# Stabilisation of the metallic state at low temperatures in HMTTF-TCNQ under pressure?

Richard H Friend, Denis Jerome, Jean-Marc Fabre, L. Giral, Klaus Bechgaard

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Richard H Friend, Denis Jerome, Jean-Marc Fabre, L. Giral, Klaus Bechgaard. Stabilisation of the metallic state at low temperatures in HMTTF-TCNQ under pressure?. J. Phys. C: Solid State Phys, 1978. hal-04989688

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# Stabilisation of the metallic state at low temperatures in HMTTF-TCNQ under pressure†

R H Friend‡¶, D Jérôme‡, J M Fabre§, L Giral§ and K Bechgaard

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

§ Laboratoire de Chimie Organique Structurale USTL 34060 Montpellier, France

‖ H C Oersted Institute, Universitetsparken 5 DK 2100 Copenhagen, Denmark

Received 21 June 1977

**Abstract.** We report measurements of the *b* axis conductivity of HMTTF-TCNQ under hydrostatic pressures up to 33 kbar, and the room temperature, ambient pressure conductivity anisotropies. The two transitions seen in the conductivity at 49 K and 43 K at ambient pressure fall in temperature when pressure is applied; the lower transition is absent above 3 kbar and the upper transition falls linearly at 1.5 K kbar⁻¹. The low-temperature insulating behaviour at ambient pressure is rapidly replaced by weakly metallic behaviour, which at 10 kbar is very similar to that seen in HMTSF-TCNQ at ambient pressure. At higher pressures the resistivity was still falling at 1.2 K. We suggest that HMTTF-TCNQ above 3 kbar and HMTSF-TCNQ at ambient pressure undergo distortions on predominantly one type of stack. A unified picture of the pressure behaviour of this series of TCNQ salts is presented; the Peierls distortions in TTF-TCNQ and TSF-TCNQ occur when the transverse conduction is diffusive and the system is in the one-dimensional regime, whereas HMTTF-TCNQ and HMTSF-TCNQ distort when transverse motion is coherent and an anisotropic three-dimensional band structure picture is appropriate.

## 1. Introduction

There has been much interest in the past few years in metallic charge transfer salts, particularly TTF-TCNQ (tetra thio fulvalenium-tetra cyano quino dimethanide) and its derivatives (see Keller (1975) and (1977) for reviews). Most of these materials show strongly anisotropic metallic properties at high temperatures, but distort to become insulators at low temperatures. One of the aims of the present effort is to find systems that remain metallic at all temperatures, but to date HMTSF-TCNQ (hexamethylene tetraselena fulvalene-tetra cyanoquino dimethanide) is the only member of this series of compounds to show (weakly) metallic behaviour at low temperatures (Bloch *et al* 1975). At high pressures this metallic behaviour is enhanced (Cooper *et al* 1976b). In contrast the sulphur analogue HMTTF-TCNQ (hexamethylene tetra thio fulvalenium-tetra cyano quino dimethanide) becomes strongly insulating at low temperatures, showing two transitions (at 49 K and 43 K) in its *b* axis resistivity (Greene *et al* 1976).

The structure of HMTTF-TCNQ, which has an orthorhombic unit cell, is that of

<footnote>† Work performed in part with a DGRST Contract n° 75-7-0820.</footnote>

<footnote>¶ Permanent address: Cavendish Laboratory, Cambridge, UK.</footnote>

<footnote>* Laboratoire associé au CNRS.</footnote>
stacks of HMTTF and stacks of TCNQ donor and acceptor molecules along the high-conductivity *b* axis, with alternating donor and acceptor molecules along the *a* and *c* axes (Greene *et al* 1976). In this respect it is similar to HMTSF-TCNQ (Phillips *et al* 1976) although there are important differences in the tilting of the stacks out of the *ac* plane.

The large differences in electrical properties between the sulphur and selenium compounds are surprising in view of the structural similarity, and it was to understand better the nature of the differences between them that we undertook this pressure study. In fact we found that HMTTF-TCNQ under pressure rapidly resembled HMTSF-TCNQ, indicating that there are only small differences between two compounds in their atmospheric pressure electronic and lattice properties.

## 2. Experimental

The preparation of the HMTTF-TCNQ used for these measurements is described by Delhaes *et al* (1977). Single crystals were obtained by recrystallisation from chlorobenzene. Sample dimensions for the *b* axis conductivity measurements were typically 2 × 0.04 × 0.04 mm. Room temperature conductivities in this direction were appreciably larger than those reported by Greene *et al* (1976) and we find a value of $\sigma_{||b} = 550 \Omega^{-1} cm^{-1}$ to be representative of the samples we investigated.

