# ORGANIC SUPERCONDUCTORS: THREE YEARS ONLY!

Denis Jerome

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Denis Jerome. ORGANIC SUPERCONDUCTORS: THREE YEARS ONLY!. Journal de Physique Colloques, 1983, 44, 10.1051/jphyscol/1983002. hal-05003872

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

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ORGANIC SUPERCONDUCTORS : THREE YEARS ONLY !

D. Jérôme

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

**Résumé** - Cet article présente une vue d'ensemble d'un domaine en expansion rapide : les supraconducteurs organiques. Nous insistons plus particulièrement sur les nombreux résultats expérimentaux qui indiquent une relation étroite entre propriétés physiques de ces matériaux et la théorie des conducteurs unidimensionnels.

**Abstract** - This article attempts to give an overview on the rapidly expanding field of organic superconductors. It emphasizes especially the numerous experimental data which suggest that One-Dimensional Physics is closely related to their physical properties.

The present survey of Organic Superconductivity in the (TMTSF)₂X series emphasizes some particularly important data which cannot be left out of the interpretation (1). Furthermore, we wish to clarify the links existing between the experimental data and the basic features of Quasi-One-Dimensional conductors, namely (i) the interplay between superconducting and dielectric (SDW or CDW) ground states, (ii) the existence of a broad temperature region where quantum and classical fluctuations of the order parameter are important and (iii) the strong sensitivity of long range order to random potentials breaking the interchain phase coherence.

I - BAND STRUCTURE ANISOTROPY

Before discussing the low temperature properties of the (TMTSF)₂X family we show how the normal state (high temperature) properties are affected by the anisotropy of the intermolecular overlap integrals.

The stacking direction (a-axis) is obviously the direction along which the overlap between near neighbour molecular orbitals is the strongest. However because of short Se...Se contacts intermolecular overlap is also significant along the transverse b-direction. The transverse c-direction along which stacks of TMTSF molecules are separated from each other by X anions represents a direction of weak interchain coupling.

The conductivity anisotropy at room temperature is related to the band structure anisotropy by the relation (2) :

$$ \sigma_a/\sigma_b = (at_a/bt_b)^2 \quad (1) $$

where a = 3.6 Å and b = 77 Å are the lattice parameters of (TMTSF)₂X neglecting the weak dimerization of the molecules along the stacking axis (this is justified at high temperature). Hence using σₐ/σᵇ = 25 of Greene et al. (3) one finds from eq.(1), tₐ/tᵇ ≈ 10. Other groups (1) have reported σₐ/σᵇ ≈ (2-4) x 10² requiring from eq.(1) tₐ/tᵇ > 30.

The anisotropy in the b-c plane is less problematic : both from conductivity (4) and critical fields anisotropies (3) one obtains tₑ/tₑ ≈ 30. Single crystal reflectance studies (5) reveal the existence of a strong reflectance of (TMTSF)₂X at low temperature even with the light polarized along the transverse b-direction provided the frequency is smaller than a plasma edge of ≈ 1000 cm⁻¹.
The analysis of the optical data (6,7) yields again $t_a/t_b \approx 10$. Furthermore, the calculation of the overlap integrals (8) leads to a comparable a to b anisotropy namely $t_a/t_b = 12$ with $t_a = 0.14$ eV and $t_b = 0.012$ eV at room temperature in $(TMTSF)_2ClO_4$. With a band structure anisotropy of about 10, the Fermi surface cannot reasonably display closed orbits unless additional folding of the surface is provided by a change of the periodicity (occurence of a SDW state at low temperature for example).

The observation of a plasmon excitation in a Q-1-D conductor with the light polarized perpendicular to the chains requires some coherence of the electron motion from chain to chain. The condition to be fulfilled is (2) :

$$ \frac{\hbar}{\tau_{\parallel}} < 2\pi t_{\perp} \qquad (2) $$

According to eq.(2) the smearing of the Fermi surface due to a finite intrachain electron time $\tau_{\parallel}$ must be smaller than the warping due to a small energy dispersion along the transverse direction.

