a molecular defect concentration of about 0.2% can stabilise the metallic state at least down to 1.2 K (Forro *et al* 1981). Figure 5 shows the curves of resistivity (log scale) against temperature for pure and irradiated TMTSF-DMTCNQ. All the sample conductivities were normalised before irradiation and pressure increase to a value of 400 (Ω cm)⁻¹. A very low concentration (10⁻⁴) increases the 4 K resistivity by a factor of 4, and the effect of such a concentration appears below 120 K. At higher doses, the curves show the usual exponential behaviour due to metallic strands. In figure 6, the same data are plotted in the form of resistivity defect-concentration curves. The resistivities are normalised with respect to the resistivities at the same temperature in the pure crystals. At high temperatures, the resistivities vary exponentially with the irradiation dose and the slopes are close to those observed at atmospheric pressure. However, at low temperatures (below 100 K) the resistivity increase shows two regimes: (i) below 0.2% molecular defects, and (ii) at higher concentrations. The second regime may be related to the ambient pressure one: in figure 6, the upper broken curve which is the slope for a 21 K irradiation with fast neutrons at atmospheric pressure, is identical

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Temperature dependence of the resistivity of pure and irradiated TMTSF-DMTCNQ under 15 kbar. All the curves have been normalised to 400 (Ω cm)⁻¹ at ambient pressure before irradiation. The curves are for percentages of 0 (A), 0.01 (B), 0.03 (C), 0.06 (D), 0.18 (E) and 0.52 (F).</figcaption></figure>
<figure><img src="image_7.png" /></figure>

**Figure 6.** Defect concentration dependence of the longitudinal resistivity of TMTSF-DMTCNQ under 15 kbar at various constant temperatures (given on curves in K), normalised to the pure-crystal resistivity. The lower broken curve shows the variation at ambient pressure (1 bar) for an x-ray irradiation, whereas the upper one shows the slope of the damage curve for an irradiation with fast neutrons also at 1 bar (Mihaly *et al* 1980).

<figure><img src="image_8.png" /></figure>

**Figure 7.** Temperature dependence of resistances normalised to 50 K values for irradiated TMTSF₂-PF₆ (where various signs correspond to different samples), and pristine TMTSF₂-PF₆ (full curve from Schulz *et al* 1981). The broken curves show the behaviours for pure (A) and irradiated TMTSF-DMTCNQ (B and C; respectively 10⁻⁴ and 3 × 10⁻⁴ molecular defects).

to the slope of the damage curve at 20 K and under 15 kbar. At atmospheric pressure and low defect concentration, in the Peierls regime, the irradiation produces a sharp decrease of the resistivity related to the destruction of the transverse coherence between the charge-density waves, needed for the achievement of the Peierls transition. This decrease is, of course, absent in the samples where the metallic state has been stabilised by pressure. On the other hand, under pressure and below 0.2% molecular defects, the resistivity increases faster than in the 'normal' metallic regime. This huge defect dependence can be related to the suppression of superconductivity fluctuations. This paraconductivity appears below 100 K. Note that the temperature dependence as well as the absolute values of the conductivity above 15 K in TMTSF-DMTCNQ are close to those of the TMTSF₂-PF₆ superconductor. These curves from Schulz *et al* (1981) are plotted in figure 7 (full curve and broken curve respectively for TMTSF₂-PF₆ and TMTSF-DMTCNQ). Furthermore, the irradiated TMTSF₂-PF₆ and TMTSF-DMTCNQ also show the same temperature dependences of their normalised resistances. The irradiation doses are 13.5 Mrad (about 10⁻⁴ molecular defects) for the least irradiated and 68.2 Mrad (about 10⁻³ molecular defects) for the most irradiated.

At lower temperatures, TMTSF₂-PF₆ becomes a superconductor. We show that the superconducting transition is strongly affected by irradiation-induced defects. In figure 8, resistance-temperature curves under 13 kbar normalised at 1 K are plotted for an irradiated sample (26.8 Mrad at about 3 × 10⁻⁴ molecular defects). At higher tem-
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Temperature dependence of the resistance at 13 kbar of irradiated TMTSF₂-PF₆ normalised to its value at 1 K in the earth's magnetic field (measured with a current of 1 µA). The superconducting transition is shifted down in temperature by the application of a transverse magnetic field (*H* = 20, 50 and 103 Oe). The four-probe resistance does not vanish to 0 at *T* = 0 K. The values of *H* (Oe) are 0 (A), 20 (B), 50 (C) and 103 (D).</figcaption></figure>

peratures, the resistivity is plotted in figure 7 (filled circles). The transition is present but does not lead to a zero-resistance state, and the resistance decreases by steps. This latest anomaly disappears when a magnetic field of about 50 Oe is applied.