A variety of high-pressure systems were used to cover the pressure range up to 33 kbar. From 1 bar to 10 kbar a helium gas set up described by Malfait and Jérôme (1969) was employed. This technique has the advantage that pressure can be conveniently kept constant when cooling down to the helium freezing point, which is always sufficiently low that any differential thermal contraction below this temperature will be very small and will cause little change to the pressure. For the present series of experiments an automatic pressure regulation system was used whereby any pressure change registered by the manganin high-pressure gauge in the pressure intensifying cell was used as a feedback to control the oil pressure on the low-pressure side of the intensifying cell. In this way pressure was kept constant to within 20 bars until the helium freezing point, and pressure loss on freezing was kept within 100 bars.

For experiments at higher pressures two hydrostatic fluid techniques were used, both based on the teflon cell principle. Up to 24 kbar a small steel pressure clamp cell was used with isopentane as the high-pressure fluid. This cell has a system of springs to reduce pressure loss at the isopentane freezing point (Malfait *et al* 1977). Above this pressure the intensifying cell described by Delaplace *et al* (1976) was used with a 1:1 mixture of isopentane and isoamyl alcohol as the high-pressure fluid. Pressure changes while cooling were estimated to be less than 1 kbar for these two systems.

Conductivity measurements were made using the standard configuration with 4 contacts, which were made with Dupont 4929 silver paint diluted with hexyl acetate. A low frequency (70 Hz) alternating current technique was used with a measuring current between 1 and 10 µA. ‘Unnested’ voltages as defined by Schafer *et al* (1974) were always less than 0.1 % and usually less than 0.01 %.

Temperature was measured with a copper-constantan thermocouple inside the pressure cell from room temperature down to 60 K, and from 60 K to 4.2 K with a thin film manganin-nickel resistance thermometer on the outside of the pressure cell. Temperatures below 4.2 K were measured from the vapour pressure of the liquid helium around the high-pressure cell. Data was always displayed directly on an x-y recorder,
and was always taken for both falling and rising temperature. Any thermal hysteresis that might be associated with either of the two resistance anomalies seen at atmospheric pressure was less than 0.5 K.

In the medium pressure range up to 10 kbar many of the crystals showed abrupt increases in resistivity when cooling, particularly between 80 and 150 K. The resistivity increase was typically 30% and the temperature dependence of the resistivity after the break was usually markedly changed. It is not clear whether this behaviour was caused by parts of the voltage or current contacts becoming detached from the sample or whether it was due to internal fracture in the crystal caused by crystal imperfections such as twinning. The effect of the break was probably to introduce components of the transverse resistivities into the measured resistivity. This tendency of the crystals to show jumps in the resistivity is very similar to the case of HMTSF-TCNQ at atmospheric pressure (Cooper et al 1976b) where even for unbroken samples there is a wide dispersion in the low-temperature resistivity (Bloch et al 1975). As will be shown later the absolute values of the low-temperature resistivity of HMTTF-TCNQ in this pressure range are similar to those measured for HMTSF-TCNQ at atmospheric pressure.

In order to obtain cooling curves on unbroken samples it was necessary to work on a fairly large number of crystals; we made over 30 high-pressure cooling runs involving over 20 crystals. All data shown are for unbroken samples, and we are confident that the behaviour we have observed is intrinsic.

### 3. Results

Figure 1 shows the rapid increase of the room temperature b axis conductivity with pressure. The rate of increase at 1 bar (25 ± 1% kbar⁻¹) is similar to that observed in TTF-TCNQ (28 ± 2% kbar⁻¹) (Cooper et al 1975) and appreciably faster than that in TSF-TCNQ (18% kbar⁻¹) (Cooper et al 1977a) and HMTSF-TCNQ (15 ± 5% kbar⁻¹) (Cooper et al 1976b).

<figure><img src="image_2.png" /></figure>

**Figure 1.** Pressure dependence of the b axis conductivity of HMTTF-TCNQ at room temperature. Results up to 10 kbar are from high-pressure helium gas experiments, and results to 33 kbar from isopentane: isoamyl alcohol high-pressure fluid experiments. Conductivities of all samples are normalised to 550 (Ω cm)⁻¹ at room temperature and atmospheric pressure.
Figure 2 shows constant pressure cooling curves between 1 bar and 8 kbar. Our results at 1 bar are similar to those previously obtained (Greene *et al* 1976); on cooling from room temperature the conductivity first increases, rising by a factor of 3·6 at 75 K. Below this temperature the conductivity falls and two sharp anomalies, presumed to be signatures of phase transitions, are clearly visible at around 49 and 43 K. These are the temperatures where −d ln ρ/dT shows maxima, and it is this somewhat arbitrary though commonly adopted definition for the transition temperature that we have taken throughout this work.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Log σ versus 1/T for HMTTF-TCNQ between 1 bar and 8 kbar. Conductivities of all samples are normalised to 550 Ω⁻¹ cm⁻¹ at room temperature and atmospheric pressure.</figcaption></figure>

