# Longitudinal and transverse transport of the quasi-one dimensional organic conductor TMTTF2PF6studied under high pressure

P Auban-Senzier, Denis Jerome, C Carcel, J M Fabre

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P Auban-Senzier, Denis Jerome, C Carcel, J M Fabre. Longitudinal and transverse transport of the quasi-one dimensional organic conductor TMTTF2PF6studied under high pressure. Journal de Physique IV Proceedings, 2004, 114, pp.41 - 44. 10.1051/jp4:2004114007. hal-05000312

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# Longitudinal and transverse transport of the quasi-one dimensional organic conductor TMTTF₂PF₆ studied under high pressure

P. Auban-Senzier<fnref n="1" />, D. Jérome<fnref n="1" />, C. Carcel<fnref n="2" /> and J.M. Fabre<fnref n="2" />

**Abstract.** We report the first extensive study of longitudinal ($ρ_a$) and transverse ($ρ_c$) transport properties versus temperature of the organic quasi one dimensional conductor TMTTF₂PF₆ over the pressure domain extending from ambient up to 26 kbar. The dimensional cross over observed around 14 kbar separates a 1D region dominated by the Mott-Hubbard gap with activated transport at low pressure from a 3D domain where the temperature range of the metallic behavior, extends up to room temperature along the chains and is progressively increased towards high temperatures in the c direction. In the 1D regime, the different activations obtained from $ρ_a(T)$ and $ρ_c(T)$ data suggest two different modes of conduction in the longitudinal and transverse directions.

**Key words.** High pressure – 1D molecular conductors – High electron-electron correlations – Luttinger liquid.

## 1. INTRODUCTION

Although quasi one dimensional (1D) TM₂X salts, where TM = TMTTF or TMTSF have been studied for more than 20 years, the interpretation of their high temperature electronic properties is still under debate [1]. The Luttinger liquid theory describing purely 1D systems, have been used to explain their metallic regime along the chains. For both transport [2] and optical conductivity [3] experiments, the data were fitted with the power laws typical of Luttinger systems, giving for the Luttinger parameter $K_ρ$ a value of 0.23 for the TMTSF₂X salts assuming a quarter-filled band. This value implies strong electron-electron correlations for these compounds. However, as a result of these correlations (and their large effect in one dimension) together with a commensurate band-filling, this metallic regime is destroyed by the opening of a Mott-Hubbard gap in the more correlated salts of the family, the TMTTF₂X ones. Because of non negligible interchain hoppings $t_b$ ($≈$ 200 K (TMTTF) - 120 K (TMTSF)) and $t_c$ ($≈$ 10 K) and their variation with pressure, a 2D then 3D anisotropic regime is restored at low temperature and high pressure, which allows the stabilisation of the ground states from spin-Peierls to superconductivity as described in their generic phase diagram [1]. This means that a dimensional cross over is expected from a Luttinger liquid behaviour to a Fermi liquid one when pressure and temperature are varied. Actually, a theoretical treatment of this cross over, performed by a dynamical mean field technique, defines a critical value of $t_⊥$ above which the Mott gap vanishes, restoring a metallic behavior [4]. We have explored this cross over region by monitoring pressure (i.e. $t_⊥$) and temperature on a TMTTF salt, in transport experiments. Choosing TMTTF₂PF₆ for which the cross over takes place above 10 kbar, releases us from performing the constant volume corrections which are necessary at lower pressure, because of large thermal contraction, to get the isochore temperature dependence of the resistivity. Moreover, both longitudinal ($ρ_a$) and transverse ($ρ_c$) components were measured as $ρ_a$ and $ρ_c$ are known not to be proportional in the incoherent 1D regime, and they should reach the same $T^2$ dependence in the 3D Fermi liquid regime.

<footnote n="1">¹Laboratoire de Physique des Solides, Bât. 510, Université Paris-Sud, 91405 Orsay, France
e-mail: auban@lps.u-psud.fr; jerome@lps.u-psud.fr</footnote>

<footnote n="2">²Laboratoire Hétérochimie et Matériaux Organiques, ENSCM/ESA-5076, 34296 Montpellier
Cedex 5, France</footnote>

<footnote>e-mail: jmfabre@cit enscm.fr</footnote>
## 2. EXPERIMENT

High hydrostatic pressure was provided in a clamp cell made of non magnetic NiCrAl alloy with silicon oil in a teflon cell as the pressure transmitting medium. In order to control the pressure when it is varied at room temperature, we have used a manganin resistive gauge located in the cell close to the sample giving an accuracy of around 100 bar. We have neglected the pressure loss occurring during cooling in the $^4$He cryostat, assuming that, above 10 kbar, it should be small and identical for all studied pressures.

