SEMI-METALLIC BEHAVIOUR OF HMTSF-TCNQ
AT LOW TEMPERATURES UNDER PRESSURE

Denis Jerome, J. R Cooper, M. Weger, D. Lefur, K. Bechgaard, A. N Bloch,

Dwaine O. Cowan

► To cite this version:

Denis Jerome, J. R Cooper, M. Weger, D. Lefur, K. Bechgaard, et al. SEMI-METALLIC BEHAVIOUR OF HMTSF-TCNQ AT LOW TEMPERATURES UNDER PRESSURE. Solid State Communications, 1976. hal-04983113

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
SEMI-METALLIC BEHAVIOUR OF HMTSF-TCNQ AT LOW TEMPERATURES UNDER PRESSURE*

J.R. Cooper,† M. Weger,‡ D. Jérôme and D. Lefur

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

K. Bechgaard

H.C. Oersted Institute, Universitetsparken 5, DK-2100 Copenhagen, Denmark
and

A.N. Bloch and D.O. Cowan

Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, U.S.A.

*(Received 27 February 1976 by P.G. de Gennes)*

Some results of electrical resistivity ($ρ$) and transverse magnetoresistance measurements on single crystals of the charge transfer compound HMTSF-TCNQ under pressure are reported. There is evidence that $dρ/dT$ remains positive over the whole temperature range under pressure, and that a $T^2$ law is obeyed from 0.19 to 2 K at 14 kbar. Together with a relatively large magnetoresistance this is an indication of semi-metallic behaviour.

THE SYNTHESIS of a new charge transfer compound belonging to the TTF-TCNQ family was recently reported.¹ Single crystals of this compound, hexa-methylene tetraselenafulvalenium tetracyanoquino-dimethanide or HMTSF-TCNQ, have the largest room temperature electrical conductivity reported so far for organic conductors, approximately 1800 ± 400 (Ω-cm)⁻¹. As T is lowered the d.c. resistivity ρ(T) reaches a broad minimum between 75 and 45 K corresponding to conductivities about 3.4 times larger. At lower temperatures ρ increases again and then flattens off around 4.2 K yielding conductivities of the order of 500 (Ω-cm)⁻¹. It was verified that the conductivity showed little further change down to 45 mK. Although the results at high T were very reproducible, the size of the low T increase in ρ was rather sample dependent. The metallic nature of the conductivity mechanism, that is, the frequency independence characteristic of delocalised states at the Fermi level, was confirmed by measurements of the microwave conductivity and dielectric constant.¹

However such conductivity behavior does not

completely rule out the possibility of a metal-semi-conductor transition occuring around 30 K. Such a transition could arise from a Peierls distortion or charge density wave, possibly smeared out because of the disorder caused by the non-planar HMTSF molecules. There seems to be evidence for this from a specific heat anomaly in that temperature region.² Alternatively HMTSF-TCNQ could be a narrow gap semiconductor even in a one electron picture, in the spirit of the work of Bernstein et al.³ on TTF-TCNQ.

In both of these pictures the low temperature metallic state would be an extrinsic property of the material. In 3 dimensions, these metallic states near $E_F$ could arise from an impurity or defect band within the narrow energy gap or from the overlap of band tails caused by disorder. The difficulty with an impurity band model⁴ here is, that in one dimension these states tend to be localised, in which case impurity conduction should be thermally activated, in contrast with the nearly temperature-independent conduction observed experimentally. However, as discussed in the following, this material has some 2-dimensional characteristics.

It was felt that conductivity experiments under pressure would be of interest for several reasons. If the metallic behaviour were intrinsic one might expect only small pressure effects at low temperature and perhaps even superconductivity. Alternatively, more pronounced semiconducting behaviour under pressure would point to a resemblance with the parent compound TSeF-TCNQ. In practice we have observed

<footnote>* Work at Orsay supported in part by DGRST-Contract No. 75-7-0820.</footnote>

<footnote>† On leave from: The Institute of Physics of the University, POB 304, Zagreb, Yugoslavia.</footnote>

<footnote>‡ On leave from Nuclear Research Centre, Negev, POB 9001 Beer-Sheva and the Racah Institute of Physics, The Hebrew University of Jerusalem, Israel.</footnote>
something in between these two possibilities which, together with the observation of relatively large magnetoresistance, seems to indicate semi-metallic behaviour under pressure.