This behaviour has been observed in all our irradiated crystals although similar anomalies have also been reported in so-called pure crystals (Parkin *et al* 1981). Due to the small jump that appears during the pressure increase and the cooling, we are not able to correlate the transition temperature with the defect concentration. However, in all cases, an irradiation-induced-defect concentration of a few 10⁻⁴ (less than 60 Mrad) suppresses completely the superconducting state. As the residual conductivity is also strongly dependent on the defect concentration (figure 7), we have plotted in figure 9 the transition temperature against residual conductivity (the conductivity just above the transition normalised to the value at 200 K). The transition temperature is defined as the maximum slope of the transition curve. The dependence of the transition temperature has been taken to be 0.87 K kbar⁻¹ (Andres *et al* 1980). The superconducting transition falls abruptly to *T* = 0 K when σ(Tc)/σ200K decreases below 5 (in pure crystals this ratio is about 50).
<figure><img src="image_10.png" /></figure>

**Figure 9.** Normalised conductivity dependence of the transition temperature defined on the maximum slope of the resistance-temperature curves for TMTSF₂-PF₆ with *P* = 12 kbar.

<figure><img src="image_11.png" /></figure>

**Figure 10.** Temperature dependence of ratio of the superconducting fluctuation conductivity to the single-particle conductivity in TMTSF-DMTCNQ under 15 kbar. The square is the result for TMTSF₂-PF₆ under 12 kbar. The full curve is the best fit of the data to a time-dependent Ginzburg-Landau theory of 1D superconducting fluctuations (Schultz *et al* 1981).

# 4. Discussion

## 4.1. *The stabilisation of the metallic state*

TMTSF-TCNQ and TMTSF-DMTCNQ exhibit contrasting behaviours under high pressure, whereas the two-chain TMTSF-DMTCNQ and the single-chain TMTSF₂-PF₆ show quite similar behaviours: the conductivities reach the same values at low temperatures and are enhanced by the contribution of superconductivity fluctuations. However, the main difference between these two compounds is related to the ground state at ambient pressure: TMTSF-DMTCNQ has a charge-density-wave ground state, whereas TMTSF₂-PF₆ has a spin-density-wave ground state. Let us remember that the stabilisation of the metallic state in TMTSF-DMTCNQ is associated with an anomaly detected by resistance and thermopower measurement (the so-called metal I-metal II transition) (Andrieux *et al* 1979). It is not impossible to relate this transition to the smearing of the charge-density-wave state and the establishment of a spin-density-wave ground state. This change in the nature of the instability could be achieved either by pressure changing the values of the coupling strengths, *g*₁(2*k*<sub>F</sub>) and *g*₂(0), corresponding to momentum transfers of 2*k*<sub>F</sub> and zero, or by magnetic impurities (Antoniou 1979, Hillenius and Coleman 1979) stabilising an unstable spin-density wave at the expense of the charge-density wave. Thus the stabilisation of the metallic state by pressure seems to be connected with the existence of superconducting fluctuations and perhaps to the spin-density-wave ground state at least in the single-chain charge-transfer organic conductors.
The stabilisation of the metallic state in TMTSF-DMTCNQ may not be related to defects as in HMTSF-TCNQ for the following reasons: firstly the sharpness of the metal-insulator transition and secondly the sudden vanishing of the insulating phase above 10 kbar. Although TMTSF-DMTCNQ is not a perfect compound: up to 1% paramagnetic centres have been found in the DMTCNQ chains which contribute less than the donor stacks to the conductivity.

The metallic state stabilised by pressure reaches the highest conductivity measured in quasi-one-dimensional organic conductors, whereas the conductivity in the low-temperature metallic regime stabilised by disorder is several orders of magnitude lower.

