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ELECTRONIC PROPERTIES OF TTF-TCNQ :A CONNECTION BETWEEN THEORY AND EXPERIMENT (*)

L. G. CARON (**), M. MILJAK (***) and D. JEROME

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

(Reçu le 29 juin 1978, révisé le 29 août 1978, accepté le 4 septembre 1978)

Résumé. 2014 La détermination expérimentale de la partie imaginaire de la fonction de réponsedes excitations magnétiques à q = 2 kF a été réinterprétée. La dépendance en température, à volumeconstant fait apparaître un maximum de Im X(2 kF). Cet argument, ainsi qu’une relation étroiteentre 03C1/T et Im ~(2 kF) ont stimulé l’établissement d’une théorie basée sur des traitements déjàexistants pour les interactions électrons-électrons intrachaînes et qui a été modifiée de façon à tenircompte des effets du pseudo-gap de phonons. La comparaison entre cette théorie et les donnéesexpérimentales de Im X(2 kF) et de la susceptibilité statique a permis d’obtenir des valeurs des para-mètres de l’interaction électron-électron et de l’interaction electron-phonon pour plusieurs tem-pératures et pressions.

Cette étude a fait ressortir l’importance des effets électrons-électrons et des effets électrons-pho-nons dans TTF-TCNQ. De plus elle a le mérite de faire le lien de façon cohérente entre les fortesaugmentations magnétiques et les propriétés des transitions de phases structurales.

Abstract. 2014 Reinterpretation of the experimentally determined imaginary part of the spin exci-tation response at q = 2 kF has led to the existence of a maximum in constant volume temperaturedependences. This fact, together with the observed similarity between 03C1/T and Im ~(2 kF), has trig-gered the development of a theory based on existing treatments for the intra-chain electron-electroninteractions modified by phonon pseudo-gap effects. Parameters for electron-electron and electron-phonon couplings have been derived from a fit with the data of Im ~(2 kF) and the static susceptibi-lity at selected pressures and temperatures. This study shows the importance of both electron-electronand electron-phonon interactions in the electronic properties of TTF-TCNQ. Moreover, it reconcilesthe large magnetic enhancement with the structural phase transition properties.

LE JOURNAL DE PHYSIQUE TOME 39, DÉCEMBRE 1978,

Classification

Physics Abstracts72.15N201371.45G

1. Introduction. - High pressure measurements [1]have had a strong impact on the experimental study ofthe electronic properties of the conducting chargetransfer salts of the TTF-TCNQ family. In particular,the very large pressure coefficients found in a varietyof physical properties suggested the inability of theone-electron theories to provide a proper understand-ing of the static susceptibility and resistivity [2].On one hand, the importance of the intra-chain

Coulomb interactions in explaining the magneticproperties of TTF-TCNQ has been emphasized byseveral authors [3, 4, 5]. Moreover, inclusion of inter-

chain Coulomb coupling is compatible with chargedensity (CD) phase transitions [6, 7, 8]. However, theimportant room temperature effects observed inthe NMR relaxation rate of TTF-TCNQ, which willbe discussed in the next section, are difficult to

understand with just these Coulomb interactions.On the other hand, conventional Peierls treatments

using a phonon mediated electron-electron interactionhappen to be fairly consistent with the existence ofstructural phase transitions, but have been unable sofar to provide a satisfactory explanation of the

magnetic properties.The purpose of this paper is to propose a theoretical

support, combining both electron-electron and elec-tron-phonon interactions, to the structural propertiesand the reinterpretation of the magnetic propertiesof TTF-TCNQ. In section 2 we develop the experi-mental background required for the theoretical model

(*) Work supported in part by DGRST contract n° 75-7-0820.(**) Permanent address : Département de Physique, Université

de Sherbrooke, Sherbrooke, Québec, JIK 2R l, Canada.(***) Permanent address : Institute of Physics of the University,

P.O. Box 304, Zagreb, Yugoslavia.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197800390120135500

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treated in section 3. The results are discussed andlimits set to the validity of the model in the followingsections.