When pressure is applied, the low-temperature conductivity increases very rapidly, and the two transitions are pushed to lower temperatures. The lower transition is quickly suppressed and is no longer present at 3 kbar, whereas the higher temperature transition falls more slowly, as can be seen in figure 3. It is clear from figure 2 that the lower temperature transition has a stronger influence on the low-temperature conductivity than the upper transition. Activation energies determined from the temperature dependence of the conductivity depend critically on the condition of the sample, but typical values of 2Δ (for the data shown in figure 2) determined at 25 K are 540 K at 1 bar, 470 K at 1·5 kbar, 150 K at 3 kbar, 120 K at 5 kbar and 20 K at 8 kbar. The rapid suppression of Δ with pressure correlates with the fall in the lower transition, whereas the upper transition has relatively less influence on the conductivity. While Δ was sample dependent, the transition temperatures determined from −d ln ρ/dT were found not to be, and figure 3 includes data for samples which showed breaks.

Cooling curves to higher pressures are shown in figure 4, along with cooling curves for HMTSF-TCNQ at ambient and at high pressures from the work of Cooper *et al* (1976b). At 8 kbar HMTTF-TCNQ shows almost identical behaviour, both in the absolute magnitude of the resistivity and in its temperature dependence, to that of
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Pressure dependence of the two phase transition temperatures in HMTTF-TCNQ, defined by maxima in -d ln ρ/dT. Sample numbers are indicated, and data from samples which have shown breaks are included.</figcaption></figure>

HMTSF-TCNQ at atmospheric pressure. By 19 kbar the resistivity of HMTTF-TCNQ is still falling at 1·2 K even though it is clear that there is still a transition (at 24 K) at this pressure. Variations in behaviour from sample to sample were often large in this pressure regime, and for samples which showed broader, more sluggish transitions than those in figure 4 - d ln ρ/dT showed no well defined maximum, and it was not possible to define a transition temperature. It does appear however that the transition temperature at high pressure follows the linear extrapolation of the data shown in figure 3, at 19 kbar the transition is clearly at 24 K, and it should be finally suppressed between 35 and 40 kbars.

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Log σ versus log T for HMTTF-TCNQ at high pressure. Conductivities of all samples are normalised to 550 Ω⁻¹ cm⁻¹ at room temperature and atmospheric pressure. Also shown (dotted curves) are data for HMTSF-TCNQ at atmospheric pressure and at 14 kbar taken from Cooper *et al* (1976). Room temperatures atmospheric pressure conductivities are normalised to 1800 Ω⁻¹ cm⁻¹.</figcaption></figure>
With increasing pressure the temperature of the conductivity maximum (75 K at 1 kbar) falls quickly and approaches the upper transition temperature. It was difficult to determine this temperature in the high-pressure regime as variations between samples were large, but we note that for the data shown in figure 4 the difference in temperature between the conductivity maximum and the maximum in $-d \ln \rho/dT$ is less than 5 K.

The approximately quadratic temperature dependence of the resistivity observed at temperatures above the phase transitions in this series of compounds (for TTF-TCNQ see Cooper *et al* (1975) Ferraris *et al* (1976), for HMTSF-TCNQ see Bloch *et al* (1975)) is also present for HMTTF-TCNQ. Figure 5 shows the resistivity plotted against $T^2$ for various pressures. There is a very large change in the coefficient of $T^2$ with pressure, between 1 bar and 33 kbar it falls by a factor of 40. Whilst the functional dependence at atmospheric pressure is usually found to be larger than two, under pressure we find the simple quadratic law to be well obeyed.

Finally we present the room temperature, atmospheric pressure resistivity anisotropies. Using the Montgomery (1971) geometry we find $\sigma_b/\sigma_a = 80 \pm 10$ and $\sigma_b/\sigma_c = 170 \pm 30$.