These results now seem to be particularly interesting because the crystal structure of HMTSF-TCNQ is significantly different from that of TCNQ-TTF and of TCNQ-TSF in several respects:⁵ The donor and acceptor stacks alternate in both *a* and *c* directions, and not just in the *a* direction. The tri-methylene bridges effectively form insulating layers perpendicular to the *c*-direction; and the Se-N distance between neighbors in the *a* direction is rather small, smaller than the sum of the van-der-Waals radii. Thus, the structure forms something like a two-dimensional metal (with conducting layers in the *a*-*b* planes). This electronic structure is also consistent with other properties, such as the lack of frequency dependence in the proton nuclear relaxation time $T_1$⁶ and an anomalously large diamagnetic contribution to the susceptibility.⁶,⁷

# 1. EXPERIMENTAL

Single crystals of HMTSF-TCNQ ($\Delta^{2,2'}$-bi-trimethylene-1,3-diselenole)-($7,7',8,8'$-tetracyano-p-quinodimethane) were prepared by slow diffusion of the rigorously purified components in dry deoxygenated $C_6H_5Cl-CH_3CN$ or $C_6H_5Cl-C_6H_5CH_3$ solutions (using small H-shaped pyrex or quartz tubes at + 65°C for 4 weeks, and 98% yield).*

Samples from two laboratories† were measured in this work, their dimensions were typically 3 × 0.05 × 0.03 mm and their room temperature conductivities were consistent with the results of reference (1). Four electrical contacts were made in the usual way using Dupont 4929 silver paint diluted with butyl or hexyl acetate; voltage contacts were painted completely around the crystal and current contacts covered the ends to give a more uniform current distribution. The sample resistances were in the range 1–10 Ω at room temperature and contact resistances were usually several Ω. Most of the measurements were made using a low frequency (70 Hz) a.c. method with a measuring current of 5 μA r.m.s. so that $R(T)$ curves could be displayed directly on an X-Y recorder. Checks were made using d.c. both at room temperature and 4.2 K under all experimental conditions of

applied pressure or magnetic field. Checks for ohmic behaviour were also made for currents from 1 to 50 μA. "Un-nested" voltages were nearly always undetectable i.e. ≤ 0.1% of the sample voltage.

Most of the pressure equipment has been described elsewhere. A He gas⁸ set up was used up to 8 kbar; during solidification of the helium a small temperature gradient was maintained across the pressure cell so that the solid phase grew from the bottom end thereby minimising pressure losses and shear stresses on solidification.

For the higher pressure runs three different systems were used, all based on the teflon cell principle and using isopentane as the pressure fluid. It was found that the sample resistance was not affected by 24 hr in isopentane at room temperature, but the constant resistances increased by a factor of three or so. Generally the samples were in isopentane at room temperature for a total of about 4 hr. A detailed description of the apparatus used for one 24 kbar run was published recently.⁹ The magnetoresistance measurements under pressure were made using a double stage CuBe cell normally used for NMR work. Finally a small steel pressure clamp was constructed especially for use in the dilution refrigerator, this had a special system of springs to reduce pressure losses on freezing the isopentane.¹⁰ In most of the experiments there were pressure losses of 1 or at most 2 kbar on freezing the isopentane.

In this work we had considerable problems with sample breakage, especially at atmospheric pressure there were often sharp jumps in the resistance around 80 K after which $dR/dT$ became negative, and the $R(T)$ curves were no longer reversible.‡ For all the curves shown in Fig. 1 there were none of these sharp breaks in $R(T)$. Because of these difficulties we have had to work with many different samples from the same batch and only on two runs could we measure the same sample at several different pressures in the low $T$ region. At room temperature, the effect of pressure was usually reversible; we did not do detailed pressure cycling studies in the low-$T$ region, but the consistency of the results indicates that the low-$T$ results are also reversible.

The transverse magnetoresistance was measured on three samples from the same batch, two runs at around 12 kbar and another at atmospheric pressure.

<footnote>* For batch B, analysis: Calculated C 42.63, H 2.39, N 8.29, Se 46.70; observed C 42.69, H 2.45, N 8.28, Se 46.60.</footnote>

<footnote>† From the Johns Hopkins University and the H.C. Oersted Institute.</footnote>

<footnote>‡ From the behaviour of the apparent contact resistances, and also from optical microscopy it appears that this was due to sample damage under the silver paint and that current flowed in and out of the voltage contact giving an extra resistance (S. Etemad, private communication).</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. Normalized resistance curves $R(T, P)/R(300,0)$ for some runs up to 14 kbar. The right hand scale shows the conductivities obtained by normalising to a room temperature value of 1800 (Ω-cm)$^{-1}$, at ambient pressure. The dashed line shows the published results¹ at ambient pressure. Open circles with error bars represent the average of 4 samples from batch B (Dr. C.S. Jacobsen, private communication). The inset shows the $T^2$ law obtained for a sample at 14 kbar down to 0.19 K.</figcaption></figure>