2. Experimental détermination of Im Z(2 kF). -

Cooper [9] has recently drawn attention to the factthat, when corrected for the effect of thermal expan-sion, the temperature dependence of the constantb-axis resistivity is strongly reduced from the observ-ed ~ T2.3 law at atmospheric pressure. The actualconstant volume resistivity along the h-axis has beenderived in some detail by Friend et al. [10]. It is cha-racterized by a linear power law, particularly above150 K. In fact, similar constant volume correctionsmust be applied for all strongly pressure dependentquantities.

In this article we wish to draw attention to theconstant volume behaviour of physical quantitiesderived from the NMR experiments. The relaxationrate of protons in selectively deuterated samplesof TTF-TCNQ has been studied as a function of

temperature, pressure and applied magnetic field [11].It was thus shown that only backward (q = 2 kF) andforward (q = 0) scatterings contribute to the nuclearrelaxation induced by the modulation of the hyperfinefield in one-dimensional conductors. The dïffusivecharacter of the q - 0 spin excitations of finite life-time electrons (Im x(q - 0) ~ Dq2) leads in one

dimension to a magnetic field dependence of therelaxation rate, TI-I ~ HO-1/2. The effect of the q = 0spin excitations is dominant upon the effect of the

q = 2 kF excitations in low fields, namely Ho 30 kOe.However, the non-diffusive q = 2 kF spin excitationshave been shown by experiment to dominate therelaxation at high fields. A very careful field depen-dence study has therefore allowed a direct experimentalaccess to the determination of the imaginary part of thespin density (SD) response function at q - 2 kF,Im x(2 kF), which is in tum proportional to the coef-ficient C2 of reference [11]. The main experimentalfeature of this article is a non-trivial constant volume

temperature dependence of Im x(2 kF) since, as shownin [11], C2 is strongly pressure dependent.We shall now develop the procedure we have used to

achieve the constant volume reduction. Reproducedon figure 1 is the constant pressure dependence of theexperimental quantity

where A is .the hyperfine interaction constant. ThusIm x(2 kF) ..

(g03BCB)2 hO) depends only on the electronic properties

of either chain considered. The striking features arethe large value and the strong temperature depen-dence of Im x(2 kF), both behaviours not usuallyobserved in normal metals [12]. Below 110 K we haveused in figure 1 the temperature dependence of

FïG. l. - Constant pressure, temperature dependence of

derived from NMR data [I1] for both chains (continuous lines).Constant volume curves for the volume of 300 K ( .... ) and forthe volume of 60 K (-----). Plot of the constant pressuredependence of p/T normalized at room temperature with the valueof lm X(2 kF) for both chains (- - -). Data of reference [10]have been used in this figure, 03C3 (60 K)/03C3 (300 K) = 25. A typicalvalue of Im X(q)/(gPB)2 hw in a normal metal should lie around

5 eV-’.

the 13C relaxation rate for the TCNQ chain [13] andthe temperature dependence of the proton relaxationrate in TTF-TCNQ (D4) samples for the TTFchain [14]. This is justified since it has been demons-trated [11] that at low temperature the dominantrelaxation mechanism is that coming from the

q = 2 kF spin excitations. We have drawn in figure 1the temperature dependence of Im x(2 kF) for twovolume that of 300 K and that of 60 K. The b-axis

parameter decreases by 2.3 % between 300 K and 60 K.This corresponds to the application of a 5 kbar

pressure at room temperature [10]. Therefore, the

300 K and 60 K values of the v(60 K) temperaturedependence are directly inferred from experiment.For the temperatures in between, we proceeded in thefollowing way. It can be noticed that the pressuredependence of Im x(2 kF) and the resistivity are similarat ambient temperature, typically [10]

On figure 1, we notice that the temperature dependenceof p/T follows closely that of lm X(2 kF) even though a

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decrease of the resistivity by a factor of 25 is now

currently observed on good quality crystals. Actuallythe agreement is especially good for the TCNQ chain.This fact may not be entirely fortuitious since first,the conductivity in TTF-TCNQ is known to be

electron-like above 60 K from thermopower [15],.Hall effect [16] and NMR [17] determinations, andsecondly, because it has been suggested [18] that theresistivity could be of magnetic origin in these 1-Dconductors, leading precisely to p/T ~ Im x(2 kF).Explanation of the resistivity is still controversial.We only make use of the analogy between pressureand temperature dependence of the resistivity and C2,setting

and otherwise following the procedure already usedfor the derivation of the constant-volume temperaturedependence of the resistivity [10].We now wish to comment on the curves of figure 1.