<figure><img src="image_6.png" /><figcaption>**Figure 5.** $\rho$ versus $T^2$ for HMTTF-TCNQ at high pressure. All sample conductivities are normalised to $550 \, \Omega^{-1} \, cm^{-1}$ at room temperature and atmospheric pressure.</figcaption></figure>

**4. Discussion**

HMTTF-TCNQ shows the most dramatic changes with pressure of any of this series of organic charge transfer salts so far investigated; at 1 bar it is at low temperatures as strongly insulating as TTF-TCNQ, but with the application of 10 kbar it remains weakly metallic. In this section we shall discuss the implications of our results for this series of charge transfer salts, particularly for HMTSF-TCNQ. Why the behaviour of HMTTF-TCNQ under pressure should be so different from that of TTF-TCNQ (Cooper *et al* 1975) and TSF-TCNQ (Cooper *et al* 1977a), where the low-temperature insulating state is more stable under pressure, will be the subject of § 5.

At present there is no diffraction work on the two transitions in HMTTF-TCNQ, neither has there been a low-temperature diffraction investigation of HMTSF-TCNQ. However, Greene *et al* (1976) have suggested that the two transitions in HMTTF-TCNQ
may be similar to the 53 K and 38 K transitions in TTF-TCNQ, at which temperatures distortions take place on the TCNQ and TTF stacks respectively (Tomkiewicz *et al* 1976, 1977a).

Delhaes *et al* (1977) conclude from EPR work that the lower transition is associated with the HMTTF stacks and that therefore the upper transition is associated with the TCNQ stacks. It is this picture of a high-temperature distortion predominantly on the TCNQ stacks, and a lower temperature distortion that is of the nature of a lock-in transition on the HMTTF stacks, that we shall follow up in this section, as it can provide a natural explanation for the observed conductivity behaviour.

When both types of stack are distorted a thermally activated conductivity is expected at low temperatures and indeed observed for the pressure regime below 3 kbar. Above 3 kbar, for the whole of the remaining pressure regime investigated in the present work, there is only one transition left, that on the TCNQ stacks. It will cause these stacks to be semiconducting, but since the measured conductivity along the *b* axis is the sum of the conductivities of the two types of stack, we must consider the influence of the TCNQ stack distortion on the HMTTF stacks in order to understand the observed conductivity behaviour. Whether or not the HMTTF stacks will feel a potential with the *b* axis, Peierls distortion, periodicity from the TCNQ stacks will depend on the transverse period of the distortion. When this potential is present, its effect on the HMTTF stacks will be to open a gap at the Fermi level. Since screening between stacks will reduce the strength of this potential, this gap will be weaker than that on the TCNQ chains; also its effectiveness in reducing the number of free carriers will depend on the degree of transverse band dispersion, (larger for HMTTF and HMTSF than for TTF and TSF materials).

For the case of TTF-TCNQ, between 53 K and 49 K the transverse period is 2a (Comès 1977) so there will be no net potential on the TTF stacks, and the reduction in the conductivity in this temperature range will come from the removal of the contribution from the TCNQ stacks. Below 49 K the transverse period starts to increase, locking into 4a at 38 K; there is a net potential (and distortion) on the TTF stacks and this is sufficiently strong to produce thermally activated conduction on the TTF stacks before the 38 K transition.

For HMTTF-TCNQ above 3 kbar we note that the total conductivity is only weakly activated (for $P \ge 3$ kbar, $2\Delta < 150$ K). This indicates a transverse period that allows a net $2k_F$ potential to be seen by the HMTTF stacks, but a potential which at moderate pressures is only just strong enough to remove all the carriers on the HMTTF stacks. At higher pressures with the weakening of the TCNQ stack distortion and an increase in the transverse band dispersion, this is no longer so, and metallic behaviour, as shown in figure 4, is seen below the distortion temperature.

We stress that metallic behaviour at low temperatures is stabilised in samples which still clearly show a transition (sample 19 in figure 4) and that complete suppression of the distortion would require a pressure of between 35 and 40 kbar. It is perhaps surprising that, in contrast to the lower transition, the upper transition temperature falls only linearly with pressure. However the compressibility of these charge transfer salts falls quickly with pressure (Debray *et al* 1977) so that equivalent volume changes require larger pressure changes at high pressures.

The results we have presented for HMTTF-TCNQ are of immediate relevance to HMTSF-TCNQ and its relation to the other members of this series of TCNQ salts. That such a change in behaviour in HMTTF-TCNQ can be brought about with moderate pressures shows that only slight changes in properties such as interchain coupling are sufficient to stabilise semimetallic behaviour at low temperature. (At ambient pressure
the difference in properties between the sulphur and selenium compounds is most likely due to the differences in *a* axis coupling, with a shorter Se...N contact (3·10 Å) than S...N (3·25 Å) (Greene *et al* 1976).