Magnetoresistance data were usually taken point by point, but on two runs (sample 14 at 12 kbar and 16 at ambient pressure), they were drawn out on an X-Y recorder because of the possible existence of De Haas-Schubnikov oscillations,* but none were observed at the $10^{-3}$ level up to 28 kilogauss. The magnetic field was reversed to check that there was no contribution from the Hall voltage.*

One problem with transverse magnetoresistance on such anisotropic samples is whether or not the current contacts short out the Hall voltage, i.e. whether we measure the standard magnetoresistance or the so-called Corbino magnetoresistance.¹¹ Probably the only way to be certain about this is to measure a long sample with several voltage contacts on it and we propose to do this in the future. However recent magnetoresistance measurements¹² on TTF-TCNQ, which is also very anisotropic, with similar sample geometry, showed little difference for the two transverse and the longitudinal field directions. This is a strong indication that geometrical effects were not important.

In either case the limiting behaviour for low fields should be $\Delta\rho/\rho \sim (\omega_c T)^2$ unless the Hall effect is extremely large.¹¹

## 2. SUMMARY OF EXPERIMENTAL RESULTS

(1) The most striking feature of the results shown in Fig. 1 is that HMSTF-TCNQ becomes more

metallic under pressure and that for the majority of runs at 4 kbar and above $d\rho/dT$ was positive over the whole temperature range. In Fig. 1 the results have been normalised to an average conductivity of 1800 (Ω-cm)$^{-1}$ at room temperature and pressure. This procedure is justified in view of the excellent reproducibility of the ambient pressure $R(T)$ curves down to 50 K. Under pressure good metallic conductivities in excess of $10^4 (\Omega$-cm)$^{-1}$ are obtained down to very low temperature.

(2) one sample was measured down to 0.19 K at 14 kbar. The law:

$$ \rho = A + BT^2 $$

was obeyed in the region up to 2 K (see the inset to Fig. 1) with $A = 90 \mu\Omega$-cm and $B = 1 \mu\Omega$-cm/K$^2$. Above 100 K the law $\rho = a + bT^\lambda$ is obeyed with $\lambda$ not so different from 2 as in TTF-TCNQ under pressure.

(3) The initial effect of pressure at room temperature is given by $(1/\rho)(d\rho/dP) = -15.0 \pm 0.5 \text{ kbar}^{-1}$, which is slightly less than that for TSeF-TCNQ ($-18 \pm 1 \text{ kbar}^{-1}$)$^{13}$ and nearly a factor of 2 less than TTF-TCNQ ($-28 \pm 2 \text{ kbar}^{-1}$)$^{14,15}$. At low temperature the pressure dependence seems to be rather small in the range 4--24 kbar.

(4) No magnetoresistance was detectable above 100 K, i.e. it is less than 1 in $10^3$ at 28 kG, but at low temperatures it was large and positive, especially under pressure as shown in Fig. 2. For example at 4.2 K and 28 kG, $\Delta\rho/\rho$ is $\approx 3\%$ at $P = 0$ and 60% at 12 kbar. The magnetoresistance does not follow the expected $H^2$ law or obey Kohler's rule. One possible reason for the latter could be that there are two types of carriers with widely differing mobilities.¹¹

## 3. DISCUSSION

Since HMSTF-TCNQ is a very complicated system for which as yet very little work has been published, at this stage we do not attempt to account completely for the observations reported here. We shall try, however, to define some pertinent questions and attempt to present at least a number of reasonable alternatives. Let us formulate the questions.

(1) Why does HMSTF-TCNQ become more metallic (particularly at low temperatures) under pressure?

(2) Why is the change in resistance between the high ($\sim 100$ K) and low temperature regimes so small under pressure?

(3) Why is the magnetoresistance large under pressure?

<footnote>* We are grateful to Dr. P. Monod for suggesting these checks.</footnote>
<figure><img src="image_3.png" /></figure>

Fig. 2. Magnetoresistance results at ambient pressure and 12 kbar. . . . . : zero field results, x x x x: in fields of 28 Kg. Inset shows ambient pressure results on an expanded scale.

(1) The low temperature conductivity of HMTSF-TCNQ can be discussed from several points of view.