A transverse plasma edge with the light polarized along the b-axis is observed in $(TMTSF)_2AsF_6$ (5) at low temperature. However when the light is polarized along the c-axis the reflectance of the crystal remains low down to the infrared region with no sign of any Drude like behaviour. The FS smearing should lie therefore in between the warpings due to both c and b-axis couplings, namely

$$ 2\pi t_c \le \frac{\hbar}{\tau_{\parallel}} < 2\pi t_b \qquad (3) $$

Hence an upper limit of $\tau_{\parallel}$ derived from eq.(3) with $t_c \sim 0.3$ meV is about $4 \times 10^{-13}$ s.

At room temperature, $\tau_{\parallel}$ is derived from the Drude fit of the longitudinal reflectance spectrum (5) i.e. $\tau_{\parallel} \sim 3 \times 10^{-15}$ s. Therefore, the factor $10^3$ increase of the conductivity between 300 K and 4.2 K in $(TMTSF)_2ClO_4$ implies $\tau_{\parallel}$ (4.2K)$\sim 3 \times 10^{-12}$ s (with 0.5 carrier/molecule and $m_e \approx m_0$) as long as the low temperature conduction is attributed to a single-particle conduction mechanism.

An electron scattering time of $3 \times 10^{-12}$s would be about ten times longer than the upper limit derived from the absence of plasma edge in the c-direction. Hence the assumption of single-particle conduction at low temperature is not consistent with the optical reflectance data of the $(TMTSF)_2X$ series. As far as the b-axis is concerned eq.(3) leads to a lower limit $\tau_{\parallel} \ge 10^{-14}$s (with $t_b \sim 10$ meV). The Drude fit of the longitudinal plasma edge for $(TMTSF)_2PF_6$ at 25 K gives (9) $\tau_{\parallel} \sim 10^{-14}$s in fair agreement with the lower limit derivation.

Summarizing, optical data show that the low temperature electron motion is coherent in the (a-b) plane but diffusive along the c-axis. The picture of (a-b) planes, weakly coupled along the c-direction is also supported by the interpretation of the nuclear spin lattice relaxation field dependence (10). Experiments show that the field of 10 kOe corresponds to a cross-over between a low-field regime with $1/T_1$ field independent ($\omega_e \tau_1^{2D} < 1$) and a high-field regime ($\omega_e \tau_1^{2D} > 1$) where $1/T_1 \sim \log \omega_e$ ($\omega_e$ is the electron Larmor frequency and $1/\tau_1^{2D}$ is the (a-b) plane to plane hopping rate.

The plane to plane hopping rate can be derived by the theory of the relaxation in low-dimensional conductors (2) which gives :

$$ \frac{1}{\tau_{\parallel}} = 2\pi t_c^2 \tau_{\parallel} \qquad (4) $$

Using the experimental values, $1/\tau_1^{2D} = 2.10^{11} s^{-1}$, $\tau_{\parallel} \sim 10^{-14}$s at low temperature (11), eq.(4) gives $t_c \sim 1$ meV. Such a weak interchain coupling along the c direction is consistent with the crystal structure of the $(TMTSF)_2X$ series.
<figure><img src="image_2.png" /><figcaption>Fig. 1 - A schematic view of the warped Fermi surface at low temperature in zero magnetic field showing diffusive electron motion in the c-direction ($\hbar\tau_{//} > t_c$) and the coherent motion in the b-direction ($\hbar\tau_{//} < t_b$).</figcaption></figure>

In summary optical reflectance and NMR data show the coherence at short distance of the electron motion along b at low temperature. However the a to b band anisotropy does not allow to consider a closed Fermi surface (this situation would require $t_a/t_b \approx 2$). Very crudely, the Fermi surface of the conducting state looks like a warped plane as sketched in figure 1.

