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 fluctuati
ons as obtained by a generalized Ginzburg-Landau approach for arrays of weakly coupled chains is embodied in the numerical solution of the semi-classical 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 connexion between theory and experiments carried out on molecular conductors is presented and critically 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-c
lassical 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.
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 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 n
ear 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 $beta sim$ 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.
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 integrat
ion 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.
The phase diagram of the one-dimensional extended Hubbard model at half-filling is investigated by a weak coupling renormalization group method applicable beyond the usual continuum limit for the electron spectrum and coupling constants. We analyze t
he influence of irrelevant momentum dependent interactions on asymptotic properties of the correlation functions and the nature of dominant phases for the lattice model under study.
The interference between spin-density-wave and superconducting instabilities in quasi-one-dimensional correlated metals is analyzed using the renormalization group method. At the one-loop level, we show how the interference leads to a continuous cros
sover from a spin-density-wave state to unconventional superconductivity when deviations from perfect nesting of the Fermi surface exceed a critical value. Singlet pairing between electrons on neighboring stacks is found to be the most favorable symmetry for superconductivity. The consequences of non uniform spin-density-wave pairing on the structure of phase diagram within the crossover region is also discussed.
This paper is written as a brief introduction for beginning graduate students. The picture of electron waves moving in a cristalline potential and interacting weakly with each other and with cristalline vibrations suffices to explain the properties o
f technologically important materials such as semiconductors and also simple metals that become superconductors. In magnetic materials, the relevant picture is that of electrons that are completely localized, spin being left as the only relevant degree of freedom. A number of recently discovered materials with unusual properties do not fit in any of these two limiting cases. These challenging materials are generally very anisotropic, either quasi one-dimensional or quasi two-dimensional, and in addition their electrons interact strongly but not enough to be completely localized. High temperature superconductors and certain organic conductors fall in the latter category. This paper discusses how the effect of low dimension leads to new paradigms in the one-dimensional case (Luttinger liquids, spin-charge separation), and indicates some of the attempts that are being undertaken to develop, concurrently, new methodology and new concepts for the quasi-two-dimensional case, especially relevant to high-temperature superconductors.
We review the properties of quasi-one-dimensional organic superconductors: the Bechgaard salts and their sulfur analogs in their normal phase precursor tolong-range order. We go through the main observations made in the normal state of these systems
at low magnetic field and tackle the issue of their description under the angles of the Fermi and Luttinger liquid pictures.
The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reaveals that the Luttinger liquid spin susceptibility $chi (T) $ a
pproaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator, in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach. Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions are given.
