By scanning tunneling microscopy (STM) we have probed the local quasi-particle density of states (DOS) of the Bechgaard salt organic superconductor (TMTSF)_2ClO_4 in slowly cooled single crystals cleaved under ultrahigh vacuum conditions. In well STM imaged crystallographic surface planes, the local DOS has been probed for different surface areas at temperatures above and below the critical temperature of superconducting or insulating spin-density wave states. While a rather homogeneous superconducting state is expected in the bulk from previous studies, depending on the degree of disorder introduced by cleavage in the anion lattice, an inhomogeneous granular state is predominantly observed at the surface. A pronounced linear V-shape profile of the local DOS is observed from intermediate to the lowest energy scale in the less disordered superconducting surface areas. This supports the existence of an unconventional d-wave like order parameter with nodes at low energy, which is preceded by more energetic fluctuations attributed to quantum criticality of the material. At higher energy disorder combined to correlations deplete further the DOS. By contrast a non-linear U-shape characterizes the local low energy DOS profile for the more disordered and insulating surface areas of the spin-density wave state. The experimental results are compared quantitatively with those predicted by the renormalization group theory of the quasi-one dimensional electron gas model and its description of the superconducting and spin-density wave states that are interlinked by quantum criticality in the Bechgaard salts.

It is indisputable that the search for high-temperature superconductivity has stimulated the work on low-dimensional organic conductors at its beginning. Since the discovery of true metal-like conduction in molecular compounds more than 50 years ago, it appeared that the chemical composition and the quasi one-dimensional crystalline structure of these conductors were determining factors for their physical properties; materials with incommensurate conduction band filling favoring the low-dimensional electron-phonon diverging channel and the establishment of the Peierls superstructure and more rarely superconductivity at low temperature, while those with commensurate band filling favor either magnetic insulating or superconducting states depending on the intensity of the coupling between conductive chains. In addition, the simple structures of these materials have allowed the development of theoretical models in close cooperation with almost all experimental findings. Even though these materials have not yet given rise to true high-temperature superconductivity, the wealth of their physical properties makes them systems of choice in the field of condensed matter physics due to their original properties and their educational qualities. Research efforts continue in this field. The present retrospective, which does not attempt to be an exhaustive review of the field, provides a set of experimental findings alluding to the theoretical development while a forthcoming article will address in more details the theoretical aspect of low dimensional conductors and superconductors.

A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle and particle-hole channels are derived in weak-coupling conditions. It is shown that lattice effects manifest themselves through the curvature of the spectrum and the dependence of the coupling constants on momenta. This method is then applied to the one-dimensional extended Hubbard model; we thoroughly discuss the evolution of the phase diagram, and in particular the fate of the bond-centered charge-density-wave phase, as the system is doped away from half-filling. Our findings are compared to the predictions of the field-theory continuum limit and available numerical results.

The behavior of three-dimensional semimetals under strong magnetic fields is a topic of recurring interest in condensed matter physics. Recently, the advent of Weyl and Dirac semimetals has brought about an interesting platform for potentially uncovering phases of matter that combine nontrivial band topology and interactions. While electronic instabilities of such semimetals at strong magnetic fields have been explored theoretically and experimentally, the role of electron-phonon interactions therein has been largely neglected. In this paper, we study the interplay of electron-electron and electron-phonon interactions in a minimal two-node model of Weyl semimetal. Using a Kadanoff-Wilson renormalization group approach, we analyze lattice (Peierls) instabilities emerging from chiral and nonchiral Landau levels as a function of the magnetic field. We consider both the adiabatic and nonadiabatic phonon regimes, in the presence or absence of improper symmetries that relate Weyl nodes of opposite chirality. We find that (i) the Cooper channel, often neglected in recent studies, can prevent purely electronic instabilities while enabling lattice instabilities that are not Bardeen-Cooper-Schrieffer-like; (ii) breaking the improper symmetry that relates the two Weyl nodes suppresses the Cooper channel, thereby increasing the critical temperature for the lattice instability; (iii) in the adiabatic phonon regime, lattice instabilities can preempt purely electronic instabilities; and (iv) pseudoscalar phonons are more prone to undergo a Peierls instability than scalar phonons. In short, our study emphasizes the importance of taking electron-phonon interactions into account for a complete understanding of interacting phases of matter in Dirac and Weyl semimetals at high magnetic fields.