Resistivity measurements were performed on single crystals, using the four contacts low frequency lock-in technique with measuring currents, ranging from 0.1 to 1 µA. For the transverse configuration (I // c) two gold pads were evaporated symmetrically on each (ab) face of the crystals, while for the longitudinal configuration (I // a), four annular gold pads were evaporated along the needle axis, the two outer ones covering also the ends of the crystals to ensure an homogeneous current flow.

In $ρ_c$ configuration, the same sample provided all the resistivity data, except for the lowest pressures (1bar, 6.5 and 8.3 kbar) for which three different samples were used. In $ρ_a$ configuration, several samples were measured as microcracks occurring during pressure and temperature variations prevented us from using the same sample for more than 5 or 6 successive pressure runs.

## 3. TRANSPORT DATA UNDER PRESSURE

Under ambient conditions, the anisotropy of resistivity, $ρ_c / ρ_a$, is around $10^4$ with $ρ_c ≈ 400 Ω.cm$ and $ρ_a ≈ 50-80 mΩ.cm$. At room temperature, the pressure dependencies of the conductivity in both configurations are nearly parallel (we observe a linear increase for $σ_c$ ($Δσ / σ_c$(1bar) = +40% / kbar) and a slightly larger non linear increase for $σ_a$) so that the anisotropy $ρ_c / ρ_a$ is only slightly increasing with pressure.

Several regimes are identified from the set of curves $ρ_c$ and $ρ_a$ (T,P) presented on figures 1 and 2.

- At low pressure, below 10 kbar, both components of the resistivity are activated. The fits with two laws of the type $ρ_c = ρ_{0c} \exp (Δ_c / T)$ and $ρ_a = ρ_{0a} \exp (Δ_a / T)$ (figures 1b and 2b) clearly show that the activation energies $Δ_c$ and $Δ_a$ are different and slightly decreasing with pressure but remain roughly proportional up to 10 kbar ($Δ_c / Δ_a ≈ 1.5$), even if the temperature ranges (T < Δ / 2) considered for the fits are not the same and depend on the pressure.

On the one hand, $ρ_a$ is activated below $T_p$, the temperature where $ρ_a$ is minimum and which is decreasing with pressure, so that the temperature range for the fit rapidly shrinks under pressure.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** a) Temperature dependence of the transverse resistivity at different applied pressures for the four studied samples. b) The same data are plotted as log ($ρ_c$) versus the inverse temperature in order to show the activated regime.</figcaption></figure>
On the other hand, ρ_c is activated from room temperature, but a gradual decrease of the activation energy appears at low temperature (below 150 K at 12 kbar) reducing also the temperature range for the fit.

- In the cross over region, 10 < P < 14 kbar, this depression of ρ_c compared to the activated law announces the formation of a maximum for ρ_c at T*, visible from 14 kbar, and the progressive appearance of a metallic state below T* at higher pressure. In this pressure range, Δ_c, determined between T* and room temperature, is only slightly decreasing with pressure while Δ_a (together with T_p) is strongly depressed and no more detectable around 14 kbar (Figure 3a).

<figure><img src="image_3.png" /></figure>

**Figure 2.** a) Temperature dependence of the longitudinal resistivity at different applied pressures for one of the studied samples. b) The same data are plotted as log (ρ_a) versus the inverse temperature in order to show the activated regime. The position of T* for each pressure has been interpolated from ρ_c (T) data.

- For higher pressures, the longitudinal transport is completely metallic down to the spin density wave (SDW) transition occurring around 20K (Figure 2a). In the mean time, as the transverse transport is concerned, Δ_c is still decreasing while T* is increasing with pressure to reach 210 K for 26 kbar (Figure 3a). We have reported on figure 2 the interpolated values of T* on ρ_a (T) curves for each pressure as this temperature separates a linear temperature dependence above T* from a sublinear one below T*.