The low-temperature metal-insulator transition requires some tri-dimensional Coulomb coupling between charge-density waves. The irradiation-induced defects disturb the coherence needed for the achievement of the phase transition, and thus the transitions are smeared and shifted to the lower temperature. Recent experiments have confirmed the metallic behaviour of the low-temperature disordered phase. At a molecular defect concentration as low as $2 \times 10^{-3}$, the Hall effect, the thermopower and the EPR linewidth show typical metallic behaviour at least down to 2 K (Forro et al 1981). However, at the same time, the defects produce potentials strong enough to divide the conducting chains into segments of variable lengths. Thus the low temperature and the defect concentration dependences of the conductivity become single activated

The new class of organic conductors TMTSF₂-X exhibits unusual behaviour. At ambient pressure, TMTSF₂-PF₆ has been observed to undergo a metal-insulator transition at 11.5 K (Mortensen et al 1981). This transition is related to the development of antiferromagnetic ordering. The transition is so low because the interstack interaction between spin-density waves is weaker than between charge-density waves. Andrieux et al (1981) have established by NMR experiments the small value of the spin-density wave amplitude in TMTSF₂-PF₆. Thus it is not surprising that paramagnetic defects created by irradiation destroy the coherence between spin-density waves and shift the transition temperature by -50 K per % molecular defects. This shift is consistent with the EPR measurements on irradiated TMTSF₂-PF₆: the linewidth divergence at the transition is temperature-depressed by -60 K per % molecular defects (Forro 1981). However, (i) the existence of a small spin-density-wave amplitude in an almost perfect nesting of the 1D Fermi surface and (ii) the observation of a very large positive magnetoresistance in the insulating state have suggested that the nature of the antiferromagnetic state in TMTSF₂-PF₆ is different from that in typical itinerant antiferromagnets. Both the spin-density-wave state and the superconducting state must be considered simultaneously. Under irradiation, the change of low-temperature resistivity in the insulating state of TMTSF₂-PF₆ is smaller than in the Peierls insulating state (by more than an order of magnitude). In TMTSF₂-PF₆, the defects are assumed (i) to destroy the 3D coherence of the spin-density waves which means that the transition cannot be achieved in the way it is for the Peierls transition: the conductivity is increased; (ii) to smear out the 1D superconducting fluctuations (see below): this contribution to the conductivity is suppressed. So we are confronted by two opposite effects.

## 4.2. 1D superconducting fluctuation

The presence of 1D superconducting fluctuation has been demonstrated by Schottky tunnelling experiments in TMTSF₂-PF₆ by More et al (1981). The huge magnetoresistance (Jacobsen et al 1981) and the variation of the thermal conductivity (Djurek and Weyl 1981) in TMTSF₂-PF₆ are also in good agreement with a contribution of supercon-
ducting fluctuations, up to 40 K, to the longitudinal conductivity. This paraconductivity is also present in TMTSF-DMTCNQ which does not show a superconductivity transition. Our irradiation experiments are consistent with these previous results. The damage curves in TMTSF-DMTCNQ (figure 6) under 15 kbar show two regimes. We have associated the linear part with a strand interruption mechanism, whereas the first large increase at low dose is related to the suppression of the paraconductivity. A molecular concentration of defects less than $2 \times 10^{-3}$ destroys the whole contribution from fluctuations. Note that the same concentration is also able to suppress the fluctuating charge-density-wave collective transport mechanism in TTF-TCNQ (Bouffard *et al* 1981). The ratio of the superconducting fluctuation to single-particle conductivities could be determined by extrapolating to zero defect concentration the linear part of the damage curves in figure 6. The results are plotted in figure 10. In TMTSF₂-PF₆ the paraconductivity could be evaluated at 1 K in another way: the defects destroy the condensate superconductivity as well as the 1D superconducting fluctuations (figure 9) whereas the single-particle conductivity is only slightly affected by such a low defect concentration. Thus, the residual conductivity when $T_c$ falls to zero could be attributed to the single-particle conductivity. In TMTSF₂-PF₆ at 1 K, the lower limit of the ratio of the two conductivities is 15 (the square in figure 10). In TMTSF-DMTCNQ, at about 35 K, the paraconductivity is already equal to the single-particle conductivity and 10 times larger at 10 K.