There is no doubt that Im x(2 kF) exhibits a maximum’in its intrinsic temperature dependence, the maximumon the 300 K volume curve being probably slightlybelow ambient temperature. We are reasonablyconfident in the constant volume profiles of the TCNQchains and to a lesser extent in those of the TTF chains.But the message still remains the same, that is theexistence of shallow maxima at constant volume forboth chains.

3. Theory. - The task at hand is to develop atheoretical model which can explain the large valuesof Im x(2 kF), the occurrence of a maximum in theconstant volume curves of figure 1, and the observedstructural transition of TTF-TCNQ. The large valuesof Im x(2 kF) can easily be explained by invokingimportant intra-chain Coulomb interactions. Meanfield [6], Parquet [19, 20, 21], or renormalization

group [22, 7, 8] treatments indeed yield considerablespin density response enhancement in such cases.

These are, however, divergent at low temperatures.This divergence can conceivably be prevented by theappearance of a pseudo-gap. We eliminate the

possibility of a SD pseudo-gap, such as predicted bya 1-D Ginzburg-Landau theory, because we believeit is incompatible with the observed Peierls transition.The Parquet or Solyom renormalization groupapproaches seem much more suitable since theypredict low temperature divergence in both SD andcharge density (CD) responses, the former beingdominant for repulsive intra-chain electron interac-tions. The maximum in the Im x(2 kF) constant volumecurves cannot be explained by inter and intra-chainCoulomb forces only, within first order renormali-zation theory [7]. Second order renormalization can,however, predict such a maximum [8]. But it is our

feeling that the ensuing constant volume temperatureprofile, whose maximum is governed by the weakbackward-scattering inter-chain Coulomb interaction,

is not so readily reconciled with figure 1 and especiallythe important room temperature effects. Moreover"the validity of second order renormalization theory ischallenged by a number of people [23, 24]. The aboveconsiderations, plus the obvious involvement of

phonons in the structural transition, lead us to focus onphonon mechanisms as a probable cause of the pseudo-gap. We thus adopted a strictly 1-D model Hamil-tonian with both electron-electron repulsion and

electron-phonon interaction.Pseudo-gap effects have been studied in the absence

of Coulomb interactions [25, 26, 27]. The effect ofphonons in thé presence of these interactions has beendiscussed by several people [6, 19, 21], but not in thecontext of pseudo-gaps. In the case of TTF-TCNQ,which has a Debye temperature OD ~ 80 K, the static

approximation [6, 27] can be used to great advantagefor the temperature range of figure 1. The effect of theelectrons on the phonons is reduced, in this limit, tothe random phase approximation to the phononpropagator :

where Do - - 2/OD is the bare phonon propagator,g is the electron-phonon interaction, and N(k) isthe CD response of the electron gas at wave number k.The feed-back effect of the phonon on the electrons isnot so simple. The correction to x(2 kF) and N(2 kF)to first order in g2 is of the self-energy type. Thissuggests using the Migdal approximation to’the self-energy [6, 27] of the electron propagator which, in thestatic approximation, is expressed as :

where T is the temperature, Wn is the Matsubara

frequency, D(k) is the effective vertex-corrected pho-non propagator to be defined shortly, G(p, icvn) is theelectron propagator

in which r is the Fermi velocity.The important electron-phonon scattering in eq. (2),

which is responsible for the pseudo-gap, occurs atk = 2 kF. There are thus logarithmic screening effectswhich modify the electron-phonon vertex. Within theusual g·ology formalism, one can write the leadingterms of the expansion of D in the bare couplingconstants gl and g2, those corresponding to the vertex-correction diagrams of figure 2a, as :

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FIG. 2. - a) Leading diagrams in the electron-phonon vertex

corrections. b) Leading diagrams in the q = 2 kF response function.

where g is the backward scattering constant, g2 is theforward scattering constant, and

EF being a quantity of the order of the Fermi energy.Using the usual renormalization group rules [22], oneobtains

where

and

The self-energy, eq. (2), will yield a pseudo-gapwhenever 1 D 1 in eq. (6) stands out well over thebackground at q = 0, that is for