We study the role of charge density wave fluctuations on the temperature dependence of Seebeck coefficient in quasi-one-dimensional conductors with a Peierls instability. The description of low-dimensional incommensurate charge density wave fluctuations as obtained by a generalized Ginzburg-Landau approach for arrays of weakly coupled chains is embodied in the numerical solution of the semiclassical Boltzmann transport equation. The energy and temperature dependence of the scattering time of electrons on fluctuations can then be extracted and its influence on the Seebeck coefficient calculated. The connection between theory and experiments carried out on molecular conductors is presented and critically discussed.

The one-dimensional extended Hubbard model with lattice dimerization and alternated site potentials is analyzed using the renormalization group method. The coupling of electrons to structural degrees of freedom such as the anion lattice and acoustic phonons is investigated to obtain the possible instabilities against the formation of lattice superstructures. Applications of the theory to anionic and spin-Peierls instabilities in the Fabre and Bechgaard salts series of organic conductors and ordered alloys are presented and discussed.

This work presents and analyzes electrical resistivity data on the organic superconductor (TMTSF)(2)ClO4 and their anion-substituted alloys (TMTSF)(2)(ClO4)(1-x)(ReO4)(x) along the least conducting c* axis. Nonmagnetic disorder introduced by finite size domains of anion ordering on non-Fermi-liquid character of resistivity is investigated near the conditions of quantum criticality taking place at x = 0. The evolution of the T-linear resistivity term with anion disorder shows a limited decrease in contrast with the complete suppression of the critical temperature T-c as expected for unconventional superconductivity beyond a threshold value of x. The resulting breakdown of scaling between both quantities is compared to the theoretical predictions of a linearized Boltzmann equation combined to the scaling theory of umklapp scattering in the presence of disorder-induced pair breaking for the carriers. The theory shows that quantum antiferromagnetic fluctuations, which are at the core of unconventional Cooper pairing and inelastic scattering of T-linear resistivity in these systems, are weakly affected by disorder while the phase coherence responsible for a finite T-c can be completely suppressed.

One-dimensional (1D) conductors such as Bechgaard and Fabre salts are a prototypal example of correlated systems where the phase diagram is controlled by sizable electron-electron repulsions. In deuterated (TMTTF)(2)PF6, where this interaction achieves charge localization at ambient pressure on donor stacks, magnetostructural coupling plays a decisive role to stabilize a spin-Peierls (SPs) ground state at T-SP = 13K. In this paper, we present the first inelastic neutron scattering investigation of SP magnetic excitations in organics. Our paper reveals the presence above TSP of sizable critical fluctuations leading to the formation of a pseudogap in the 1D antiferromagnetic (AF) S = 1/2 magnetic excitation spectrum of the donor stack, concomitant with the local formation of singlet of paired spins into dimers below T-SP(MF) approximate to 40 K. In addition, the inelastic neutron scattering investigation allows us also to probe the SP critical lattice dynamics and to show that at ambient pressure these dynamics are of relaxation or order-disorder type. Below TSP, our paper reveals the emergence of a two gap SP magnetic excitation spectrum towards a well-defined S = 1 magnon mode and a continuum of two excitations, as theoretically predicted. Our measurements allow us to locate the ambient pressure SP phase of (TMTTF) 2PF6 in the classical (adiabatic) limit close to the classical/quantum crossover line. Then we provide arguments suggesting that pressurized (TMTTF) 2PF6 shifts to the quantum (antiadiabatic) SP gapped phase, which ends in a quantum critical point allowing the stabilization of an AF phase that competes with superconductivity at higher pressure. Finally, we propose that the magnetostructural coupling mechanism in the Fabre salts is caused by dimer charge/spin fluctuations driven by the coupling of donors with anions.

In the framework of the weak coupling renormalization group technique we examine the possible instabilities of the extended quasi-one-dimensional electron gas model with both intrachain and interchain electron-electron interactions, including the influence of umklapp scattering and the coupling of spins to a magnetic field. In the limit of purely repulsive intrachain interactions, we confirm the passage from singlet d-wave like superconductivity to an inhomogeneous FFLO state under magnetic field. The passage is accompanied by an anomalous increase of the upper critical field that scales with the antinesting distance from the quantum critical point joining superconductivity to antiferromagnetism in the phase diagram, as well as the strength of interactions. Adding weak repulsive interchain interactions promotes the passage from singlet to triplet $f$-wave superconductivity which is expanded under field by the development of a triplet FFLO state with zero angular momentum projection for the Cooper pairs. The connection between theory and experiments on the anomalous upper critical field in the Bechgaard salts is discussed.

