# Pressure investigation of the metal-semiconductor transition in TTF-TCNQ

Denis Jerome, W Müller, M Weger

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## To cite this version:

Denis Jerome, W Müller, M Weger. Pressure investigation of the metal-semiconductor transition in TTF-TCNQ. Journal de Physique Lettres, 1974, 35, pp.77 - 80. 10.1051/jphyslet:0197400350507700. hal-04967875

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Physics Abstracts
8.150

# PRESSURE INVESTIGATION OF THE METAL-SEMICONDUCTOR TRANSITION IN TTF-TCNQ

D. JÉROME, W. MÜLLER (*) and M. WEGER (**)

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

(Reçu le 20 février 1974)

**Résumé.** — Nous présentons dans cette communication des résultats suggérant que la température de Peierls du TTF-TCNQ décroît fortement sous pression hydrostatique et que le couplage entre les électrons et un phonon optique est responsable de la transition métal-semiconducteur.

**Abstract.** — This note reports pressure data suggesting that the Peierls temperature in TTF-TCNQ decreases strongly under hydrostatic pressure and that the coupling of the electrons to an optical phonon is responsible for the metal-semiconductor transition.

We wish to report measurements of the resistivity of two TTF-TCNQ samples, as function of temperature and pressure, which seem to suggest that two transitions are present in this material.

A maximum in the electrical conductivity of TTF-TCNQ around 60 K has been reported by Coleman et al. [1], Ferraris et al. [2] and others. Above this temperature the material behaves like a one-dimensional metal, while below it, it behaves like a semiconductor. The transition around 60 K is generally described as a Peierls transition characteristic of linear chains. The question whether TTF-TCNQ or similar materials would be superconducting if the Peierls transition could be suppressed is of some interest [1], [3].

Chu et al. [4] applied a nearly hydrostatic pressure between 7 and 20 kbar to TTF-TCNQ and report that the room temperature conductivity increases significantly with pressure (by a factor of 4.5 at 20 kbar), while the temperature of the metal to semiconductor transition is only slightly affected by the pressure, increasing roughly by 15 K at 16.4 kbar.

Their measurements were conducted using a 1 : 1 mixture of n-pentane and isoamyl alcohol as the pressure transmitting medium.

We report here measurements conducted in the pressure range 0-6 kbar using helium gas as pressure transmitting medium [5, 6].

The motivation of this measurement was, (i) helium

gas ensures perfectly hydrostatic pressure condition down to freezing temperature of the fluid at low temperature [7] while oil may cause some shear strains at the freezing point and even within the solid phase of the pressure transmitting medium, (ii) helium gas is perfectly inert chemically speaking, (iii) the conductivity at ambient temperature doubles at a pressure of approximately 3 kbar; thus, the pressure range in which interesting things may happen may be expected to be around this pressure.

The resistivity along the *b*-axis of TTF-TCNQ single crystals was measured with an a. c. 4-probe technique at 70 Hz. It has been recently pointed out [8] that in strongly anisotropic material such as TTF-TCNQ non collinearity of the contacts may lead to an apparent conductivity much higher than the actual longitudinal conductivity. We checked that the collinearity was not perfect and in particular a small non-zero voltage was detected in the *unnested* leads arrangement (about 10 %). However we do not believe that this feature would prevent us from obtaining a reasonable result for the relative behaviour of the longitudinal conductivity.

The resistivity as function of temperature at pressures in the range 0-3 kbar is shown in figure 1.

The crystal tends to crack, or the contacts to fall off, as it is cooled and warmed several times, so there is some difference between different runs.

The sample showed an increase of conductivity $\sigma_{max}/\sigma_{RT}$ of ≈ 60 at zero pressure. We can see clearly that at 1.5 kbar there are two distinct anomalies quite reversible in temperature; one at 52 K and one at 32 K. While at 3 kbar, only one transition at 53 K

<footnote>(*) On leave from: University of Karlsruhe.</footnote>

<footnote>(**) Permanent address: The Hebrew University of Jerusalem, Racah Institute of Physics, Israël.</footnote>
<figure><img src="image_3.png" /><figcaption>FIG. 1. — Temperature dependence of the resistance of TTF-TCNQ under pressure.</figcaption></figure>

was observed because the temperature was not lowered below 34 K to prevent freezing of the helium gas, which might damage the crystal. At 1.5 kbar, the anomaly around 52 K is observed as a minimum in the resistivity, whereas the transition at 32 K corresponds to a discontinuity in the derivative of the resistivity with respect to the temperature. At zero pressure the resistance increases steeply below 50 K similarly with the data of Coleman [1].

