(TM) 2 X organic superconductors: prototypes of
one-dimensional conductors

Denis Jerome, Pascale Auban-Senzier

► To cite this version:

Denis Jerome, Pascale Auban-Senzier. (TM) 2 X organic superconductors: prototypes of one-dimensional conductors. Synthetic Metals, 2003, 10.1016/s0379-6779(02)00241-2. hal-05023355

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

Distributed under a Creative Commons Attribution 4.0 International License
(TM)₂X organic superconductors: prototypes of
one-dimensional conductors

P. Auban-Senzier, D. Jérome*

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

**Abstract**

Organic superconductivity has been discovered in 1979 in the one-dimensional organic conductor (TMTSF)₂PF₆. This discovery has to be considered in the framework of a long quest for new superconductors which started 15 years earlier with the suggestion made by W. Little for a new pairing mechanism in organic conductors. The extensive studies carried out over the last 20 years have revealed the existence of a vast series of isostructural compounds, (TM)₂X, exhibiting signatures of a non-Fermi behavior at high temperature and a variety of ground states at low temperature. Besides superconductivity, low dimensional organic conductors have brought a wealth of new concepts in physics.

© 2002 Elsevier Science B.V. All rights reserved.

Keywords: (TMTSF)₂PF₆; Organic superconductivity; Luttinger liquids; 1D conductors

1. The pre-(TM)₂X period

The prerequisite for the formation of a molecular con-
ductor is first the requirement for having charged molecules
in a solid and second to allow their charge to delocalize
between molecular entities. Charging the molecules can be
achieved either by a charge transfer reaction or by the
formation of an organic salt. The first case has been realized
in TTF-TCNQ by a transfer of charge between the donor
molecule TTF and the acceptor molecule TCNQ [1,2] and
the second route gave rise to the synthesis of the first organic
superconductor (TMTSF)₂PF₆ in 1979 [3]. Actually, it is the
study of the two-chain charge transfer compounds (TMTSF-
DMTCNQ), (TM-DM) where the donor is the tetramethyl
selenide derivative of TTF which drew chemists and phy-
sicists' attention on the role of the TMTSF molecule. The
outcome of this study has been decisive for the quest of
organic superconductivity [4]. This 1D conductor undergoes
a Peierls transition at 42 K [5] where unlike TTF-TCNQ a
distortion occurs simultaneously on both chains [6]. Several
other results have triggered our attention. X-ray experiments
had shown that the charge transfer is only r = 0.5 leading to
a quarter-filled band situation [6]. Transport and thermo-
power data emphasized the dominant role played by the
TMTSF chain in the mechanism driving the Peierls transi-
tion and also in its contribution to the conduction at high

temperature [7]. The really new and unexpected finding has
been the suppression of the Peierls transition under pressure
and the conductivity remaining metal-like reaching the
unprecedented value of 10⁵ (Ω cm)⁻¹ under 10 kbar at
the temperature of liquid helium [8]. The conducting state
of TM-DM was also remarkable in displaying a huge
transverse magnetoresistance below 50 K [9].

Since all these phenomena, were new and unexpected the
effort was put on a structure made of only one organic stack
comprising the lucky TMTSF molecule. Such a structure
was already known from the early work of the Montpellier
chemistry group who synthesized and studied the series of
isostructural (TMTTF)₂X organic salts [10] where TMTTF
is the sulfur analog of TMTSF and X is a monoanion such
as ClO₄⁻, BF₄⁻ or SCN⁻ etc., ... see Fig. 1. All these
compounds turn into strong insulators at low temperature.
This is the reason why they did not attract much interest until
recently when they have been practically rediscovered after
20 years of studies which were mainly devoted to the
selenide series, (TMTSF)₂X.

2. The (TM)₂X era

Several exciting properties of (TMTSF)₂PF₆, an increase
of the metal-like conductivity up to 10⁵ (Ω cm)⁻¹ at 12 K
where an abrupt metal-insulator transition of SDW nature
takes place [11], the absence of any noticeable lattice
modulation in X-ray measurements [6]; (the very weak

