Abstract:
We study the Mott transition, antiferromagnetism and superconductivity in layered organic conductors using Cellular Dynamical Mean Field Theory for the frustrated Hubbard model. A d-wave superconducting phase appears between an antiferromagnetic insulator and a metal for $t^{\prime}/t=0.3-0.7 $, or between a nonmagnetic Mott insulator (spin liquid) and a metal for $t^{\prime}/t\geq 0.8$, in agreement with experiments on layered organic conductors including $\kappa $-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$. These phases are separated by a strong first order transition. The phase diagram gives much insight into the mechanism for d-wave superconductivity. Two predictions are made.

Abstract:
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.

Abstract:
We review the current understanding of superconductivity in the quasi-one-dimensional organic conductors of the Bechgaard and Fabre salt families. We discuss the interplay between superconductivity, antiferromagnetism, and charge-density-wave fluctuations. The connection to recent experimental observations supporting unconventional pairing and the possibility of a triplet-spin order parameter for the superconducting phase is also presented.

Abstract:
We study the magnetic-field-induced spin-density-wave (FISDW) phases in TMTSF organic conductors in the framework of the quantized nesting model. In agreement with recent suggestions, we find that the SDW wave-vector ${\bf Q}$ deviates from its quantized value near the transition temperature $T_c$ for all phases with quantum numbers $N>0$. Deviations from quantization are more pronounced at low pressure and higher $N$ and may lead to a suppression of the first-order transitions $N+1\to N$ for $N\ge 5$. Below a critical pressure, we find that the N=0 phase invades the entire phase diagram in accordance with earlier experiments. We also show that at T=0, the quantization of ${\bf Q}$ and hence the Hall conductance is always exact. Our results suggest a novel phase transition/crossover at intermediate temperatures between phases with quantized and non-quantized ${\bf Q}$.

Abstract:
Superconductivity of quasi-one-dimensional organic conductors with a quarter-filled band is investigated using the two-loop renormalization group approach to the extended Hubbard model for which both the single electron hopping t_{\perp} and the repulsive interaction V_{\perp} perpendicular to the chains are included. For a four-patches Fermi surface with deviations to perfect nesting, we calculate the response functions for the dominant fluctuations and possible superconducting states. By increasing V_{\perp}, it is shown that a d-wave (singlet) to f-wave (triplet) superconducting state crossover occurs, and is followed by a vanishing spin gap. Furthermore, we study the influence of a magnetic field through the Zeeman coupling, from which a triplet superconducting state is found to emerge.

Abstract:
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.

Abstract:
I apply a two-step renormalization group method to the study of the competition between antiferromagnetism (AFM) and superconductivity in an anisotropic 2D Hubbard model. I show that this simple model captures the essentials of the ground-state phases of the quasi 1D organic conductors. As found experimentally, the ground-state phase diagram is mostly AFM. The AFM is localized in the strong-coupling limit where the electrons are confined in the chains. It is an SDW in the weak-coupling limit where interchain hopping is present. There is a tiny region in the weak-coupling regime where transverse two-particle hopping is dominant over magnetism.

Abstract:
The $\kappa$-(ET)$_2$X layered conductors (where ET stands for BEDT-TTF) are studied within the dimer model as a function of the diagonal hopping $t^\prime$ and Hubbard repulsion $U$. Antiferromagnetism and d-wave superconductivity are investigated at zero temperature using variational cluster perturbation theory (V-CPT). For large $U$, N\'eel antiferromagnetism exists for $t' < t'_{c2}$, with $t'_{c2}\sim 0.9$. For fixed $t'$, as $U$ is decreased (or pressure increased), a $d_{x^2-y^2}$ superconducting phase appears. When $U$ is decreased further, the a $d_{xy}$ order takes over. There is a critical value of $t'_{c1}\sim 0.8$ of $t'$ beyond which the AF and dSC phases are separated by Mott disordered phase.

Abstract:
The d-wave pairing correlations along with spin correlation are calculated with quantum Monte Carlo method for the two-dimensional Hubbard model on lattice structures representing organic superconductors $\kappa$-(BEDT-TTF)$_2$X and (TMTSF)$_2$X. In both cases the pairing correlations for superconducting order parameters with nodes are found to be enhanced. The symmetry and the enhancement of the pairing is systematically correlated with the spin structure factor, suggesting a spin-fluctuation mediated pairing. We have further found that, as we deform the Fermi surface to make the system approach the half-filled square lattice, the coherence of the pairing saturates while the local pairing amplitude continues to increase.

Abstract:
Layered organic superconductors are on the verge of the Mott insulator. We use Gutzwiller variational method to study a Hubbard model including a spin exchange coupling term. The ground state is found to be a Gossamer superconductor at small on-site Coulomb repulsion U and an antiferromagnetic Mott insulator at large U, separated by a first order phase transition. Our theory is qualitatively consistent with major experiments reported in organic superconductors.