(a) The material is a metal, with extra scattering at low temperatures from the Rice-Fukuyama mechanism, i.e. a specifically 1-dimensional enhancement of the impurity scattering. This point was mentioned in reference 1. In this model we find it hard to account for the actual decrease in resistivity as the temperature is lowered below 20 K under pressure. Therefore we shall not pursue it further.

(b) The material is a semiconductor at ambient pressure, and becomes a semi-metal as pressure is applied. A semiconductor to semimetal transition may arise in several ways.

(i) The transition could be the result of band crossing, i.e. a 1-electron effect, as in Yb¹⁶ for example. (The results in Fig. 1 bear a strong resemblance to those obtained for Yb as the pressure is lowered). Such a picture is in the sprit of Bernstein *et al.*³

(ii) Such a transition may be due to the reduction of effective interactions which tend to create a “Peierls” insulator or electron hole (Coulomb) interactions which tend to create an “excitonic” insulator.¹⁷ In this picture the state at pressures higher than ≈ 2 kbar is described as a semimetal with $\epsilon_F^*$ (i.e. the effective band overlap) of order 20–30 K. There are many possible ways in which the pressure could affect the interactions, by hardening of the lattice which could decrease electron-phonon interactions, or by making the material more 3-dimensional and thus interfering with the nesting (as in NbSe₂¹⁸) or with the Peierls

transition,¹⁹ or by affecting the details of the band structure.²⁰

In this picture the zero pressure state is an extremely narrow band semiconductor (band gap of order 20–30 K) with impurity states in the gap (qualitatively like lightly doped InSb). These impurities form a degenerate band (rather than Anderson-localised states) and thus the conductivity is neither frequency nor temperature dependent (at low T) as observed in reference 1. The “impurities” may be chemical or mechanical and thus the zero temperature conductivity is strongly sample dependent. However under pressure in the semimetallic state these impurities probably do not play a major role in determining the qualitative nature of the conductivity.

(c) The material is a semi-metal at ambient pressure too, but with a smaller effective number of carriers, such as caused by a gap opening on part of the Fermi surface, as in some layer compounds.¹⁸,²¹

(2) A rough estimate of the band-structure parameters of TTF-TCNQ has been given by Berlinsky *et al.*²² From them a rough idea of the band structure may be obtained. At high temperatures ($k_B T > t_⊥$ where $t_⊥$ stands for all the various transverse transfer integrals, $t'_Q$, $t'_F$, $j = t'_QF$ etc, defined in reference 3), there are effectively two one-dimensional bands, one due to HMTSF and one due to TCNQ. $K_F$ measured from the centre of the Brillouin zone is the same for these two bands, since the crystal as a whole is neutral. At low temperatures [the cross-over temperature is estimated in (19) and (23)] the $t_⊥$ integrals bring about an effectively 3-dimensional band structure with narrow cylindrical sheets of electrons and holes perpendicular to the b direction. The details of the structure depend critically on the relative magnitudes of the transverse integrals,²⁰ which would be rather different in HMTSF-TCNQ from TTF-TCNQ. The question arises as to why the change in conductivity is so small, although the effective number of carriers may fall by approximately 3 orders of magnitude. We may account for this as follows: the conductivity is given by $\sigma = ne^2\tau/m^* = ne^2l/P_F$.† Let us assume that for $T < 100$ K, $l$ is given essentially by the distance between scattering centres and that the scattering of each centre is only slightly T-dependent. Thus $l$ is only weakly T-dependent. In the metallic state $n$ is approximately 0.74 electrons/molecule²⁴ and $P_F \approx 0.37\pi/b$, roughly. In the semi-metallic state, both $n$ and $P_F$ are much

<footnote>† The argument given here can also be shown to be valid using the standard formula for the conductivity from the Boltzmann equation.</footnote>
smaller. $P_F$ is effectively half the average width of the
cylinder in the $K_b$ direction. It is clear that the effec-
tive number of carriers $n_{\text{eff}}$, is proportional to $P_F$ as
long as the cylinders that form the Fermi surface are
flat and extend over most of the $K_a-K_c$ plane. In that
case $n_{\text{eff}}/(P_F)_{\text{eff}}$ does not change very much from the
high temperature, metallic to the low temperature
semi-metallic state, although $n_{\text{eff}}$ and $(P_F)_{\text{eff}}$ may
change individually by as much as 3 orders. The small-
ness of the change in the conductivity may be
accounted for in this way.