## II - INTERPLAY BETWEEN SUPERCONDUCTIVITY AND MAGNETISM.

The existence of a common border line between a SDW semiconducting ground state and the superconducting state is now well established in the (T,P) phase diagram of (TMTSF)$_2X$ salts (1) for which no extra potential with periodicity $2k_F$ opens a gap at the Fermi level. Typical representatives of these systems are salts of anions with hexahedral symmetry $PF_6$, $AsF_6$...

However, a competition between superconductivity and a SDW state is also observed under certain circumstances in (TMTSF)$_2ClO_4$: a salt with tetrahedral anions. If (TMTSF)$_2ClO_4$ is cooled at a slow enough rate down to helium temperature a so-called relaxed (R)-state is obtained (12,13). $ClO_4^-$ ions order uniformly below 24 K (14). Such ion ordering with a wave-vector $4k_F$ does not affect the density of states at the Fermi level. The R-state undergoes a transition towards a superconducting state below 1.2 K without any up-turn of the resistivity below 5 K as it is observed in fast-cooled samples (15,16).

The superconducting order (with nearly complete flux expulsion for transverse fields and zero resistivity) is destroyed by the application of a magnetic field exceeding the upper critical field $H_{c2}$. At $H > H_{c2}$, the resistance is finite and strongly rising with magnetic field but no oscillations of the magnetoresistance can be observed unless the field is larger than a "turn-on" field which depends critically on the orientation of the crystal (16,17,18). The "turn-on" field corresponds to a phase transition induced by the applied field.

The phase diagram (T,H) of the R-state of (TMTSF)$_2ClO_4$ (with $H // c$:) is displayed in figure 2. The high field state which becomes stable at fields larger than $\approx 50$ kOe is semimetallic with a low density of states at the Fermi level (19) and a closed Fermi surface (17). Moreover, $^{77}$Se NMR studies (20) have clearly established the magnetic nature of the high-field state. Internal magnetic fields due to the onset of a SDW suppress the $^{77}$Se NMR line of the high-field stabilized state. In addition, proton (21) and selenium (20) relaxation experiments show also the existence of a narrow peak of $1/T_1$ related to the magnetic character of the phase
<figure><img src="image_3.png" /></figure>

Fig. 2 - Phase diagram of (TMTSF)₂ClO₄ (R-state). The phase transition line has been drawn from data of Shubnikov-de Haas, specific heat and NMR experiments. The shaded portion in low fields corresponds to the superconducting state.

transition. An estimate of the carrier density of the high-field phase derived from the period of the Shubnikov de-Haas oscillations leads to $n \sim 10^{-2}/molecule$ (17).

In summary, the high-field state is semimetallic and magnetic whereas the phase stable at lower fields is non-magnetic and highly conducting.

The interplay between superconductivity and magnetism is an essential property of the microscopic description of 1-D conductors (1). However a remarkable feature of figure 2 is the existence of a wide field domain extending from ~1 kOe to ~50 kOe at zero temperature where neither superconducting nor magnetic long range order is achieved at low temperature. We wish to emphasize that such an absence of long range order is not expected in the theory of Q-1-D conductors. This fact indicates some limitations of the present models to understand the properties of the (TMTSF)₂X family.

### III - PRECURSOR EFFECTS

Several experimental studies have shown that $N(E_F)$ of organic superconductors is strongly affected at low temperature by the proximity of the superconducting phase. For example, the contribution to the specific heat linear in temperature is magnetic field dependent (22). In (TMTSF)₂ClO₄, C/T increases from 10 to 20 mJ/mole. $K^2$ between $H_{C2} \sim 1$ kOe and 20 kOe. Furthermore the thermal conductivity of (TMTSF)₂ClO₄ (23) shows a significant drop below 50 K which is interesting for two reasons :

(i) In the same temperature region $\sigma_{DC}$ is strongly enhanced (24) and reaches $\sim 3 \times 10^5 (\Omega cm)^{-1}$ at 4.2 K. Thus one could expect heat to be carried by the electrons according to the Wiedemann-Franz law $K_e/\sigma = LT$.