The width of the peak is given by the renormalizationgroup approach, eq. (5), as Aq - T/v = ç-l, ç beingidentified as the phonon coherence length. Under theseconditions, and further neglecting all contributions

foreign to the pseudo-gap, eq. (2) becomes [26, 27],

where

and

In as much as 4 > T, the concept of a pseudo-gap ismeaningful. Ideally, a consistent treatment would

require replacement of all the bare electron propa-gators in the Parquet diagrams by the self-energycorrected one

One can, however, estimate the impact of the pseudo-gap on the electronic responses,

where v’ = max (go, l’q, T)/ EF, by realizing that it willattenuate the logarithmic divergence at small v’ and

saturate it whenever v’ ;5 A/EF. We then propose afourth energy cut-off d such that

Within this approximation scheme, the electronic

responses N(2 kF) and x(2 kF) can be calculated self-consistently with eq. (10).Our primary interest is with Im X(2 kF). This

quantity can be calculated within the Solyom renor-malization group approach by calculating the leadingterms in the bare coupling expansion, those corres-ponding to the diagrams in figure 2b,

where x°(2 kF + q, w) is the SD response of the non-interacting electron gas. The renormalization grouprules then give us

where

The effect of the pseudo-gap as proposed in eq. (13),although sufficient for the real part of the response

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functions, is incomplete as far as the imaginary part isconcerned. This latter quantity is quite sensitive to theelectronic density of states D(0) within the pseudo-gap,

We then propose to replace D(0)2 in this last equationby D(O)2, the average being calculated by the substi-tution of G for G in the definition of x°, which thenbecomes

A second correction is needed, namely for the bandedge effects of a more realistic tight binding band. Thiscan be estimated by comparing

for the non-interacting gas to the same tight bindingquantity [6]

where TF is the Fermi energy. We thus propose to

replace EF by 4.56 TF.In order to try out our model, we decided to cha-

racterize each type of chain, TTF and TCNQ, withsix parameters : v, Â, g1 (300 K), g2 (300 K), g 1 (60 K),g2 (60 K), which we could adjust to reproduceIm x(2 kF) at the 60 K volume, for T = 60 K and300 K, and at the 300 K volume, for T = 300 K,further adjusting the position of the maximum at thislatter volume to its approximate position in figure 1.

This left two independent parameters. In order torestrict the arbitrariness further, we chose to cal-

culate the static magnetic susceptibility and adjust itto the experimental value at 300 K. We made use ofthe Landau Fermi liquid formula proposed byLee et al. [7]

where

We further corrected for pseudo-gap effects bycombining the effect of the renormalized Fermi

velocity r* and the pseudo-gap Li in an averageD*(0) = - 2 Re XO(O) calculated from eq. (18) but

with v* substituted for i, in eqs. (3), (9) which entereq. (12). This correction should be reasonable pro-vided the pseudo-gap is not too large.

TABLE 1

Typical values for these fits at 60 K and 300 K forboth values of the ratio XTTI(O)/XTIIQ(o) = 3/2, 7/3current in the literature, are shown in table I. In the

calculations, we have allowed for thermal expansioneffects on the bandwidths, i.e. on r and À, which

change by 6 % and 12 % for TTF and TCNQ res-pectively, but not for changes in band occupancy [28].The temperature profile for Im x(2 kF) and x(0) whichresult from these fits, and the further assumption of anexponential dependence of the bare coupling cons-tants on the intermolecular spacing b, are shown in

FIG. 3. - calculated temperature dependence of

for both chains at constant pressure. Constant volume temperaturedependences for the volume of 300 K and 60 K (- - -). The

experimental points used in the fit have been marked (2022).

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FIG. 4. - Calculated temperature dependence of the total staticsusceptibility (- - -) compared with experiment (continuousline). The value of x(0) at room temperature is the only experimental

point used in the fit.