Note that if the width of the cylinders in the $K_a$
or $K_c$ direction is small, this argument no longer holds
because the area of the Fermi surface is lower in the
semi-metallic state.

In this picture there is some difficulty in account-
ing for the increase in conductivity (by 20% or so) as
the temperature is lowered below 20 K, since the resist-
ance in the region $20 < T < 80$ K is regarded as
residual. Perhaps the change in the nature of the wave-
packets from 1-dimensional to 2 or 3-dimensional as
the temperature is lowered, makes it easier for them to
bypass scattering centres and thus decreases the effec-
tive cross-section, increasing the mean free path $l$. How-
ever it is not obvious why such a phenomenon gives
rise to a $T^2$ law in the region $0.2 < T < 2$ K.

An alternative explanation is that the low tem-
perature $T^2$ law arises from electron-hole scattering<sup>25</sup>
which saturates around 20 K, and above 80 K another
scattering process sets in. In this model the tempera-
ture of the plateau, around 20-30 K, gives some
estimate of the overlap of the two bands.

(3) We may account for the large magnetoresis-
tance in the semi-metallic state in a number of ways:

(a) $\omega_c\tau$ may become large, due to an increase in $\tau$ as the temperature is lowered.

(b) $\omega_c$ may be of the order of the effective
Fermi energy in the semi-metallic state, $\epsilon_F^*$.

(c) The overlapping bands of the semi-metallic
state may be shifted with respect to each other by the
magnetic field.

(a) For an effective mass of $m^* = 5$ m the cyclotron frequency at 30 kG is given by $\omega_c \approx 10^{11} \text{sec}^{-1}$. In the metallic state (at about 100 K)$\tau \approx 10^{-13}-10^{-14} \text{sec}$. Thus $\omega_c\tau$ appears to be of order $10^{-2}$. However from the discussion of the previous section it appears, that even if $l$ stays constant the decrease in

$V_F$ in the semi-metallic state may bring about an in-
crease in $\tau$ by two orders.

(b) We estimate $\epsilon_F^*$ to be about 20-30 K in the semi-metallic state. If the effective mass falls to $0.2m_e$ roughly then we may have $\omega_c \approx \epsilon_F^*$. Such a small effective mass appears unlikely at first sight but we should note that if energy levels of HMTSF and TCNQ that cross in the metallic state are split by a $t_\perp$ integral, the curvature near the points of approach may give rise to a very small effective mass [of order $(t_\perp/\epsilon_F)m_e$, where $\epsilon_F$ is the energy in the metallic state namely about 200 meV]. Alternatively we may refer to the cross-sectional areas of the Fermi surface, and if $H \approx (\hbar c/2\pi e)S$ where $S$ is such an area we may be in the extreme quantum limit. If $\delta K_b \approx 10^{-3} \pi/b$, $\delta K_a \approx \pi/a$ we could account for the magnetoresistance this way.

(c) The two overlapping bands may be shifted
relative to one another by the magnetic field, like in
Bi, giving rise to a less conducting state.

The disappearance of the magnetoresistance
above 80 K is not surprising since the metallic state
should not possess an appreciable magnetoresistance in
any case, moreover the one dimensional band structure
should further eliminate whatever magnetoresistance
that were present. However the rather small magneto-
resistance at $P=0$, at low temperatures is more
difficult to account for.

Clearly the key for understanding the behaviour
of HMTSF-TCNQ lies in understanding the band struc-
ture. It seems that only very small changes in the
band structure parameters and in the electron-
phonon coupling constant are needed to bring about
a change from insulating to semi-metallic behaviour.

Apparently HMTSF-TCNQ is in its properties
somewhere between TTF-TCNQ and (SN)X<sup>26</sup> and we
conclude that experimentally the semimetallic be-
haviour of HMTSF-TCNQ under pressure seems to be
well established.

*Acknowledgments* – We are pleased to acknowledge
helpful discussions with Dr. C. Weyl, Dr. G. Soda,
Dr. S. Etemad and with Dr. R.E. Pyle, Dr. R.H. Banks,
Dr. T.O. Poehler. This work would not have been
possible without the excellent technical assistance of
G. Malfait, and G. Delplanque. We are also grateful to
Dr. C.S. Jacobsen for making low temperature conduc-
tivity measurements at ambient pressure.
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*Note added in proof:* The magnetoresistance has subsequently been measured again several times as a function of pressure and temperature. This work indicates that at ambient pressure the points at 4.2 and 10 K shown in Fig. 2 are somewhat uncertain and the magnetoresistance is nearly the same as at 1.3 K.