<figure><img src="image_4.png" /></figure>

**Figure 3.** a) Pressure dependence of the activation energy Δ_c (full circles) and T* (open circles) deduced from ρ_c (T, P) and of the activation energy Δ_a (squares and triangles for several samples) deduced from ρ_a (T, P). The full and open stars indicate the corresponding values of Δ_c and T* obtained from ρ_c data on TMTSF₂PF₆ at ambient pressure and 7 kbar [2]. The ground states stabilised below 30K are also indicated. b) Temperature dependence of the transverse resistivity for P = 16.8 kbar with both the exponential ρ_c (T) = ρ₀c exp(Δ_c/T) and power law ρ_c (T) = A T^(1-2α) fits above T*.
At high pressure, above 18 kbar, ρ_c(T) and ρ_a(T) are nearly proportional, however, the 3D like T² variation is not yet observed perhaps because of the fluctuating regime above the SDW transition starting around 30 K. As this T² variation is expected in the range T < t_c, we can tell that t_c is still lower than 30 K, even at 26 kbar, and a higher pressure is needed to observe the Fermi liquid regime.

Together with Δ_a, Δ_c and T* values determined for TMTTF₂PF₆, we have reported on figure 3a, Δ_c and T* values measured on ρ_c (T) for TMTSF₂PF₆ [2]. The activation energy (Δ_c = 360 K) is derived from a calculated constant volume curve (for 1 bar and 50 K) while T* values were directly measured on constant pressure curves (for 1 bar and 7 kbar). The agreement with TMTTF₂PF₆ results requires a shift of 15 kbar taking into account the different positions of the two compounds in the generic phase diagram.

## 4. DISCUSSION AND COMPARISON WITH 1D CUPRATES

In the localised regime, the temperature dependence of ρ_c can also be analysed in the frame of weakly coupled metallic Luttinger liquids for which a power law of the type $σ_⊥(T) ∼ T^{2α-1}$ with α = 1/4 (K_ρ + 1/K_ρ)-1/2 was found for the interchain conductivity [5]. A fit of the experimental data with this power law was performed for all the studied pressures but the values found for the exponent α (0.85 to 1.43 from the highest to the lowest pressures) are too high to be compatible with other determinations of K_ρ (K_ρ = 0.23 gives α = 0.64). An example of this fit ρ_c(T) = AT^(1-2α) compared to the exponential fit is given in figure 3b for P= 16.8 kbar. Consequently, the Mott gap (2Δ_c) is still dominating the transverse transport, although power laws deduced from a Luttinger liquid model could be valid for the metallic regime along the chains.

Analogues of TM₂X salts can be found in the cuprates family: MBa₂Cu₄O₈, where M is a rare earth. Actually, the conductivity of the CuO double chains in the perovskite structure can be studied when the conductivity (and superconductivity) of CuO₂ planes is suppressed by the substitution of Y by Pr. In the quasi-1D cuprate (1/4 filled hole-doped) PrBa₂Cu₄O₈, transport measurements transverse to the chains show dimensional crossovers (observation of a semiconductor then a metallic behaviour when cooling down) in both transverse directions, while the resistivity along the chains is always metallic [6] [7]. The 1D character at high temperature was demonstrated by optical conductivity which fits the Luttinger liquid power law with a K_ρ exponent of 0.24 indicating strong correlations. Moreover, the Fermi liquid regime is observed at low temperature as both longitudinal and transverse resistivities follow the T² dependence below a temperature which corresponds, for the two transverse directions, to the interchain hopping [7].

In conclusion, the difference observed between the activations evaluated from ρ_a and ρ_c data in TMTTF₂PF₆ at low pressure suggests two different modes of conduction in the 1D regime. The conduction could be assured by 1D objects such as solitons (with activation Δ_a) along the chains and by quasi-particles through the Mott gap (2Δ_c) in the transverse direction. An analogy can be made with the soliton conductivity observed in commensurate charge density wave compounds such as K₁.₇₅[Pt(CN)₄]·1.5H₂O [8]. This feature is difficult to observe in the other TM₂X salts where constant volume corrections of the resistivity are more important. However, the dimensional cross over indicated by the maximum of ρ_c (T) and its evolution with pressure is a general feature of the TM₂X family.

## Acknowledgements

The authors are grateful to A. Georges (ENS Paris) and T. Giamarchi (Genève) for helpful discussions.

## References

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