FIG. 5. - Initial pressure coefficient of the conductivity for TTF-TCNQ, versus temperature, for two samples. Calculation of

ô In Im X(2 KF)ID In b (dashed line) for TCNQ.

figures 3 and 4. In view of the close analogy observedbetween Im x(2 kF) and p/T for TCNQ in figure 1, wehave also calculated the TCNQ

and plotted its temperature dependence in figure 5.Finally in an attempt to make some sort of statement

on the phase transitions and the pressure dependenceof the transition temperature Tc, we have used theGinzburg-Landau theory of weakly coupled metallicchains of Menyhard [29] which predicts a transitionwhen

where g~1 is a transverse Coulomb coupling constantand XCDW1-D(2 kF) is the total one-dimensional chargedensity response. We estimated that

A representative pressure profile of Tc for the TTFand TCNQ stacks is shown in figure 6, assuming aconstant inter-chain coupling. It is interesting to notethat the value of g 1 j2 ni, required for an ambientpressure Tc of 60 K is of the order of 0.01, in quite goodagreement with the estimate of Lee et al. [7].

FIG. 6. - Calculated profile of the transition temperature as afunction of the relative change of the lattice constant b, in a trans-

verse mean-field approximation.

We wish, at this point, to draw attention on the factthat the results shown in figures 3 to 6 are quite insen-sitive to the exact ratio XTTF(O)IXICIQ(o) used in thefits.

4. Discussion. - There are a number of points wenow wish to discuss with regard to the applicability ofthe previous theory to TTF-TCNQ electronic pro-perties.

Let us first examine the values of the fitted para-meters in table I. The values for g 1 /2 ni, and g2/2 03C0l’indicate that the intra-chain Coulomb interaction is

long-range in contrast with the more usual Hubbarddelta type interaction. These parameters are alsoseen to vary considerably with inter-molecular spacing.This indicates highly important non-logarithmicscreening effects which increase with pressure and tendto equalize gl and g2. The values of the band andelectron-phonon coupling parameters are also seen tobe in good agreement with the theoretical estimatesbased on molecular orbital calculation [30]. Thebandwidths are also compatible with the thermopowermeasurements in TTF-TCNQ [15]. It should be

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mentioned at this point that, even though there is someleeway in the value of the parameters of table I, thequality of the fits does not allow for much morethan 10 % uncertainty in all parameters. As to thevalue of À, an upper limit can be derived from thebehaviour of the resistivity. Rather crudely forgettingabout the existence of chains of different nature, theobserved resistivity of TTF-TCNQ can be writtenp(T) = po + pph(T) + pi(T) where po and pph(T)are the residual (temperature independent) and thephonon temperature dependent

terms respectively. Actually, these last two contri-butions cannot explain the very large initial pressurec,oefficient of the conductivity observed aroundambient temperature. Near 300 K, we can expectPph > po and

.

is the axial Gruneisen constant equal to~ ln 03B8D

where Yb is thé axial Gruneisen constant equal to è ln band obtained from the compressibility experiments [3].

~ ln PphThis value of 8 ln; is almost one order of magnitudeô In b’

smaller than the observed initial pressure coefficient

~ ln 03C3 ~ 50-60 [10]. One is led to conclude that,alnb 2013 50-60 [10]. One is led to conclude that,

at least in the low pressure domain, the resistivityof TTF-TCNQ is governed by the contribution pi,

Pi > Pph > PO, which must be strongly pressuredependent. The high pressure situation, however, is

presumably different since ~ in 03C3 becomes quitep y ô In b q

significantly smaller under pressure [32]

We thus believe that, under these high pressureconditions, the phonon contribution to the resistivitymight be as important as the resistivity of unknownorigin p;, the temperature dependence of the constant-pressure resistivity approaching the linear power law.An upper limit to the electron-phonon couplingconstant can thus be derived from the high pressureresistivity since [33]

all factors being taken at 30 kbar. With the use ofaplaT = 10-6 03A9 cm. K-1 [32] and wp = 1.4 eV [28]at 30 kbar, eq. (22) leads to À30kbar = 0.35. In the tightbinding band picture  - ti, and therefore with

Atllltll 10~30 kbar ~ 36 %, we can expect Ào 5 0.26.