<footnote>* Corresponding author. Tel.: +33-1-69155301; fax: +33-1-69156086.
E-mail address: jerome@lps.u-psud.fr (D. Jérome).</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. View of the (TM)₂X structure, courtesy of IMN, Nantes.</figcaption></figure>

signature of a CDW has been reported recently by Pouget and Ravy [12]), stimulated its further investigation under pressure and allowed the stabilization of a metallic state down to liquid helium temperature at a pressure of about 9 kbar. The finding of a very small and still non-saturating resistivity at 1.3 K extrapolating linearly to a practically zero value at $T = 0$ K was a sufficient motivation to trigger further study in a dilution refrigerator and a zero resistance state was stabilized below 1 K [3]. Shortly after the discovery of superconductivity in (TMTSF)₂PF₆ many other members of the same series with a variety of anions have also been found superconducting in the vicinity of 1 K in the 10 kbar pressure domain [13]. However, (TMTSF)₂ClO₄ is

the only member of the (TMTSF)₂X series to show superconductivity under atmospheric pressure [14]. The discovery of superconductivity in the (TMTSF)₂X family has been a very exciting phenomenon since it was the first time such an instability could be stabilized in an organic compound. This happened about 15 years after the publication of Little's suggestion [15] and 10 years after the holding of an international symposium organized by Little at Hawaii on the Physical and Chemical Problems of Possible Organic Superconductors, [16]. Probably the most surprising feature of superconductivity in (TMTSF)₂X is the common border existing between antiferromagnetic (SDW) and superconducting phases with the region of maximum $T_c$ for superconductivity located right at the border [17].

## 2.1. High pressure physics

The role of pressure in (TMTTF)₂PF₆ stabilizing an antiferromagnetic ground state instead of the spin-Peierls phase at ambient pressure has initiated a reinvestigation of the sulfur-analog series, (TMTTF)₂X, aiming at the stabilization of superconductivity in this series as well. This has been successfully achieved only recently with (TMTTF)₂Br under 26 kbar [18] and (TMTTF)₂PF₆ at 47 kbar [19,20]. (TMTTF)₂PF₆ is the only member so far of the (TM)₂X series to exhibit all three different ground states allowing therefore to render the phase diagram a genuine property of these Q-1D conducting salts.

Thanks to a variety of experimental studies and emergent theories we have now reached a certain level of under-

<figure><img src="image_3.png" /><figcaption>Fig. 2. The generic (Pressure, Temperature) phase diagram for (TM)₂X salts and (EDT-TTF-CONMe₂)₂AsF₆. The origin on the pressure axis is fixed for (TMTTF)₂PF₆, $\Delta_p(\sim T_p)(P)$ and $T_{SP}(P)$ are indicated for (EDT-TTF-CONMe₂)₂AsF₆ (Λ, Δ) and for (TMTTF)₂PF₆ (ó, Ł) (from [35]).</figcaption></figure>
standing in the physical properties of these 1D conductors namely, the (TMTTF)₂X and (TMTSF)₂X salts which both belong to the extended (TM)₂X family [21], Fig. 2.

The salient feature of the (TM)₂X diagram is first the existence of a wide variety of ground states occurring below 20 K or so.

Moving towards the right across the (TM)₂X phase dia-
gram a succession of ground states is revealed either chan-
ging compounds or changing pressure on a given compound.
The compound at the extreme left in the (TM)₂X diagram,
(EDT-TTF-CONMe₂)₂AsF₆, is actually quite interesting
since the coupling between the chains derived from quantum
chemistry calculations is not particularly weak. In spite of
this fact the compound exhibits the hall marks of one-
dimensional physics, [22].

(TMTTF)₂PF₆ is the only system which can be driven
through the entire series of ground states under high pres-
sure: spin-Peierls, Néel antiferromagnetism, SDW phase
with an incommensurate magnetic modulation and ulti-
mately superconductivity [23].

As far as the non-ordered high temperature phase is
concerned, its character in the phase diagram depends
crucially on the nature of the corresponding ground state.
Crudely speaking, all compounds which are located left of
(TMTTF)₂Br in the diagram are insulators at high tempera-
ture whereas those on the right are highly conducting and
display a metal-like conductivity down to the transition into
the SDW insulating phase or superconductivity.

2.2. Far infrared conduction

It is also illuminating to have a look at the conductivity in
the far infrared regime. A large gap of order 2000 K is
observed in the frequency dependence of the FIR conduc-
tivity of sulfur compounds. This is in line with the activation
energy of the DC conductivity of those compounds. How-
ever the surprise arises for selenium compounds which
behave apparently like highly conducting metals in spite
of a marked gap at 200 cm⁻¹ observed at low temperature in
the FIR regime [24].

This feature suggests that all (TM)₂X compounds exhibit a
FIR gap, the amplitude of which depending on the actual
position in the phase diagram. Given the unified phase
diagram established experimentally and the recent proposal
of theoretical ideas in 1D physics applying specifically to 1D
conductors with a commensurate band filling we have
reached a plausible theoretical description which we intend
to summarize very briefly in the rest of this article, (for an
almost up to date review see [25]).

