A. O. Anokhin

ON THE THEORY OF THE MOTT TRANSITION IN THE PARAMAGNETIC PHASE

A critical consideration of some approaches to the metal-insulator transition problem, starting from the many-electron representation, is carried out within the framework of the Hubbard and classical s-d models in the far-paramagnetic region. The analytical properties of the corresponding one-electron Green functions are discussed, the importance of terms of sufficiently high orders in l/z being demonstrated. The total energy, electronic specific heat and corrections to the local moment are calculated. The Hubbard-III approximation in the Hubbard model (but not in the s-d model) is shown to lead to difficulties when calculating thermodynamic properties.

On the effect of strong electron correlations on various superconductivity mechanisms

Abstract The Eliashberg equations for singlet pairing are derived taking into account the many-electron renormalization of one-particle Green functions in the normal state of a highly correlated system. The electron-phonon and exciton superconductivity mechanisms, and influence of magnetic impurities on T c are investigated. It is demonstrated that the “usual” superconductivity mechanisms are not influenced by correlation effects, if the Fermi-liquid picture holds, but they are strongly suppressed in the “marginal” Fermi-liquid. In the Mott-Hubbard systems with a strong electron damping at E F , described by Hubbard-III type approximations, the electron-phonon interaction cannot lead to superconductivity.

The effect of electronic localized states at dislocations on the 'chemical' impurity-dislocation interaction

Abstract The electronic contribution to the interaction energy between impurities and edge dislocations, which is related to the existence of localized electronic states at the dislocation, is calculated within the framework of a simple model. It is shown that the interaction energy varies within the limits of 10−2−-10−1 of the bandwidth and depends essentially on the lattice structure, the Burgers vector b, the type of impurity (‘donor’ or ‘acceptor’) and on the conduction-band filling. These effects are expected to be important in intermetallics with the B2 structure, where plastic deformation is governed by dislocations with b = a{100) (NiAl, CoAl, etc.).

ON THE PHONON-INDUCED SUPERCONDUCTIVITY OF DISORDERED ALLOYS

A model of alloy is considered which includes both quenched disorder in the electron subsystem (“alloy” subsystem) and electron-phonon interaction. For given approximate solution for the alloy part of the problem, which is assumed to be conserving in Baym’s sense, we construct the generating functional and derive the Eliashberg-type equations which are valid to the lowest order in the adiabatic parameter. The renormalization of bare electron–phonon interaction vertices by disorder is taken into account consistently with the approximation for the alloy self-energy. For the case of exact configurational averaging the same set of equations is established within the usual T-matrix approach. We demonstrate that for any conserving approximation for the alloy part of the self-energy the Anderson’s theorem holds in the case of isotropic singlet pairing provided disorder renormalizations of the electron-phonon interaction vertices are neglected. Taking account of the disorder renormalization of the electron-phonon interaction we analyze general equations qualitatively and present the expressions for Tc for the case of weak and intermediate electron-phonon coupling. Disorder renormalizations of the logarithmic corrections to the effective coupling, which arise when the effective interaction kernel for the Cooper channel has the second energy scale, as well as the renormalization of the dilute paramagnetic impurity suppression are discussed.

One- and two-channel Kondo model with logarithmic Van Hove singularity: A numerical renormalization group solution

Abstract Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the s–d coupling J. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior.

Exchange interactions in a dinuclear manganese (II) complex with cyanopyridine-N-oxide bridging ligands

Abstract The magnetic properties of dinuclear manganese(II) complex [Mn(hfa) 2 cpo] 2 (where hfa is hexafluoroacetylacetonate anion and cpo is 4-cyanopyridine-N-oxide) are presented. The non-monotonous dependence of magnetic susceptibility is explained in terms of the hierarchy of exchange parameters by using exact diagonalization. The thermodynamic behavior of pure cpo and [Mn(hfa) 2 (cpo)] 2 is simulated numerically by an extrapolation to spin S =5/2. The Mn–Mn exchange integral is evaluated.

Evolution of the spectrum and the metal-insulator transition in local approximations for many-electron models

In terms of the Shubin-Vonsovskii many-electron s-d exchange model and Hubbard model, self-consistent equations for the one-particle retarded Green’s function are derived in the representation of many-electron Hubbard X operators using the method of decoupling of chains of equations of motion. An analysis is given of the general structure of single-site approximations and of their relation to the coherent-potential approximation (CPA) and the dynamic mean-field theory (DMFT). Using the self-consistent approximations, the evolution of the electron spectrum upon the variation of the bare parameters of the model (coupling constants, charge-carrier concentrations) is investigated in detail. Effects of various factors (Kondo many-electrons scattering, damping-induced smearing, proper dynamics of the subsystem of localized momenta) on the shape of the density of states N(E) with allowance for interaction are discussed. It is shown that the use of the locator representation makes it possible in some cases to avoid nonanalyticities in the approximate expressions for the Green’s functions. This approach permits the reproduction (at certain values of the parameters) of the three-peak structure of the DOS near the metal-insulator transition.

Single-particle spectrum for a model of fermions interacting with two-level local excitations on a lattice : A dynamical CPA approach

The problem of motion of a single electron interacting with a periodic lattice of two-level systems is investigated within a spinless fermion model. The Greens function is calculated in a single-site dynamical coherent potential approximation which is equivalent to DMFT. The picture of one-electron density of states is obtained for various values of the tunnel splitting and coupling between the electron and two-level system. The occurrence of a band splitting with increase of the coupling is demonstrated.