Bechgaard Salts Research Articles

Electronic structure and anion ordering in(TMTSF)2ClO4and(TMTSF)2NO3: A first-principles study

A first-principles density functional theory study of the Bechgaard salts ${(\mathrm{TMTSF})}_{2}$${\text{ClO}}_{4}$ and ${(\mathrm{TMTSF})}_{2}$${\text{NO}}_{3}$, with special emphasis on the anion ordering transition, is reported. It is found that the main effect of the anion ordering on the band structure occurs through the deformations induced in the TMTSF layers and not through the Coulomb potential of the anions, as it has been almost invariably assumed. It is shown that the anion ordering in ${(\mathrm{TMTSF})}_{2}$${\text{ClO}}_{4}$ leads to a modulation of the dimerization in successive chains and to a noteworthy polarization of the two partially filled bands around the Fermi level into either the TMTSF A or TMTSF B donors. The calculated anion ordering half gap ${\ensuremath{\Delta}}_{AO}$ is found to be small but definitely non-nil, $\ensuremath{\sim}$14 meV. The suppression of the SDW instability in the relaxed samples is attributed to the deterioration of the Fermi surface nesting in the anion ordered phase. The possible nodal structure of the superconducting gap is discussed in relation with the newly calculated split Fermi surface. Anion ordering in ${(\mathrm{TMTSF})}_{2}$${\text{NO}}_{3}$ leads to a smaller half gap, 8.9 meV. The anion ordering in this salt leads to a larger charge transfer between the two donors but to a smaller polarization of the two partially filled electron and hole bands. The weak influence of anion ordering into the low-temperature physics of this salt is related to the different periodicity of the anion ordering which leaves the nested parts of the Fermi surface almost unaltered.

Band structure effects on the superconductivity in Hubbard models

We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find that (1) as a function of increasing nematicity, starting from the square-lattice (zero nematicity) limit where a nodal $d$-wave state is strongly preferred, there is a smooth evolution to the quasi-1D limit, where a striking near-degeneracy is found between a $p$-wave- and a $d$-wave-type paired states with accidental nodes on the quasi-one-dimensional Fermi surfaces---a situation that may be relevant to the Bechgaard salts. (2) In a bilayer system, we find a phase transition as a function of increasing bilayer coupling from a $d$-wave to an ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave state reminiscent of the iron-based superconductors. (3) When an antinodal gap is produced by charge-density-wave order, not only is the pairing scale reduced, but the symmetry of the pairs switches from ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ to ${d}_{xy}$; in the context of the cuprates, this suggests that were the pseudogap entirely due to a competing CDW order, this would likely cause a corresponding symmetry change of the superconducting order (which is not seen in experiment).

Coexistent symmetries in a two-band organic superconductor

We have revisited the phase diagram of perchlorate Bechgaard salts under magnetic field at small temperature, using a spin ladder model with a Hubbard Hamiltonian. Using a non-perturbative Gor'kov method, we have calculated the free energies of all possible phases, including a phase with coexisting singlet and triplet superconducting pairs. With our choice of coupling parameters, this coexisting phase proved not favorable. Nevertheless, this study opens new fields of investigation, while the search of such a coexisting phase seems a realistic and promising goal.

First nanoparticles of Bechgaard salts

Abstract Well-dispersed nanoparticles of the superconducting Bechgaard salts, namely (TMTSF)2PF6 and (TMTSF)2ClO4, have been electrochemically grown in organic solution in the presence of a supporting electrolyte either being an ionic liquid or a long alkyl-chains quaternary ammonium salt. Nanoparticles exhibit sizes in the 20-75 nm range. Nanoparticle powders have been characterized by infrared, Raman, visible absorption spectroscopy, and by preliminary transport measurements at room temperature.

Electrodynamics of Bechgaard Salts: Optical Properties of One-Dimensional Metals

The electrodynamic properties of the quasi-one-dimensional organic conductors (TMTSF)2X are discussed, with particular emphasis on important deviations from the simple Drude model, the transition from a Luttinger-liquid to a Fermi-liquid behavior at the dimensional crossover when pressure is applied or temperature reduced, indications of a pseudogap as well as a low-frequency collective mode. Superconductivity and spin-density-wave ground states breaking the symmetry and gaps should occur in the excitation spectra. The previous literature is summarized and the current status of our understanding presented. Novel THz experiments on (TMTSF)2PF6 and (TMTSF)2ClO4 not only shine light into some of the open questions, but also pose new ones.