2.3. 1D physics and (TM)₂X compounds

What 1D physics means is that instead of the usual
description of low lying excitations in terms of quasi particle
states in the Landau–Fermi liquid model, a collective mode
description with decoupled spin and charge modes is a more

appropriate approach [26,27]. Such a model for 1D con-
ductors has been proposed starting from a linearized energy
spectrum for excitations close to the Fermi level and adding
the relevant Coulomb repulsions which are responsible for
electron scattering with momentum transfer 2kF and 0. This
is the popular Luttinger model for a 1D conductor in which
the spatial variation of all correlation functions exhibits a
power law decay at large distance, characterized by a non-
universal exponent Kρ which is a function of the microscopic
coupling constants [28]. The Luttinger model requires a
band filling of the conduction band which is not commen-
surate with the underlying lattice. Very few organic con-
ductors fulfill this requirement. TTF[Ni(dmit)]₂ is one of
them as the HOMO-LUMO energy difference which is large
compared to the bandwidth makes the system semi-metallic
[29–31]. Consequently, NMR is able to measure the expo-
nent Kρ of the Luttinger liquid down to low temperature [32].

However, (TM)₂X conductors are rather peculiar systems
which deviate from the Luttinger model since the stoechio-
metry imposes half a carrier (hole) per TM molecule inde-
pendent of the applied pressure. If the molecules are
uniformly spaced along the stacking axis (a situation which
is actually met in (TMTSF)₂ClO₄, the unit cell contains half
carrier, i.e., the conduction band is quarter-filled although
the existence of a slight dimerization of the molecules along
the stacks in sulfur compounds could contribute to make
them half-filled band compounds (wide infra). The com-
mensurate band filling opens a new scattering channel
(Umklapp scattering) of the carriers between both sides
of the Fermi surface. This leads to important modifications
in the model of the gapless Luttinger liquid which in turn
becomes a Wigner type insulator with a gap in the charge
sector [33] subjected to the condition Kρ < 0.25 for 1/4
filling although no gap exists in the spin channel. The gap in
the density of states at the Fermi energy reads:
2Δρ ≈ W(gU/W)¹/(²-2n²Kρ) and gU is the coupling constant
W(U/W)³ where n = 2 in the Hubbard limit.

According to band calculations, the transverse overlap $t_⊥$ along the b-direction is of the order of 120 and 200 K for sulfur and selenium compounds respectively. Therefore, it is quite natural to expect first 1D theory to govern the physics of these quasi 1D conductors, at least in the high temperature regime when $T > t_⊥$ and second, to observe a cross-over towards higher dimensionality physics below room temperature. As observed very early in the study of (TMTSF)₂PF₆ a plasma edge for a light polarized along the b-axis becomes thus observable below 100 K [34].

The striking behavior of the transport properties emerges
from a comparison between the temperature dependence of
longitudinal and transverse components of the resistivity
[35]. The longitudinal resistivity of (TMTSF)₂PF₆ is metal-
like down to the SDW transition at 12 K, varying like T<sup>0.93</sup>
from 300 to 150 K once the thermal contraction is taken into
account and more like T<sup>2</sup> below 150 K [36]. However, the
behavior of the resistance along the direction of weakest
coupling i.e., along the c-axis displays an insulating character
with a maximum around 120 K and becomes metallic below although still orders of magnitude above the critical Mott value. This behavior is quite general in the (TM)₂X series and is independent of the shape of the anion provided the effect of thermal contraction on the transport properties is properly taken into account [37]. Similarly, the Hall constant displays a marked temperature dependence below room temperature, passing through a minimum at the same temperature where the c-axis resistivity displays a maximum [38].