(ii) The drop of K is strongly suppressed by the application of a magnetic field (23). Therefore in terms of the W-F law this field dependence of K is very striking since opposite field dependences are observed for $\sigma$ and K.

The sensitivity to a magnetic field suggests that the drop of K is related to a decrease of $N(E_F)$ which can be partly suppressed by the application of a magnetic field. Various spectroscopic techniques have provided an estimate of the energy width of the depression. Schottky tunneling performed on (TMTSF)₂PF₆ (25) under 11 kbar or on (TMTSF)₂ClO₄ (26) at ambient pressure point to an approximate width of $2\Delta_0 \sim (3-4)$ meV. Likewise, far-infrared reflectance of (TMTSF)₂ClO₄ reveals a sharp optical absorption threshold (sensitive to magnetic field) around the same energy range of ~3.8 meV (27).
Although a drop of the DC conductivity is expected at low temperature according to the FIR data, this is exactly the opposite situation which is observed experimentally. Furthermore, a study of $\sigma(\omega)$ (28) provides a low and magnetic field independent conductivity of about 2000 ($\Omega$cm)$^{-1}$ for $\omega > 30$ cm$^{-1}$. Since the dc conductivity reaches $\approx 3 \times 10^5$ ($\Omega$cm)$^{-1}$ at helium temperature and is also strongly magnetic field dependent the existence of a narrow collective mode is expected at zero-frequency ($\Delta\omega \approx 1-2$ cm$^{-1}$).

### III - INFLUENCE OF RANDOM POTENTIALS

Non-magnetic impurity potentials which usually have very little effect on superconductivity of metals play a crucial role in the stability of the long range ordered superconductivity of the (TMTSF)₂X series. The superconducting state of (TMTSF)₂C10₄ is suppressed by disorder of the conducting chain in the (TMTSF)₁-x(TMTTF)ₓC10₄ solid solution (29) with x > 0.2 %. Disorder on the anion chain is also efficient since superconductivity is removed by ~ 3 % of ReO₄ in the system (TMTSF)₂(C10₄)₁-xReO₄x (30). Orientational disorder is present in the metastable quenched (Q)-state of (TMTSF)₂C10₄ according to X-ray diffuse scattering data (14) and enhanced entropy at low temperature relative to the R-state (13). Frozen-in C10₄ disorder in (TMTSF)₂C10₄ (Q-state) governs the balance between SDW and superconductivity (15). With fast quenching times a semiconducting (SDW) state is observed below 4 K with no further transition at lower temperatures (31). For intermediate cooling rates, the SDW state establishes below ~ 4 K but superconductivity is recovered at a temperature T ~ 0.9 K lower than the critical temperature of the R-state (16).

### IV - CONCLUDING REMARKS

The experimental study of (TMTSF)₂C10₄ shows clearly a depression of the density of states of the Fermi level occuring below 25 K or so. In the same temperature interval a gap becomes observable in the frequency dependence of the conductivity below 30 cm⁻¹. However a zero-frequency collective mode (of width ~ 1-2 cm⁻¹) grows as the system is cooled down to 4.2 K. The DC conductivity at 4.2 K is larger than $10^5$ ($\Omega$cm)$^{-1}$ and also strongly diminished by the application of a magnetic field perpendicular to the conducting chain axis.

Can we consider magnetic fluctuations towards SDW ordering as the origin of both the collective-mode and the pseudo-gap since in some cases of the (TMTSF)₂X family a SDW ground state is stabilized? We infer that such an interpretation is very unlikely for the following reasons:

(i) There are no detectable signs of magnetism at low temperature in the R-state of (TMTSF)₂C10₄ as shown from NMR (12) and EPR data (15). Both techniques are known to be very sensitive to the onset of magnetism. Whenever SDW fluctuations contribute to the nuclear spin-lattice relaxation rate this effect is restricted to a very narrow temperature domain at the onset of SDW ordering (12).