There has been much speculation as to the cause for the gentle rise in the resistivity of HMTSF-TCNQ below 30 K; whether this is an indication of a weak Peierls transition, whether at ambient pressure it is a narrow gap semiconductor (Cooper *et al* 1976b, Jérôme and Weger 1977), or, in view of the strong sample dependence of the actual magnitude of the resistivity rise, whether this low-temperature rise is entirely due to the presence of defects and impurities (Bloch *et al* 1975). The cooling curves shown in figure 4 indicate clearly that HMTSF-TCNQ at atmospheric pressure shows the same low temperature rise as HMTTF-TCNQ at around 10 kbar. This is in the pressure range where one of the two atmospheric pressure transitions has been suppressed, but where the other is still present. Thus we infer that at atmospheric pressure HMTSF-TCNQ undergoes a distortion on one type of stack only, probably TCNQ. In contrast to HMTTF-TCNQ, the resistance anomaly in HMTSF-TCNQ can be driven out altogether at moderate pressures, as is shown in figure 4 which reproduces data for HMTSF-TCNQ from the work of Cooper *et al* (1976b).

The picture we have presented for HMTSF-TCNQ at atmospheric pressure and for HMTTF-TCNQ above 3 kbar, that of a low temperature distortion on predominantly the TCNQ stacks, can provide a simple explanation for the strong sample dependence of the magnitude of the resistivity rise below the transition temperature, by taking into account the transverse conductivity. While conduction along the stacking axis can take place independently on each type of stack, transverse conduction for materials with the HM structure (alternating donors and acceptors in both the *a* and *c* directions) must require participation from both types of stack. When the TCNQ stacks distort and become semiconducting it is to be expected that the transverse resistivity will rise, as has been reported by Cooper *et al* (1976a). A comparable situation exists for the layered compound 4H$_b$TaS$_2$, which shows similar Fermi surface driven distortions. It consists of alternating layers of octahedrally and trigonal prismatically coordinated TaS$_2$, and at low temperatures the octahedrally coordinated layers are insulating while the trigonal prismatic layers remain metallic. An increase in the anisotropy is seen at low temperatures (Wattamaniuk *et al* 1975). For a system where the anisotropy increases rapidly at the transition it is clear that any transverse component in the measured resistivity (arising from contact misalignment and crystal defects, and thus sample dependent) will show up strongly at the distortion temperature although it may be undetectable at higher temperatures. Thus much of the increase in the *b* axis resistivity in for example HMTSF-TCNQ at atmospheric pressure (Bloch *et al* 1975) may come from transverse components of the resistivity, consequently varying from sample to sample.

The mechanism for the *T*² dependence of the resistivity, and its very rapid change with pressure has yet to be settled. Our results for HMTTF-TCNQ confirm that this pressure-sensitive *T*² law is a general feature for all compounds in this series of charge transfer salts. The explanation put forward by one of the present authors is that Coulomb effects play an important role (Jérôme *et al* 1977) particularly since the susceptibility (considered to be enhanced by Coulomb effects) is the only other parameter so far measured that is as pressure sensitive as the resistivity. There are alternative explanations however involving coupling to libron modes (Weger and Friedel 1977, Gutfreund and Weger 1977) or involving phonon induced localisation (Cohen *et al* 1975, Gogolin *et al* 1975).

In the light of the strong similarities between HMTSF-TCNQ and HMTTF-TCNQ under pressure, the structural differences between them are a little surprising, and a further,
comparative structural study may prove interesting. There remains an urgent need for a diffraction investigation of the low-temperature phases of both HMTSF-TCNQ and HMTTF-TCNQ before a fuller picture for these compounds can be put together.

## 5. The effect of pressure on the Peierls distortion—a unified picture for the TCNQ charge transfer salts

In the previous section the strong similarities in the high-pressure behaviour of HMTTF-TCNQ and HMTSF-TCNQ were discussed, and taken as evidence for the similarity in the low-temperature distorted phases of the two compounds. In contrast for the other two TCNQ salts so far investigated, high-pressure stabilises the distorted phase. Thus in TTF-TCNQ the upper transition temperature rises at 1.4% kbar⁻¹ (Chu *et al* 1973, Jérôme *et al* 1974, Cooper *et al* 1975), and in TSF-TCNQ the distortion temperature rises at 6% kbar⁻¹ (Cooper *et al* 1977a) up to 10 kbar, although a subsequent saturation between 10 and 32 kbar has been seen recently (Cooper and Jérôme 1977). Since in many other aspects, such as optical properties (Tomkiewicz *et al* 1977b) and susceptibility (Delhaes *et al* 1977), HMTTF-TCNQ behaves similarly to these materials, we feel that the reasons for these differences in high-pressure behaviour require clarification.