In the high temperature limit, as $T > \Delta_ρ$, we shall make the assumption that the existence of the Wigner localization can be neglected at first sight. The longitudinal transport is expected to vary according to a power law $\rho_{//}(T) \approx T^{4n^2K_ρ^{-3}}$, [33], whereas the transport along c being incoherent should probe the density of quasiparticle states in the (a-b) planes. In the high temperature regime, the picture of non-coupled chains is approached. Therefore, the density of quasiparticle states should resemble the situation which prevails in a Luttinger liquid namely, $N(E) \approx |\omega|^{\alpha}$ where a is related to $K_ρ$ by $\alpha = 1/4(K_ρ + 1/K_ρ - 2)$. At energies $\omega > \Delta_ρ$, the actual density of states should be reminiscent of the density of states of the gapless Luttinger liquid. Therefore, a temperature dependence of the transport $\rho_c(T) \approx T^{-2\alpha}$ is expected in the 1D regime, $T > T^*$, [35]. The far infrared (FIR) conduction of (TMTSF)₂PF₆ exhibits also very unusual properties. There exists a FIR gap (which amounts to $\Delta_ρ = 200 \text{ cm}^{-1}$ in (TMTSF)₂PF₆ which has been taken as the signature of the (Wigner) gap. The experimental data and the theoretical power law dependence $\sigma(\omega) \approx \omega^{4n^2K_ρ^{-5}}$ at $\omega > 2\Delta_ρ$ also lead to $K_ρ = 0.23$ [24]. This value for $K_ρ$ would fit the 1/4 filled scenario with $W = 12000$ K (from band structure calculations and plasma edge measurements), $\Delta_ρ = 200 \text{ cm}^{-1}$ (from FIR data) and $U/W = 0.7$ (which is in fair agreement with the enhancement of the spin susceptibility at low temperature) [25]. Since the Wigner gap varies exponentially low with $K_ρ$ even a small variation of the ratio between the Coulomb interaction and the bandwidth under pressure would be sufficient to explain a decrease of $K_ρ$ moving left in the diagram. Both optical and transport data lead to $2\Delta_ρ = 1000$ K in (TMTTF)₂PF₆ at ambient pressure [36]. The difference between $K_ρ$ for selenium and sulfur compounds in which $K_ρ = 0.18$ can be accounted by the difference of their bare bandwidths. The temperature $T^*$ corresponding to the c-resistance maximum moves up under pressure and reaches room temperature under 10 kbar. This temperature can be attributed to the beginning of a cross-over between 1D and 2D regimes.

The strong pressure dependence of the cross-over temperature $T^*$ is a remarkable phenomenon of the (TM)₂X physics. According to the pressure data of $\rho_c$, the pressure dependence of $T^*$ is about ten times larger than that of $t_⊥$ which is typically 2% kbar⁻¹. This feature suggests that $T^*$ is actually a renormalized version of $t_⊥$ due to the 1D confinement via intra-stacks electron-hole interactions [25]. The compound (EDT-TTF-CONMe₂)₂AsF₆ located at the extreme left in the diagram of Fig. 2 is a remarkable illustration for the 1D confinement of carriers due to strong intra-chain interactions.

Admittedly, the theory of the dimensionality cross-over in a 1D conductor will require some refinements taking also into account the role of the (Wigner) commensurability gap which has been overlooked so far. Some preliminary calculations are being performed towards this direction [39].

Apparently, the finite dimerization of the intrastack bonds is not large enough to make the half-filled Umklapp scattering a pertinent mechanism in the formation of the 1D (Wigner) phase. As far as the selenium compounds are concerned this feature could be related to the transverse b-direction bandwidth ($W_b \approx 1500$ K) being larger than the dimerization gap (900 K) and thus smearing out the role of the 1D dimerization. This argument may still be valid for the sulfur series in which the dimerization gap and the transverse bandwidth are both in the same energy range.

### 3. Conclusion

To summarize, the picture emerging for the (TM)₂X phase diagram is that of a Wigner insulating phase with a correlation gap decreasing from sulfur to selenium compounds, Fig. 2. As long as the Wigner gap is large (say larger than 300 K) the 1D confinement is quite active and the single particle interstack hopping is meaningless despite an unrenormalized value of the transverse coupling which is still of the order of 100 K. Moving towards the right in the phase diagram, the Wigner gap decreases (because of the band broadening under pressure) and the renormalization of the transverse hopping integral become less pronounced. (TMTSF)₂PF₆ is a compound where $T^*$ and $2\Delta_ρ$ are both of the same order of magnitude ($\approx 150–200$ K), and $T^*$ reaches room temperature in (TMTSF)₂ClO₄ under ambient pressure according to the data of $\rho_c$ [40]. Below $T^*$ the system becomes an anisotropic conductor, first two-dimensional with high energy excitations governed by the Wigner gap and ultimately an anisotropic three-dimensional Fermi liquid around 5 K (for (TMTSF)₂ClO₄ under ambient pressure). A recent extension of the renormalization calculations in the cross over regime [41] has shown that SDW and superconducting orders are still interfering constructively in this temperature domain although only the singlet superconducting coupling is enhanced with respect to the triplet channel. The same theory predicts the possibility of first order reentrant superconductivity within the SDW phase close to the border with superconductivity. However, recent experimental studies in (TMTSF)₂PF₆ have clearly identified a wide pressure domain where both superconducting and SDW regions segregate at a macroscopic scale [42]. It is a pleasure to quote the words of our friend Paul Chaikin, “(TMTSF)₂PF₆ is the most interesting material ever discovered”.

### Acknowledgements

This article is the opportunity to acknowledge the cooperation of our co-workers who have contributed at Orsay and
Copenhagen to the development of the physics and chemistry of 1D organic conductors. This field has also greatly benefited from a close cooperation with the theoreticians at Orsay and Sherbrooke.

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