Structural Aspects of the Bechgaard and Fabre Salts: An Update

We review structural aspects of the Bechgaard and Fabre salts in relationship with their electronic, magnetic and superconducting properties. We emphasize the role of bond and charge modulations of the quarter filled organic stack in the various instabilities and ground states exhibited by these salts. A special consideration is also devoted to the influence of anions and methyl groups in these processes. In particular we point out the importance of the anions in achieving the inter-stack coupling by either direct or indirect (via the polarization of the methyl group cavities) interactions with the donors. In this framework we discuss the role of anions and methyl group disorders in the inhibition of the divergence of the high temperature bond order wave instability of the Bechgaard salts. We analyze the modulation in the magnetic ground states by considering explicitly the coupling of the magnetization with structural degrees of freedom. We consider the role of the anions and methyl groups in stabilizing the charge ordering pattern in the Fabre salts. We also discuss the spin-Peierls transition of the Fabre salts in relation with the charge ordering transition and the adiabaticity of the phonon field. We review the anion ordering transitions by considering more particularly the influence of the ordering process on the electronic structure and on the ground states which results. In this framework we show that the texture of the anion ordered structure has direct consequences on the superconducting properties of (TMTSF)2ClO4. Finally we conclude on the essential implication of the structural degrees of freedom on the generic phase diagram of the Bechgaard and Fabre salts.

Extended quantum criticality of low-dimensional superconductors near a spin-density-wave instability

We use the renormalization group method to study the normal state of quasi-one-dimensional superconductors nearby a spin-density-wave instability. On the basis of one-loop scattering amplitudes for the quasi-one-dimensional electron gas, the integration of the renormalization group equations for the two-loop single particle Matsubara self-energy leads to a nonFermi-liquid temperature downturn of the momentum-resolved quasi-particle weight over most part of the Fermi surface. The amplitude of the downturn correlates with the entire instability line for superconductivity, defining an extended quantum critical region of the phase diagram as a function of nesting deviations of the Fermi surface. One also extracts the downward renormalization of interchain hopping amplitudes at arbitrary low temperature in the normal phase. By means of analytical continuation of the Matsubara self-energy, one-particle spectral functions are obtained with respect to both energy and temperature and their anomalous features analyzed in connection with the sequence of instability lines of the phase diagram. The quasi-particle scattering rate is found to develop an unusual temperature dependence, which is best described by the superimposition of a linear and quadratic $T$ dependences. The nonFermi-liquid linear-$T$ component correlates with the temperature scale $T_c$ of the superconducting instability over an extended range of nesting deviations, whereas its anisotropy along the Fermi surface is predicted to parallel the momentum profile of a d-wave pairing gap on the Fermi surface. We examine the implications of our results for low dimensional unconventional superconductors, in particular the Bechgaard salts series of quasi-1D organic conductors, but also the pnictide and cuprate superconductors where several common features are observed.

Superconductivity and antiferromagnetism as interfering orders in organic conductors

Superconductivity in the Bechgaard salts series of quasi-one-dimensional organic conductors occurs on the verge of spin-density-wave ordering when hydrostatic pressure is applied. The sequence of instabilities is intimately connected to normal state anomalies in various quantities like the temperature dependence of electrical transport and nuclear spin-lattice relaxation rate. We discuss how such a connection takes its origin in the interference between the different pairing mechanisms responsible for antiferromagnetism and superconductivity, a duo that can be comprehended in terms of a weak coupling renormalization group theory. The recent developments along this line of though are presented in relation to experiments.

Upper critical field of the molecular organic superconductor (DMET)2I3

We report the temperature dependence of the upper critical magnetic field in the quasi-one-dimensional molecular organic superconductor (DMET)${}_{2}$I${}_{3}$, for magnetic field applied along the intrachain, interchain, and interplane directions. The upper critical field tends to saturation at low temperature for field in all directions and does not exceed the Pauli paramagnetic limit. Superconductivity in (DMET)${}_{2}$I${}_{3}$ thus appears to be conventional spin singlet, in contrast to the status of the isostructural Bechgaard salts. We also discuss a magnetic field-induced dimensional crossover effect in the normal metallic state which had previously appeared to be associated with superconductivity.

Linear-T scattering and pairing from antiferromagnetic fluctuations in the (TMTSF)2X organic superconductors

An exhaustive investigation of metallic electronic transport and superconductivity of organic superconductors (TMTSF)2ClO4 and (TMTSF)2PF6 in the pressure-temperature phase diagram between T = 0 and 20 K and a theoretical description based on the weak coupling renormalization group method are reported. The analysis of the data reveals a high temperature domain (T ≈ 20 K) in which a regular T 2 electron-electron Umklapp scattering obeys a Kadowaki-Woods law and a low temperature regime (T < 8 K) where the resistivity is dominated by a linear-in temperature component. In both compounds a correlated behavior exists between the linear transport and the extra nuclear spin-lattice relaxation due to antiferromagnetic fluctuations. In addition, a tight connection is clearly established between linear transport and T c . We propose a theoretical description of the anomalous resistivity based on a weak coupling renormalization group determination of electron-electron scattering rate. A linear resistivity is found and its origin lies in antiferromagnetic correlations sustained by Cooper pairing via constructive interference. The decay of the linear resistivity term under pressure is correlated with the strength of antiferromagnetic spin correlations and T c , along with an unusual build-up of the Fermi liquid scattering. The results capture the key features of the low temperature electrical transport in the Bechgaard salts.