We may note that the upper transition (around 52 K) agrees with the transition reported by Chu *et al.* [4].

However, the lower transition, which is strongly pressure dependent has not been reported by them. Extrapolating, we would expect the temperature of this transition to drop to zero at a pressure in the vicinity of 4 kbar, thus it is not surprising that this transition has not been observed at pressures of 6 kbar or more.

From mean-field theory [3], $k_B T_p = 2 E_F \exp(-2/s)$ where $s$ is the dimensionless electron-phonon coupling parameter, related to $g$ in the Fröhlich hamiltonian by :

$$g^2 = \frac{E_F s(\hbar\omega_0)}{n_0}$$

where $n_0$ is the electron density. If we neglect the pressure dependence of $n_0$ and of $\omega_0$, we get :

$$\frac{d \ln T_p}{dP} = (1 - 2/s) \frac{d \ln E_F}{dP} + 4/s \frac{d \ln g}{dP} \quad (1)$$

$s \approx 0.4$ for TTF-TCNQ [3]. The electronic conductivity is given by $n_0 e^2 \tau 2 E_F / \rho_F^2$; assuming that at ambient temperature, $1/\tau \propto g^2 / E_F$ [9] we get :

$$\frac{d \ln \sigma}{dP} = 2 \left( \frac{d \ln E_F}{dP} - \frac{d \ln g}{dP} \right).$$

Thus, if

$$| d \ln g/dP | \ll | d \ln E_F/dP |,$$

then

$$\frac{d \ln T_p}{dP} \approx - \frac{2 \ln \sigma}{dP} \quad (2)$$

while if

$$| d \ln g/dP | \gg | d \ln E_F/dP |,$$

then

$$d \ln T_p/dP \approx -5 d \ln \sigma/dP.$$

Thus, $|d \ln T_p/dP|$ and $|d \ln \sigma/dP|$ may be expected to be of the same order of magnitude, roughly, unless there is an accidental cancellation between the $E_F$ and $g$ terms; but it is unlikely that such a cancellation will occur over a wide pressure and temperature range. We may also note that with the assumption $|d \ln g/dP| \ll |d \ln E_F/dP|$ a decrease of $T_p$ by a factor 1.8 at 1.5 kbar would correspond to a decrease of the density of states at Fermi level by a factor 1.15.

For coupling of the electrons with an acoustical phonon,

$$g^2 = (\nabla \langle k + q | V | k \rangle)^2 / 2 NM\omega_0$$

when

$$m^* \gg m \quad (\text{or}, \langle k + q | \nabla V | k \rangle^2 / 2 NM\omega_0)$$

when $m^* \approx m$).

The matrix element of $V$ is strongly pressure dependent being roughly proportional to $\exp(-Qr)$, where $Q$ is the Slater parameter. Thus $g$ should increase strongly with $P$. However, $E_F$ is also proportional to the same matrix element, therefore

$$d \ln g/dP \approx d \ln E_F/dP,$$

and $T_p$ should actually *increase* with $P$. However, if the coupling is to an *optical* phonon (i. e. to an intra-molecular vibration), then $g$ is a molecular property, approximately independent of the intermolecular separation; it can be related to the change in bond length, $dR/dn$, as the molecule gains (or loses) an electron [3]; we have

$$g^2 = (dR/dn)^2 (M\omega_0^2) (\hbar\omega_0)/n_0.$$

Thus $g$ should be pressure independent and $T_p$ should *decrease* with increasing $P$.

