An electronic structure and normal and superconducting properties are reviewed for layered organic materials on the basis of bis(ethylenedithio)tetrathiafulvalene molecule (BEDT-TTF, hereafter ET) with essential intraET electron and cross-dimer κ-packing in ET-plane. The metall-insulator phase transition is derived for realistic model of κ-ET2X salts. Based on the Fermi-surface topology and electron correlations the d-symmetry of superconducting order parameter is obtained with interplay between its nodes on the Fermi surface and superconducting phase characteristics. The results are in agreement with measured nonactivated temperature dependencies of NMR-relaxation rate of central carbon 13C spins in ET and superconducting specific heat.

The kappa-ET(2)X compounds are classified as strongly correlated electron systems. The tight-binding approach for correlated electrons is applied to the kappa-ET(2)X family. The electronic spectrum and density of states are calculated. The singlet superconducting pairing of different symmetries is studied based on the symmetry of the lattice model of ET(2)-layer, and the superconducting coupling constants are calculated. The comparison of the theoretical speculations with available experimental data is made for normal and superconducting phases in kappa-ET(2)X.

We claim that superconducting ruthenate, newly discovered by Maeno et al., is a strong electron correlation system similar to cuprates. On the basis of the kinematic interaction model proposed by us for cuprates, we predict that the critical temperature, being around 1 K for the discovered nominally stoichiometric ruthenate, should substantially increase and then decrease on reducing the number of 4d electrons, exhibiting the familiar bell-shaped dependence on the carrier density.

Based on a characteristic energy scale the correlated model of κ-ET2X salts is reduced to the effective Hubbard model with two dimers or two ET2+/sites per a unit cell mapped on a ET2-lattice. It is shown that intradimer electron interactions provide an insulating state of the system without any order parameter. The insulator-metal phase transition of the Mott-Hubbard kind is derived in agreement with available experimental data and empirically observed regularity.

The fullerides AxC60 (A denotes alkali metal dopants in fullerite C60) are classified as isotropic “dirty” superconductors of the second kind with phonon mediated electron-electron pairing. In the proposed three square-well model the AxC60 is characterized by windows of low-frequency intermolecular phonons, high-frequency intramolecular ones and Coulomb energy ranges with cutoffs ωer, ωra and ωC, respectively. For the reason of the inherent imperfections of fullerides the extremely short collision lifetime of electrons force one to assume the “impurity representation” and to include every cutoff frequency ωer, ωra, ωC in the starting equations of superconductivity according to the Anderson theorem for potential spinless scattering. The different energy scales lead to renormalization of the calculated coupling constant and to abandonment of intermolecular phonons for superconducting pairing in AxC60 due to the logarithmic terms of the Tolmachev-Bogoliubov-Tyablikov kind. To illustrate the usefulness of the suggested model of AxC60 the superconducting critical temperature (Tc) for conventional fullerides K3C60 and Rb3C60, the carbon and alkali metal exponents, and the pressure effect for Tc are estimated.

Hubbard model of two layers of strongly correlated electrons with interlayer hopping is investigated. The temperature T(c) of superconducting transition and magnetic suspectibility are calculated. The external pressure dependence of T(c) is discussed.

A purely electronic kinematical mechanism of pairing is studied within the periodic Anderson model. It is found that a singlet superconducting phase occurs at suitable electron densities with a non-monotonic dependence of the superconducting critical temperature on the electron concentration.

The electronic structure of a strongly correlated electron system determined by correlation splitting of Slater-Koster bands by I (Hubbard), U (Coulomb) and J (Hund) intra-atomic interactions has been shown. The developed method of tight-binding for correlated electrons allows for description of d-electron systems of TM compounds of principal cubic and hexagonal crystal structures.

In the Hubbard model U = infinity the energy lowering due to exchange interaction of electrons of opposite spin in states with opposite bonding character is taken into account. In the electron concentration range 0 < n < 1 nonmonotonous dependence m(n) analogous to Slater-Pauling curves has been obtained. The Curie temperature having nonmonotonous dependence on n, saturated magnetization, the temperature dependences of magnetization have been obtained.

The chain of itenerant electrons and impurity with exchange interaction between them is discussed The integrability of this model is proposed with taking into account both incident and reflected electronic waves.

The narrow-band system of electrons hopping between the Wannier states of neighbouring lattice sites with an intransite Anderson-Hubbard energy U is discussed. Both correlated q- and traditional t-hopping have been allowed for in this model of HTSC's. The T(c) is calculated on the basis of kinematical high-T(c) mechanism. In limiting cases previous results are obtained.

The magnetic phase diagrams in correlated models of high-Tc superconductors are discussed. The obtained results agree with experiments semi-quantitatively.

For realistic triangular lattice of BEDT-TTF (hereafter ET) molecules with thereof dimerized κ-arrangement the electronic structure and the Fermi surface (FS) topology are obtained with emphasis of an intraET electron-electron correlations. Based on a symmetry of derived band structure, the nonspecified superconducting pairings of different symmetries are found. The binding state of electronic pair is evaluated in an empty lattice and the preferable d-pairing is found in the condensate with interplay between nodes of superconducting order parameter and properties of κ-ET2X salts. The obtained results are applicable for an analysis of specific heat, London penetration depth, NMR and baric measurements in ET2X compounds and related materials.