The important feature that distinguishes the two HM materials from TTF-TCNQ and TSF-TCNQ is the difference in the transverse ordering of the donor and acceptor stacks. In the monoclinic TTF-TCNQ structure layers of TTF and TCNQ alternate along the *a* axis (Kistenmacher *et al* 1974), whereas in the orthorhombic HM structures, donor and acceptor molecules alternate along both the *a* and *c* axes (Phillips *et al* 1976, Greene *et al* 1976). This results in a stronger transverse coupling in the HM structures. Evidence for this comes from the conductivity anisotropy and from the NMR proton relaxation rate.

Conductivity anisotropies are collated in table 1. The anisotropy in the direction of the *a* axis is systematically weaker for the HM structures. Soda *et al* (1977) relate the conductivity anisotropy to the transverse and longitudinal overlap integrals, and for the type of behaviour shown by all these compounds at room temperature, they find (equation 17') $\sigma_{\perp}/\sigma_{\parallel} \propto (t_{\perp}/t_{\parallel})^2$. Thus a direct comparison of the band structure anisotropies can be made. Interestingly, the *c* axis conductivity is the same (3–4 Ω⁻¹ cm⁻¹) for all these materials.

A study of the magnetic field dependence of the proton relaxation time $T_1$ in TTF-TCNQ as a function of magnetic field (Soda *et al* 1977) has revealed a change from a field

<table><caption>**Table 1.** Room temperature conductivity anisotropies for the TCNQ charge transfer salts.</caption><thead><tr><th></th><th>σ<sub>b</sub>/σ<sub>a</sub></th><th>σ<sub>b</sub>/σ<sub>c</sub></th><th>σ<sub>b</sub>(Ω cm)<sup>-1</sup></th></tr></thead><tbody><tr><td>TTF-TCNQ</td><td>300<sup>a</sup><br>500<sup>b</sup></td><td>120<sup>b</sup></td><td>400<sup>a</sup></td></tr><tr><td>TSF-TCNQ</td><td>300<sup>a</sup></td><td>280<sup>a</sup></td><td>800<sup>a</sup></td></tr><tr><td>HMTTF-TCNQ</td><td>80<sup>c</sup></td><td>160<sup>c</sup></td><td>550<sup>c</sup></td></tr><tr><td>HMTSF-TCNQ</td><td>30<sup>a</sup></td><td>450<sup>a</sup></td><td>1800<sup>a</sup></td></tr></tbody></table>

(a) Cooper *et al* (1976b, 1977a)

(b) Heeger and Garito (1975)

(c) This work
independent $T_1$ below 10 kOe to a $T_1 \propto H^{1/2}$ field dependence above. This square root field dependence has been attributed to the one-dimensional propagation of the carriers restricted to a single chain; the life time of a carrier on a particular chain is related to the crossover to field independent behaviour, and this life time is estimated as typically $\tau_\perp \sim 10^{-11}$ s. In HMTSF-TCNQ no field dependence of $T_1$ has been observed (Soda et al 1976) and an upper limit of $\tau_\perp \sim 10^{-12}$ s has been established, confirming the stronger tunnelling type transverse coupling in the HM structure.

It has been recognised that an important distinction in the behaviour of these systems can made: whether or not the transverse motion of the carriers is diffusive or coherent (Soda et al 1977). If transverse motion is coherent then an anisotropic three-dimensional band structure description is appropriate, and this will predict large Hall voltages, an appreciable magnetoresistance and a Landau-Peierls diamagnetic contribution to the susceptibility (observed experimentally in HMTSF-TCNQ at low temperatures (Cooper et al 1976a, Soda et al 1976); for Hall effect measurements in TTF-TCNQ see Cooper et al 1977b). We term this regime of behaviour as three-dimensional coherent. When transverse motion is diffusive Soda et al (1977) have shown that the lifetime of a carrier on a particular chain $\tau_\perp$ is proportional to the reciprocal of the diffusion time within the chain $\tau_v$, $\tau_\perp \propto 1/\tau_v$. This results in a pressure independent conductivity anisotropy, which has indeed been observed in TTF-TCNQ and TSF-TCNQ at room temperature (Cooper and Jérôme 1977). We term this regime of behaviour as one-dimensional diffusive.