This upper limit for À is in good agreement with thevalue derived from the fit in table I.The measurement of the initial pressure coefficient

of the resistivity in TTF-TCNQ has been extendedtowards higher temperatures - 360 K. The experi-ments have been conducted with a helium gas pressureequipment between 0 and 2 kbar. The temperature,measured inside the pressure cell with a copper-constantan thermocouple, was kept constant within± 0.1 K as the pressure was slowly varied. In order to

derive the value of ô In a we have used a longitudinalôlnb g

compressibility of 0.47 % kbar-’ 1 at ambient tem-

perature [31]. The relative temperature dependence ofthe compressibility has been derived from the LAphonon branch determined by inelastic neutron

diffraction [34]. The results are displayed on figure 5for the two samples studied. The agreement with

. ~ ln 03C3

previous measurements of a In a between 60 K and300 K is satisfactory. The new feature is the existence

of a maximum in ~ ln 03C3 around 300 K. The calculatedôlnbô In lm y(2 kF) .

values of a ln b which are also plotted in thesame figure, show the same magnitude although themaximum is shifted roughly by 100 K towards thelower temperature. The position of the maximum,here as in the constant volume curves of figure 2,does not seem too reliable and should not be taken too

literally. Figure 5 nevertheless tends to support theproportionality relation between Im x(2 kF) and p/Talready mentioned in the introduction.

It now seems proper to discuss the limit of vali-

dity of our theoretical model. Towards the low

temperature side, the static approximation usedfor the phonons might be expected to break downwhenever T 0D [6,27], whereas interchain tunnellingeffects, leading to a three dimensional band picture,come into consideration when h/Tv = tl [1, 11]. Thislatter condition is fulfilled in TTF-TCNQ around 60 Kat ambient pressure. Towards the high temperatureside, one can question an expansion in In (EF/T), as inthe Parquet or renormalization group approaches,whenever x(2 kF) ~ x(0). This occurs for

that is near ambient temperature in TTF-TCNQ usingthe band parameters of table I. Moreover, the Landau-Fermi liquid formula, eq. (19), used for the static

magnetic susceptibility, is itself of limited temperaturerange. This formula predicts a continuous increaseof X(O) with temperature. This is obviously incorrect.For instance, the Shiba-Pincus [35] computer simu-lation for a half-filled tight-binding band clearlyexhibits a maximum in X(O) at the pseudo-magneticordering temperature T - tTI/g1. This maximum is

expected to occur near ambient temperatures for

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TTF-TCNQ again using the values in table 1 [36] incontrast, for instance, with the case of TSeF-TCNQwhich shows no maximum in x(0) up to 375 K [37] butwhich is also expected to have much smaller valuesof g 1/2 Ter. There is finally one last limiting criterionfor applicability of our model to TTF-TCNQ. Thechains are expected to lose their coherent 1-D cha-racter and become diffusive whenever the electronmean free path becomes of the order of the inter-molecular spacing. This again occurs at ambient

temperature [11].We shall finally comment on the pressure depen-

dence of the transition temperature calculated fromthe extrapolated lattice spacing dependence of g, 1and g2 between 60 K and 300 K, correspondingto Ab/b - 2.3 %. Figure 6 shows the predictedpressure dependence of T,, as calculated by a trans-verse mean-field theory, up to Ablb ~ - 8 % cor-responding to ~ 30 kbar in TTF-TCNQ. The mainfeature is the possibility of a minimum in Tc, dependingon the values of the parameters. This minimum isassociated to a change of regime between a Parquet-type situation dominated by the Coulomb intra-chaininteraction and a mean-field type situation (theV > 1 U 1 limit of reference [6]). As to comparisonwith the actual experimental phase diagram of

TTF-TCNQ [38], a minimum has actually beenobserved at 30 K and 5 kbar in what is believed to bethe transition of the TTF stack. However, the tran-sition of the TCNQ stack is found to increase slightlyunder pressure, going through a sluggish maximumtill a pressure of 15 kbar where both transitions mergeinto a single one. These experimental facts can still

perhaps be reconciled with figure 6 in the followingway. It is evident that the Parquet is incomplete in thesense that it does not include, for instance, the effectof the higher order terms in the Solyom renorma-lization group approach [22]. With the g,12 ni, and92/2 ni, parameters in table I, the second ordercontribution is about half of the first order one at 60 Kwhile it is nearly the same size at 300 K. It is thenobvious that already at 60 K the Parquet stands to becorrected while it is definitely insufficient at 300 K,in the line with the discussion of the previous para-graph. It is not even certain that the renormalizationgroup to any finite order can even be used at 300 K.A totally different approach, perhaps like the one