(ii) Commensurability of the SDW's would prevent fluctuations from contributing to the dc conduction (32), especially at very low temperature when $kT < \omega_{pin}$ (where $\omega_{pin}$ is the pinning energy of the commensurate SDW).

(iii) Whenever a SDW state is observed in the (TMTSF)₂X series it is further stabilized by the application of a magnetic field (33) whereas the depression of $N(E_F)$ is suppressed under field (23).

(iv) The very large magnetoresistance of the conducting state of (TMTSF)₂C10₄ (R-state) or (TMTSF)₂PF₆ under pressure (34) cannot be interpreted in terms of small pockets of carriers on the Fermi surface since no magnetic instability is detected by EPR or NMR. However superconducting fluctuations in a system of weakly coupled chains provide a qualitative understanding to the large magnetoresistance above the superconducting transition (35).

The properties of the (TMTSF)₂X reveal several features closely connected to the behaviour of 1-D Physics. In particular as far as superconductivity is concerned, the phase transition at $T_C$ is not directly related to the strength of the pairing interaction $2\Delta_0$ between electrons within each chain. Instead, $T_C$ involves the amount of interchain tunneling coupling and consequently $kT_C \ll 2\Delta_0$. At elevated tempera-
tures ($T > T_C^c$ where $kT_C^c \approx 2\Delta_0$) the superconducting response function diverges following the 1-D laws $\chi_{1-D} \sim T^{-\gamma}$ where $\gamma$ is defined by the 1-D theory. In the high $T$ domain the transverse coherence length $\xi_\perp$ remains smaller than the inter-chain distance. If a Landau-Ginzburg functional is used to describe the free-energy of the system in terms of the order parameter (1), the region $T > T_C^c$ corresponds to an energy $F(\Delta)$ with a single minimum at $\Delta = 0$. In this temperature regime the fluctuations are characterized by a local finite amplitude of $\Delta$ (amplitude fluctuations). At low temperatures $T < T_C^c$ the divergence becomes 3-D like, i.e. $\chi_{3D} \sim (T - T_C)^{-1}$ and $\xi_\perp \ll d$. In this temperature domain the free energy presents a minimum at $|\Delta_0|$ but the phase of the order parameter is not fixed. There is no restoring force acting against variations of the phase. This is the phase fluctuation regime where the order parameter correlation function is given by $\langle\Delta(x)\Delta^*(0)\rangle = |\Delta|^2 \exp[-x/\xi(T)]$ with $\xi \sim 1/T$.

A treatment of the onset of long range order at $T_C$ in a system where short range order of individual chains is strongly developed has been given recently by Schulz and Bourbonnais (36) including zero-point motion of the phase quantum effects). Furthermore it is shown that in spite of the well established 1-D fluctuations with the related pseudo-gap in the density of states at the Fermi level the critical region associated with the 3-D ordering at $T_C$ is quite narrow, in agreement with the sharpness of the transition detected by resistive or specific heat techniques. With the model of quantum phase fluctuations scattering from non-magnetic impurities increases the quantum character and therefore acts to decrease the 3-D ordering temperature in marked contrast to the usual BCS theory.

Finally experimental data interpreted in terms of the present description of superconductivity in Q-1-D conductors suggest that short-range superconducting order on individual chains develops already at fairly high temperatures, of the order of 20-30 K possibly.

This short survey of Organic Superconductors three years only after their discovery has shown the broad variety of striking phenomena observed in the $(TMTSF)_2X$ family. The main issue in the search for future organic superconductors at temperatures significantly higher than the helium range has become now a serious problem of molecular engineering: finding possible new molecules outside the fulvalene-like series and enhancing the three dimensional character of the conducting systems.

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