Schulz *et al* (1981) have treated the superconducting fluctuations in a time-dependent Ginzburg-Landau theory. According to the ratio of the transverse coherence length ($\epsilon_\perp$) to the interchain distance ($d_\perp$), this theory provides two different regimes for the superconducting fluctuation conductivity: (i) a 3D regime, in the vicinity of $T_c$ when $\xi_\perp/d_\perp > 1$ and thus $\sigma_\parallel^{3D} \approx T^{1/2} (\ln T/T_c)^{-1/2}$ and (ii) a 1D regime ($\xi_\perp/d_\perp < 1$) where $\sigma_\parallel^{1D} \approx T^{-1/2} (\ln T/T_0)^{-3/2}$ ($T_0$ is 1D mean field temperature). In these organic compounds, $T_c$ is below 1.5 K; thus we can assume that we are in a 1D regime above 5 K. If we take a T-independent single-particle conductivity below 40 K, the ratio $\sigma_\parallel^{1D}/\sigma_\parallel^{1P}$ is proportional to $T^{-1/2} (\ln T/T_0)^{-3/2}$. Given the above assumption, we have plotted in figure 10 the theoretical results (full curve) with $T_0 = 7$ K (this value is very close to those found in TMTSF₂-PF₆: $T_0 = 5.6$ K (Schulz *et al* 1981)). This theory on 1D superconducting fluctuations in TMTSF-DMTCNQ gives excellent agreement with experiment over the temperature range 10–100 K. If we allow slightly T-dependent single-particle conductivity above 40 K, the result is quite similar.

However, evidence on the existence of the 1D superconducting fluctuations is still conflicting. Some authors argue that the Fermi surface of the TMTSF salts is two-dimensional (Kwak *et al* 1981) and thus they interpret the experiments using a model of a two-dimensional semi-metallic band (Greene *et al* 1981).

### 4.3. Superconductivity transition

We have observed a transition to a non-zero resistance state in irradiated crystals and anomalies in the transition curves (figure 8). These two behaviours are not yet understood. However similar results have been observed in powdered TaSe₃ (Briggs *et al* 1981), irradiated NbSe₃ (Fuller *et al* 1981) and irradiated NbSe₂ (Mutka 1980), and they have been interpreted as evidence for inhomogeneous materials or fibrous superconductors. In our case, the sample size was about 4 mm × 0.1 mm × 0.05 mm; in such a light material, the x-ray damage is perfectly homogeneous, and defects are produced by photoelectrons that are directly created in the crystal (8 keV photoelectrons).
The results of these experiments show the huge defect dependence of the superconductivity transition. A few $10^{-4}$ molecular defects suppress the superconductivity state while ten times more defects are needed to obtain the same result in NbSe$_3$ (Fuller et al 1981). According to Mutka, several per cent of defects are needed to destroy the superconductivity in the layered compound 2H-NbSe$_2$.

However, differences between two experiments on organic compounds do occur and these could be interpreted as due to variable defect concentration in pristine crystals or as defects produced by increasing pressure or temperature cycling.

In quasi-one-dimensional organic conductors, irradiation produces unpaired spins. These unpaired spins act on the superconductivity like magnetic impurities: they depress the critical temperature and destroy the superconducting regime. However, the nature of the electron pairing is not yet known in these compounds, so we cannot discuss the question of the effect of unpaired spins on the electron pairing.

The correlation between the transition temperature and the residual conductivity agrees well with the model of Schulz on the 3D superconducting fluctuation conductivity in the vicinity of $T_c$: $\sigma_{\parallel}^{3D} \sim T^{1/2} (\ln T/T_c)^{-1/2}$. It is not reasonable to fit the experimental data by a theoretical law because we have too many parameters: $\sigma_{\parallel}^{1P}$, the defect dependence of the paraconductivity when $T_c$ is lower than 0.4 K etc. However the shapes of the curves are quite similar.

## 5. Conclusions

By performing irradiation-induced defect experiments, we are able to confirm the existence of a large contribution from superconducting fluctuations up to 50 K in TMTSF$_2$-PF$_6$ as well as in TMTSF-DMTCNQ. We show that this paraconductivity is at least 10 times larger than the single-particle conductivity at 10 K under 15 kbar in TMTSF-DMTCNQ, and equal to it at about 35 K. The 1D superconducting fluctuation conductivity follows the Ginzburg-Landau theory, developed by Schulz, of 1D superconducting fluctuations. The paraconductivity is extremely sensitive to defects: $10^{-3}$ molecular defects suppresses this contribution. The superconducting state in TMTSF$_2$-PF$_6$ is destroyed by $10^{-4}$ molecular defects.

## Acknowledgments

We wish to thank L Zuppiroli for fruitful discussions and S S P Parkin for a critical reading of the manuscript.

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