Superconducting phases in Bechgaard salts in an applied magnetic field

The superconducting critical fields in quasi-1d organic Bechgaard salts are very large. Such large values are not compatible with a uniform singlet phase. Therefore, two different order parameter symmetries have been proposed to account for these large values of the critical fields: (i) a non-uniform singlet FFLO phase or (ii) a triplet phase. The real three-dimensional character of the crystal structure has to be taken properly into account. Experimental data indicate the following orders of magnitude for the three transfer integrals along the main crystal axis: t a=3000 K, t b=300 K and t c in the 5–10 K range. The spin effect, as well as the orbital effect has been taken into account to calculate the critical field. We find that the critical field strongly decreases as a function of t c, as a result of a strong orbital pair breaking. A value of t c=5 K is enough to reduce the FFLO critical field to about 0.3 T. Therefore, a finite and even not very large Pauli limit exists in the FFLO phase. On the contrary, a re-entrant superconductivity is still present in the triplet phase. Thus, we expect that, in large enough applied field, a singlet–triplet field-induced phase transition should occur. The NMR experimental data of Shinagawa et al. seem a good indication of this phenomenon.

Correlation between linear resistivity andTcin the Bechgaard salts and the pnictide superconductorBa(Fe1−xCox)2As2

The quasi-1D organic Bechgaard salt (TMTSF)$_2$PF$_6$ displays spin-density-wave (SDW) order and superconductivity in close proximity in the temperature-pressure phase diagram. We have measured its normal-state electrical resistivity $\rho_a(T)$ as a function of temperature and pressure, in the $T \to 0$ limit. At the critical pressure where SDW order disappears, $\rho_a(T) \propto T$ down to the lowest measured temperature (0.1 K). With increasing pressure, $\rho_a(T)$ acquires a curvature that is well described by $\rho_a(T) = \rho_0 + AT + BT^2$, where the strength of the linear term, measured by the $A$ coefficient, is found to scale with the superconducting transition temperature $T_c$. This correlation between $A$ and $T_c$ strongly suggests that scattering and pairing in (TMTSF)$_2$PF$_6$ have a common origin, most likely rooted in the antiferromagnetic spin fluctuations associated with SDW order. Analysis of published resistivity data on the iron-pnictide superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ reveals a detailed similarity with (TMTSF)$_2$PF$_6$, suggesting that antiferromagnetic fluctuations play a similar role in the pnictides.

Interfering antiferromagnetism and superconductivity in quasi-one-dimensional organic conductors

In this short note we summarize recent results obtained by the renormalization group approach to quasi-one-dimensional electron gas model. The approach is applied to the Bechgaard salts series ( TMTSF ) 2 X and the results are shown to give a satisfactory account of the interdependence between antiferromagnetism and superconductivity featured by their phase diagram, the anomalous enhancement of the nuclear relaxation and the electron–electron scattering rate under pressure.

Strain induced on (TMTSF)2ReO4microwires deposited on a silicon substrate

We present the successful recrystallization of Bechgaard salts with the microwire shape using the drop casting method. The samples are deposited on a substrate with previously prepared patterns made by optical lithography. The physical properties of the microwires are shown. The excellent transport properties show that this technique provides a new method for the tuning of the physical properties of molecular conductors and the first step toward applications. The pressure effects of the substrate on the conduction are discussed.

Geometrical and orbital effects in a quasi-one-dimensional conductor

The angular dependent magnetoresistance of (Per)2[Au(mnt)2] under pressure has revealed geometrical effects associated with the crystallographic parameters. Pressure suppresses the charge density wave ground state of the material, and in the metallic state both geometrical and orbital quantum interference effects appear. Through magnetic field dependence and orientation, the orbital and geometrical effects are independently identified. We compare the results from (Per)2[Au(mnt)2] with previous studies of the well-known Bechgaard salts.