We study the influence of inelastic electron-electron scattering on the temperature variation of the Seebeck coefficient in the normal phase of quasi-one-dimensional organic superconductors. The theory is based on the numerical solution of the semi-classical Boltzmann equation for which the collision integral equation is solved with the aid of the electronic umklapp scattering vertex calculated by the renormalization group method. We show that the one-loop renormalization group flow of momentum and temperature dependent umklapp scattering, in the presence of nesting alterations of the Fermi surface, introduce electron-hole asymmetry in the energy dependence of the anisotropic scattering time. This is responsible for the enhancement of the Seebeck coefficient with respect to the band $T$-linear prediction and even its sign reversal around the quantum critical point of the phase diagram, namely where the interplay between antiferromagnetism and superconductivity along with the strength of spin fluctuations are the strongest. Comparison of the results with available data on low dimensional organic superconductors is presented and critically discussed.

The renormalization group technique is applied to one-dimensional electron-phonon Hubbard models at half filling and zero temperature. For the Holstein-Hubbard model, the results of one-loop calculations are congruent with the phase diagram obtained by quantum Monte Carlo simulations in the (U, g(ph)) plane for the phonon-mediated interaction g(ph) and the Coulomb interaction U. The incursion of an intermediate phase between a fully gapped charge-density-wave state and a Mott antiferromagnet is supported along with the growth of its size with the molecular phonon frequency omega(0). We find additional phases enfolding the base boundary of the intermediate phase. A Luttinger liquid line is found below some critical U* approximate to g(ph)*, followed at larger U similar to g(ph) by a narrow region of bond-order-wave ordering which is either charge or spin gapped depending on U. For the Peierls-Hubbard model, the region of the (U, g(ph)) plane with a fully gapped Peierls-bond-order-wave state shows a growing domination over the Mott gapped antiferromagnet as the Debye frequency omega(D) decreases. A power-law dependence g(ph) similar to U-2 eta is found to map out the boundary between the two phases, whose exponent is in good agreement with the existing quantum Monte Carlo simulations performed when a finite nearest-neighbor repulsion term V is added to the Hubbard interaction.

We propose a theory of longitudinal resistivity in the normal phase of quasi-one-dimensional organic superconductors near the quantum critical point where antiferromagnetism borders with superconductivity under pressure. The linearized semi-classical Boltzmann equation is solved numerically, fed in by the half-filling electronic umklapp scattering vertex as derived from one-loop renormalization group calculations for the quasi-one-dimensional electron gas model. The momentum and temperature dependence of umklapp scattering has an important impact on the behaviour of longitudinal resistivity in the the normal phase. Resistivity is found to be linear in temperature around the quantum critical point at which spin-density-wave order joins superconductivity along the antinesting axis, to gradually evolve towards the Fermi liquid behaviour in the limit of weak superconductivity. A comparison is made between theory and experiments performed on the (TMTSF)$_2$PF$_6$ member of the Bechgaard salt series under pressure.

We use the renormalization group method to examine the effect of phonon-mediated interaction on d-wave superconductivity, as driven by spin fluctuations in a quasi-one-dimensional electron system. The influence of a tight-binding electron-phonon interaction on the spin-density-wave and d-wave superconducting instability lines is calculated for arbitrary temperature, phonon frequency, and antinesting of the Fermi surface. The domain of electron-phonon coupling strength where spin-density-wave order becomes unstable against the formation of a bond-order wave or Peierls state is determined at weak antinesting. We show the existence of a positive isotope effect for spin-density-wave and d-wave superconducting critical temperatures which scales with the antinesting distance from quantum critical point where the two instabilities merge. We single out a low phonon frequency zone where the bond-order-wave ordering gives rise to triplet f-wave superconductivity under nesting alteration, with both orderings displaying a negative isotope effect. We also study the electron-phonon strengthening of spin fluctuations at the origin of extended quantum criticality in the metallic phase above superconductivity. The impact of our results on quasi-one-dimensional organic conductors like the Bechgaard salts where a Peierls distortion is absent and superconductivity emerges near a spin-density-wave state under pressure is emphasized.