As for the electronic conductivity at ambient, the electrons are coupled to many phonon modes; for a polyatomic molecular crystal like TTF-TCNQ, there are many more optical phonon modes than acous-
tical ones, hence the average pressure dependence of $g$ may be weak, and the $dE_F/dP$ term may be the dominant one. At reduced temperatures, the optical phonons should contribute less to the electron scattering, because their frequency is higher than that of the acoustical phonons and will exceed $k_B T$; then $g$ should be more strongly pressure dependent, and reduce the contribution of the $E_F$ term, and $|d\sigma/dP|$ should decrease. Also, for the conductivity around 60 K, if it is limited by scattering from impurities or defects, then $\sigma = n_0 e^2 l/p_F$ where $l$ is the distance between defects; none of the quantities in this expression is strongly pressure dependent, thus it is not surprising that $\sigma$ is not strongly pressure dependent in this range. However, we should note that several other theories for the conductivity in this temperature range exist in the literature [10, 11].

Figure 1 also shows that the change of resistivity of the lower transition is big (more than an order of magnitude increase as the temperature changes by less than 10 K); just like the transition around 50 K at zero pressure is. Thus, the lower transition seems to correspond to the Peierls transition of a linear chain.

As for the upper anomaly, whose temperature is hardly pressure dependent, the resistance change associated with it is rather small. We may perhaps speculate that it is associated with some property of the individual molecules, rather than with the chain structure.

<figure><img src="image_4.png" /><figcaption>FIG. 2. — Resistance versus pressure for two single crystals of TTF-TCNQ at room temperature.</figcaption></figure>

The data of figure 1 indicate $T_p = 32$ K at 1.5 kbar and $T_p \approx 60$ K at ambient pressure, leading to a ratio $T_p(0)/T_p(1.5) = 1.8$. If the variation of $E_F$ is the only contribution to the change of $T_p$ under pressure, we get from the eq. (2) a ratio

$$ \sigma(0)/\sigma(1.5) \approx 0.75 $$

which is in good agreement with the observed enhancement of the conductivity under 1.5 kbar, figure 2. These results would tend to indicate that the $g$ term in eq. (1) exhibits a pressure dependence much smaller than the $E_F$ term and thus that the coupling of the electrons is likely to be with optical phonons.

In conclusion, TTF-TCNQ appears to be more complicated than the simple linear chain metal postulated by several authors [10, 11, 12], and the possibility of several types of instabilities such as different kinds of phonons, coupled with the electrons, has to be considered. Recently Bright et al. [13] have obtained from the reflectivity at infrared wavelengths a dip located at 6.7 µm. Therefrom, we obtain the coupling strength of the $C \equiv N$ bond vibration and the conduction electrons, $s \approx 0.5$. This value fits beautifully with the value needed to give $T_p$, namely $s \approx 0.4$. This appears to be an excellent confirmation of our suggestion that the Peierls transition is due to an optical phonon, specifically the $C \equiv N$ bond vibration.

**Acknowledgments.** — One of us (M. W.) benefited from a stay at Yeshiva University with Dr. Halpern and Y. Juravel, stimulating discussions with Dr. Garito and Heeger, extensive discussions with Dr. Tomkievicz and discussions with Dr. Chu regarding his unpublished data.

The present work would not be possible without the work and assistance of Drs. Von Molnar and B. A. Scott who prepared the samples at the IBM laboratories and encouraged and assisted us throughout this work.

**Addendum.** — After this note has been accepted for publication, a preprint of M. J. Cohen et al. appeared mentioning that the existence of two extrema of the anisotropy ratio could lead to the observation of a double peak in the apparent conductivity parallel to the b-axis in false conductivity measurements. Therefore, it is important to point out that in our work, the atmospheric pressure run has been performed after the 1.5 and 3 kbar runs. The conductivity which has been followed down to 10 K (not represented on figure 1) is in good agreement with the zero pressure data reported in Khanna, Ehrenfreund, Garito, Heeger to be published and in particular no other anomaly is ever observed below 58 K. We believe thus, that, on a clean sample, the intrinsic effect of pressure is a shift of the metal-semiconductor transition to a lower temperature. This new result is indeed corroborated by a very similar pressure effect observed on KCP salts which will be published in a forthcoming note by W. Müller and D. Jérome.
References

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