The crossover between these two regimes takes place when $t_\perp \tau_v/\hbar \sim 1$ (Soda et al 1977); if $t_\perp \tau_v/\hbar$ is larger than one, transverse motion is coherent, if smaller than one, diffusive. In the product $\tau_v t_\perp$ the transverse overlap integral is nearly temperature independent and only weakly pressure dependent $\sim 2\%$ kbar, from measurements of thermal expansion (Schultz et al 1976) and compressibility (Debray et al 1977). However $\tau_v$ (or the longitudinal conductivity) is strongly temperature and pressure dependent. Thus it is the temperature and pressure behaviour of $\tau_v$ that largely determine the possibility of a diffusive to coherent transition (DCT), and we define $T^*$ as the temperature at which $t_\perp \tau_v(T^*) = \hbar$. At ambient pressure and temperature all compounds are in the one dimensional diffusive regime and it is clear that either lowering the temperature or increasing the pressure may induce a DCT. Whether transverse motion is diffusive or coherent when the Peierls distortion temperature is reached will determine the pressure behaviour of the distortion temperature. $T^*$ and $T_p$ are shown in table 2; $T^*$ was estimated from the conductivity anisotropy along the a axis, the band filling, the plasma frequency and the

<table><caption>**Table 2.** Estimates for $T^*$, the diffusive to coherent transition temperature, and values of $T_p$, the Peierls transition temperature (taken to be the highest transition temperature in the cases of TTF-TCNQ and HMTTF-TCNQ).</caption><thead><tr><th></th><th colspan="2">TTF-TCNQ</th><th colspan="2">TSF-TCNQ</th><th colspan="2">HMTTF-TCNQ</th><th colspan="2">HMTSF-TCNQ</th></tr><tr><th></th><th>p = 1 bar</th><th>p = 10 kbar</th><th>p = 1 bar</th><th>p = 10 kbar</th><th>p = 1 bar</th><th>p = 10 kbar</th><th>p = 1 bar</th><th>p = 4 kbar</th></tr></thead><tbody><tr><td>T*(K)</td><td>&lt;60</td><td>&lt;60</td><td>&lt;60</td><td>&lt;60</td><td>100</td><td>300</td><td>200</td><td>400</td></tr><tr><td>T<sub>p</sub>(K)</td><td>53<sup>a</sup></td><td>56<sup>a</sup></td><td>29<sup>b</sup></td><td>40<sup>b</sup></td><td>49<sup>c</sup></td><td>35<sup>c</sup></td><td>25<sup>d</sup></td><td>0<sup>d</sup></td></tr></tbody></table>

<footnote>(a) Cooper et al (1975)</footnote>

<footnote>(b) Cooper et al (1977a)</footnote>

<footnote>(c) This work</footnote>

<footnote>(d) Cooper et al (1976a)</footnote>
escape time $\tau_\perp$ from NMR. Note that $T_p > T^*$ for TTF-TCNQ and TSF-TCNQ, but $T_p < T^*$ for the two HM structures. (A further requirement for the three-dimensional band picture to be valid is that $kT < t_\perp$ (Jérôme and Weger 1977), but since in all compounds studied here, $t_\perp/k$ and $T^*$ are of the same order of magnitude, the condition $T < T^*$ is sufficient for the band picture to be applicable). We now consider the pressure behaviour in each regime.

(i) Structural phase transition above the DCT

This is the situation for TTF-TCNQ and probably for TSF-TCNQ. In this regime Fermi surface 'nesting' is perfect, and the mean field energy gap equation gives $T_p^0 \sim E_F \exp(-1/\lambda)$, where $\lambda$ is the coupling constant. Interchain coupling, tunnelling and Coulombic, is believed to suppress one dimensional fluctuations so that the actual transition temperature is close to $T_p^0$ (thus the maximum in conductivity in TTF-TCNQ at 57 K is close to the distortion at 53 K). Cooper et al (1977a) have analysed their results for TTF-TCNQ and TSF-TCNQ to determine $\lambda$ and its pressure dependence, using the mean field theory (its applicability is discussed by Jérôme and Weger (1977) and Horn and Rimai (1976)). They find for TTF-TCNQ $d\lambda/dp = -0.19\% \text{ kbar}^{-1}$ and for TSF-TCNQ $d\lambda/dp = +0.8\% \text{ kbar}^{-1}$. $\lambda$ will include contributions from both electron phonon coupling which drives a CDW distortion, and Coulombic effects which favour a SDW, and in the treatments of Chan and Heine (1973) and Barisic (1976) will have the form

$$ \lambda = N(E_F) \{2(I^2/M\omega^2) - U\}, $$

where $N(E_F)$ is the density of states at the Fermi level, $I$ the electron phonon matrix element, $M\omega^2$ the lattice force constant, and $U$ the Coulomb interaction. Since the two terms in the bracket are believed to be quite similar (Soda et al 1977) the pressure dependence of $\lambda$ is not easy to predict; Cooper et al (1977) use the tight binding theory of Barisic (1972) for $d/dp(I^2/M\omega^2)$ and find that it is physically reasonable to attribute all of $d\lambda/dp$ to this term, but since $U$ is believed to fall with pressure (Jérôme et al 1977) this effect will also increase $T_p$ with pressure. The faster increase in $T_p$ for TSF-TCNQ than for TTF-TCNQ is however difficult to reconcile as $U$ for TSF-TCNQ at 1 bar is considered to be smaller than for TTF-TCNQ (the susceptibility enhancement for TSF-TCNQ is less than for TTF-TCNQ. Tomkiewicz et al 1977a).