We report an investigation of charge, spin, and lattice effects in the spin-Peierls state of the organic compound MEM(TCNQ)(2). The 16.5-GHz dielectric function along the chain axis shows an enhancement below the spin-Peierls transition temperature near 18 K consistent with the charge coupling to the elastic strain involved in the transition. The velocity of two elastic modes perpendicular to the chain axis presents anomalies at the transition, which can be explained with a Landau free-energy model including a linear-quadratic coupling energy term between the appropriate elastic strain e and the spin-Peierls magnetic gap Delta(q). The analysis of the dielectric and elastic features aims toward an order parameter with an associated critical exponent beta similar to 0.36, which is similar to the three-dimensional behavior seen in other spin-Peierls materials. All these effects studied in a magnetic field up to 18 Teslas appear also compatible with a mean-field model of a quasi-one-dimensional spin-Peierls system.

An inductive method is used to follow the magnetic-field–dependent susceptibility of the coupled charge density wave (CDW) and spin-Peierls (SP) ordered state behavior in the dual-chain organic conductor perylene2[Pt(mnt)2]. In addition to the coexisting SP-CDW state phase below 8 K and 20 T, the measurements show that a second spin-gapped phase appears above 20 T that coincides with a field-induced insulating phase. The results support a strong coupling of the CDW and SP order parameters even in high magnetic fields, and provide new insight into the nature of the magnetic susceptibility of dual-chain spin and charge systems.

The Peierls instability in one-dimensional electron-phonon systems is known to be qualitatively well described by the mean-field theory, however the related self-consistent problem so far has only been able to predict a partial suppression of the transition even with proper account of classical lattice fluctuations. Here the Hartree-Fock approximation scheme is extended to the full quantum regime, by mapping the momentum-frequency spectrum of order-parameter fluctuations onto a continuous two-parameter space. For the one-dimensional half-filled SuSchrieffer-Heeger model the ratio d = Omega/2 pi T-c(0), where Omega is the characteristic phonon frequency and 2 pi T-c(0) the lowest finite phonon Matsubara frequency at the mean-field critical point T-c(0), provides a natural measure of the adiabaticity of lattice fluctuations. By integrating out finite-frequency phonons, it is found that a variation of d from the classical regime d = 0 continuously connects T-c(0) to a zero-temperature charge-density-wave transition setting up at a finite crossover d = d(c). This finite crossover decreases within the range 0 <= d approximate to 1 as the electron-phonon coupling strength increases but remaining small enough for weak-coupling considerations to still hold. Implications of T-c suppression on the Ginzburg criterion is discussed, and evidence is given of a possible coherent description of the charge-density-wave problem within the framework of a renormalized mean-field theory encompassing several aspects of the transition including its thermodynamics close to the quantum critical point.

We use the renormalization group method to study normal-state properties 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 non-Fermi-liquid temperature downturn of the momentum-resolved quasiparticle 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 quasiparticle scattering rate is found to develop an unusual temperature dependence, which is best described by the superimposition of a linear and quadratic T dependencies. The non-Fermi-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-one-dimensional organic conductors, but also the pnictide and cuprate superconductors where several common features are observed.

We report an ultrasonic study of the magneto-elastic coupling of the hydrogenated and deuterated (TMTTF)(2)PF6 organic salts. For both salts the temperature dependence of the longitudinal velocity along the c* axis displays a monotonic stiffening of the C-33 compressibility modulus upon cooling. Below the characteristic temperature scale 40 K the modulus stiffening becomes markedly enhanced, in concomitance with the reduction of spin degrees of freedom previously seen in magnetic measurements as low-dimensional precursors of the spin-Peierls transition. The magneto-elastic coupling appears to be much weaker in the hydrogenated salt due to the highly inhomogeneous elastic behavior induced by the proximity of the charge ordering transition to the spin-Peierls phase. For the deuterated salt, an important anomaly in the ultrasound velocity is observed below the spin-Peierls transition temperature T-SP in agreement with scaling of the elastic deformation with the spin-Peierls order parameter. In spite of the weakly inhomogeneous character of the spin-Peierls phase transition, the magnetic field dependence of T-SP is well captured with the mean-field prediction for the lattice distorted Heisenberg spin chain.