Superconducting and magnetic phases in quenched perchlorate Bechgaard salts

(TMTSF) 2ClO 4 is a quasi-1D organic conductor, in which the non-centrosymetric anion ClO 4 undergoes an orientational order at 24 K. Structural studies have shown that in (TMTSF) 2ClO 4, samples cooled down through the anion ordering transition at 24 K, a certain amount of disorder is quenched: there appear, in the low T state, domains in which the anions are orientationaly ordered and domains in which they are disordered, with concentrations and sizes can be varied by varying the cooling rate. Such a structure is essential for the stability of the various phases which can appear. Here, the relevant parameter is not the mean anion potential, but the real values of the anion potential within each domain. When the sizes of the domains are larger than the coherence lengths, a functional renormalization group analysis shows that a d-wave superconducting order is more stable in the ordered domains, because of the gap opened on the Fermi surface by the periodic anion potential, while in the disordered domains, a SDW order is the stable one. There is a large range of cooling rates, in which these two kinds of domains coexist. In that case, in the low T state, a superconducting order and a SDW order exist together. These phases do not really coexist, but are indeed spatially segregated. When the sizes of the disordered domains are much smaller than the superconducting coherence length, they behave as non-magnetic impurities in the superconducting phase, which decrease the superconducting critical temperature, according to the Abrikosov–Gorkov law. Our results are in good agreement with recent experimental.

Link between antiferromagnetism and superconductivity probed by nuclear spin relaxation in organic conductors

The interdependence of antiferromagnetism and superconductivity in the Bechgaard salts series of organic conductors is examined in the light of the anomalous temperature dependence of the nuclear spin-lattice relaxation rate. We apply the renormalization-group approach to the electron gas model to show that the crossover from antiferromagnetism to superconductivity along with the anomalous nuclear relaxation rate of the Bechgaard salts can be well described within a unified microscopic framework. For sizable nesting deviations of the Fermi surface, scaling theory reveals how pairing correlations enhance short-range antiferromagnetic correlations via magnetic Umklapp scattering over a large part of the metallic phase that precedes superconductivity. These enhanced magnetic correlations are responsible for the Curie-Weiss behavior observed in the NMR relaxation rate.

Spin fluctuations and the pseudogap in organic superconductors

We show that there are strong similarities in the spin lattice relaxation of non-magnetic organic charge transfer salts, and that these similarities can be understood in terms of spin fluctuations. Further, we show that, in all of the kappa-phase organic superconductors for which there is nuclear magnetic resonance data, the energy scale for the spin fluctuations coincides with the energy scale for the pseudogap. This suggests that the pseudogap is caused by short-range spin correlations. In the weakly frustrated metals k-(BEDT-TTF)_2Cu[N(CN)_2]Br, k-(BEDT-TTF)_2Cu(NCS)_2, and k-(BEDT-TTF)_2Cu[N(CN)_2]Cl (under pressure) the pseudogap opens at the same temperature as coherence emerges in the (intralayer) transport. We argue that this is because the spin correlations are cut off by the loss of intralayer coherence at high temperatures. We discuss what might happen to these two energy scales at high pressures, where the electronic correlations are weaker. In these weakly frustrated materials the data is well described by the chemical pressure hypothesis (that anion substitution is equivalent to hydrostatic pressure). However, we find important differences in the metallic state of k-(BEDT-TTF)_2Cu_2(CN)_3, which is highly frustrated and displays a spin liquid insulating phase. We also show that the characteristic temperature scale of the spin fluctuations in (TMTSF)_2ClO_4 is the same as superconducting critical temperature, which may be evidence that spin fluctuations mediate the superconductivity in the Bechgaard salts.

Fractional vortex lattice structures in spin-triplet superconductors

Motivated by recent interest in spin-triplet superconductors, we investigate the vortex lattice structures for this class of unconventional superconductors. We discuss how the order parameter symmetry can give rise to U(1)×U(1) symmetry in the same sense as in spinor condensates, making half-quantum vortices (HQVs) topologically stable. We then calculate the vortex lattice structure of HQVs, with particular attention on the roles of the crystalline lattice, the Zeeman coupling and Meissner screening, all absent in spinor condensates. Finally, we consider how spin–orbit coupling leads to a breakdown of the U(1)×U(1) symmetry in free energy and whether the HQV lattice survives this symmetry breaking. As examples, we examine simpler spin-triplet models proposed in the context of NaxCoO2·yH2O and Bechgaard salts, as well as the better known and more complex model for Sr2RuO4.

Phase diagram and critical fields of organic quasi-1d superconductors in an applied magnetic field

No consensus has been reached about the symmetry of the Bechgaard salts superconducting phase. An RG analysis is in favor of interactions dominant in the singlet channel, but very close and sub-dominant in the triplet channel. We study the properties, in a magnetic field along the b′ direction, of a d-wave singlet phase, as well as of an f-wave triplet phase. Recent data about NMR Knight shift, as well as upper critical fields have brought strong indications about the possible symmetries. We have analyzed theoretically the consequences of these experimental data: our results are in favor of a singlet phase in low field, but of a triplet phase in large fields.