Two further effects should also be considered. Firstly, one dimensional fluctuations which may depress $T_p$ from $T_p^0$ are likely to be driven out by pressure, thus increasing $T_p$. As previously mentioned these fluctuations are considered not to depress $T_p$ by more than a few degrees, and their suppression would not be sufficient to explain the observed increases in $T_p$. Note that in contrast fluctuations dominate the pressure behaviour of KCP (Thielemans et al 1976).

Secondly, the smearing of the Fermi surface by the finite intrachain lifetime, $\tau_v$, must be taken into account. Its effect will be to reduce $T_p$ by $\sim h/\tau_v$ in the limit of large $\tau_v$, and since $\tau_v$ increases with pressure, this should cause $T_p$ to increase with pressure as well. The problem of finite lifetimes has been considered for the analogous case of excitonic insulators (Zittartz 1969), and is very similar to that of magnetic impurities in superconductors (Abrikosov and Gorkov 1964).

In this one-dimensional diffusive regime the treatment of Horovitz et al (1975) where $T_p$ is depressed as $\eta = t_\perp/t_\parallel$ approaches $(kT_p^0/E_F)$ is not applicable as the diffusive nature of the transverse conduction forces the Fermi surface to appear planar (although smeared out by thermal broadening and finite intrachain lifetimes).
### (ii) Structural phase transition below the DCT

This is the situation for HMTSF-TCNQ and HMTTF-TCNQ. In this regime the treatment of Horovitz et al (1975) is applicable; experimentally it is usually the case that $η$ is sufficiently large to suppress one-dimensional fluctuations, and the transition will be close to the mean field distortion temperature. In this regime, where $T_p$ falls with pressure, most of the pressure dependence must come from the increase in $t_⊥$, which if $t_⊥/t_∥ \sim (kT_p^0/E_F)$ will hinder Fermi surface nesting and depress $T_p$. For a system where $τ_v$ is still quite short, the effectiveness of $t_⊥$ in reducing $T_p$ should be increased with pressure as $τ_v$ becomes larger and the system moves further into the three dimensional regime.

In conclusion, we have suggested that both regimes of behaviour outlined in (i) and (ii) above are seen in this series of compounds, as shown in table 2. We emphasise that pressure increases three dimensionality not so much through $t_⊥$ but more through $τ_v$. In the treatment we have presented we have not needed to understand the nature of the scattering mechanisms that determine $τ_v$, although $τ_v$ and $t_⊥$ are in fact probably related since strongly coupled compounds are those which show the largest conductivities.

We summarise the picture we have developed in this section in figure 6.

<figure><img src="image_7.png" /></figure>

**Figure 6.** Simplified picture for the effect of pressure on the Peierls distortion temperature. $T_p$ for the TCNQ series charge transfer salts. Of the parameters determining $T_p$, $λ$ is taken to be constant with pressure, while $τ_v$ the intrachain lifetime and $t_⊥$ the transverse transfer integral both increase with pressure, $τ_v$ more quickly than $t_⊥$. At low pressures $T_p$ is depressed from its mean field, one-dimensional value $T_p^0$ by the lifetime broadening from $τ_v$ and one dimensional fluctuations, and the system is in the one-dimensional transverse diffusive regime. As the pressure is raised $τ_v$ becomes longer, $T_p$ rises and when $t_⊥τ_v = ħ$ at $T_p$ the system enters the three-dimensional transverse coherent regime. As the pressure is further raised the behaviour of $T_p$ is dominated by $t_⊥$, and $T_p$ will fall as the Fermi surface becomes more three dimensional and Fermi surface nesting is weakened. Arrows indicate the positions at atmospheric pressure of the various TCNQ salts discussed in § 5. Note that this picture implicitly assumes the correlation between $t_⊥$ and $τ_v$ which is experimentally observed for both varying pressure and composition.

## Acknowledgments

We thank J Friedel, S Alexander and J R Cooper for many fruitful discussions. We are grateful to M Weger for a critical reading of the manuscript. We thank G Malfait and A Andrieux for technical help.
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