proposed by Hubbard [40], is possibly needed. It is ourfeeling that any attempt to further correlate theelectrons beyond the Parquet, which is after all only animproved mean-field like approximation [6], wouldincrease the spin fluctuations at the expense of the CDones and increase the fitted value for 2 nVÎ/jg2(1). Thisshould put TTF-TCNQ closer to the change in regimedescribed above.As a consequence, the curve of figure 6 labelled

for TCNQ might conceivably correspond to the TTFstack, while the real TCNQ behaviour at ambient

pressure would correspond to the one near minimum,

that is Tc increasing slightly with pressure as predictedby a more conventional mean-field picture. The slightdecrease of the TCNQ transition noticed between 10and 15 kbar, could be explained by the depressiveeffect of either or both of the tunnelling [39] or theforward scattering between TCNQ chains [7]. In theregion of the phase diagram above 15 kbar, the

pressure increase of the single phase transition, asid-efrom longitudinal lock-in considerations, can possiblybe explained by an enhancing effect of the forward-scattering interaction between stacks of different

nature [7]. In this respect, it is our belief that TSeF-

TCNQ, from the pressure dependence of its singlephase transition, may be located around 15 kbar in themore general phase diagram of TTF-TCNQ (32, 41].

Finally we wish to comment again about the largevolume dependence derived for the intra-chain repul-sions g and g2 in this work. The surprising result beingactually the contrast between the moderate volumedependence of the bandwidth (explainable by a tightbinding model) and the large volume dependenceof gl and g2. We already said above that part of thisvolume dependence may be attributed to importantnon-logarithmic intra-chain screening effects not takeninto account in our Parquet approximation. But acomparison between the properties of TTF-TCNQand HMTSF-TCNQ suggests also other possibilities.These two compounds do not have significantlydifferent bandwidths. This feature is indicated eitherby a tight binding band structure estimate

or by the measurement of very similar plasma fre-quencies for both systems.However, susceptibility and Tl conductivity are

quite different in these two compounds [2, 42] ;HMTSF-TCNQ behaving as a weakly magneticcompound compared to TTF-TCNQ.The only significant difference in the structures is the

existence of much stronger interchain couplings(presumably through the nitrogen-chalcogen bonds)in HMTSF-TCNQ than in TTF-TCNQ.

Therefore, as another possibility for the largescreening effects of g and g2 we would like to suggestthe interchain coupling. This is supported by the

HMTSF-TCNQ, TTF-TCNQ comparison and the

large volume dependences. This would mean that thevolume dependence of g 1 and g2 in table I, is mainlydue to changes in the a and c directions. We noticethat such a suggestion is also strongly supported bythe finding of large piezo-resistivity for the longi-tudinal resistivity connected with the transverse

strains [43]. The volume dependence and the scréeningof g, and g2 will be discussed in a forth-comingpublication [44].

5. Conclusion. - Even though the bare 4 kF res-

ponse function has been estimated by Lee et al. [7],

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the exact nature of the non-logarithmic screening atthis wave number eludes the Parquet approach andprevents any numerical estimates being made.

In conclusion, the proposed approach which

combines summation of Parquet diagrams and phononpseudo-gap effects does reconcile several crucial

aspects of the physics of TTF-TCNQ :

i) large enhancement of magnetic response,

ii) strong volume dependence,

iii) existence of an intrinsic maximum in the cons-tant volume temperature dependence of Im x(2 kF),even though the phase transition occurring at lowtemperatures are of the CDW-PLD type,

iv) a decrease of x(0) by a factor of 2 from 300 Kto 60 K.

Acknowledgments. - The authors wish to thankS. Barisic, J. Friedel and W. L. McMillan for severalprofitable discussions.

References

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[2] JÉROME, D., SODA, G., COOPER, J. R., FABRE, J. M., andGIRAL, L., Solid State Commun. 22 (1977) 319.

[3] TORRANCE, J. B., in reference [1], page 137.[4] EMERY, V. J., in reference [1], page 1.

[5] JÉROME, D. and GIRAL, L., Proceedings of the InternationalConference, Siofok, Hungary 1976, Lecture Notes in

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