Superconductivity in a Toy Model of the Pseudogap State

We analyze superconducting state (both s and d - wave) in a simple exactly solvable model of pseudogap state, induced by short - range order fluctuations (e.g. antiferromagnetic), which is based upon model Fermi - surface with "hot patches". It is shown that superconducting energy gap averaged over these fluctuations is non zero even for the temperatures larger than mean - field T_c of superconducting transition in a sample as a whole. For temperatures T>T_c superconductivity apparently exists within separate regions ("drops"). We study the spectral density and the density of states and demonstrate that superconductivity signals itself in these already for T>T_c, while at T_c itself nothing special happens from this point of view. These anomalies are in qualitative agreement with a number experiments on underdoped cuprates.Comment: 12 pages, 6 figures, RevTeX 3.0, Postscript figures attache

Combinatorics of Feynman Diagrams for the Problems with Gaussian Random Field

The algorithm to calculate the generating function for the number of ``skeleton'' diagrams for the irreducible self-energy and vertex parts is derived for the problems with Gaussian random fields. We find an exact recurrence relation determining the number of diagrams for any given order of perturbation theory, as well as its asymptotics for the large order limit. These results are applied to the analysis of the problem of an electron in the Gaussian random field with the ``white-noise'' correlation function. Assuming the equality of all ``skeleton'' diagrams for the self-energy part in the given order of perturbation theory, we construct the closed integral equation for the one-particle Green's function, with its kernel defined by the previously introduced generating function. Our analysis demonstrate that this approximation gives the qualitatively correct form of the localized states ``tail'' in the density of states in the region of negative energies and is apparently quite satisfactory in the most interesting region of strong scattering close to the former band-edge, where we can derive the asymptotics of the Green's function and density of states in the limit of very strong scattering.Comment: 23 pages, 6 figures, RevTeX 3.0, Postscript figures attached, Submitted to JET

High Temperature Superconductivity in Transition Metal Oxypnictides: a Rare-Earth Puzzle?

We have performed an extensive ab initio LDA and LSDA+U calculations of electronic structure of newly discovered high-temperature superconducting series ReO(1-x)F(x)FeAs (Re=La,Ce, Pr, Nd, Sm and hypothetical case of Re=Y). In all cases we obtain almost identical electronic spectrum (both energy dispersions and the densities of states) in rather wide energy interval (about 2 eV) around the Fermi level. We also debate that this fact is unlikely to be changed by the account of strong correlations. It leads inevitably to the same critical temperature Tc of superconducting transition in any theoretical BCS-like mechanism of Cooper pair formation. We argue that the experimentally observed variations of Tc for different rare-earth substitutions are either due to disorder effects or less probably because of possible changes in spin-fluctuation spectrum of FeAs layers caused by magnetic interactions with rare-earth spins in ReO layers.Comment: 5 pages, 5 figures, 2 table

Mott-Hubbard Transition and Anderson Localization: Generalized Dynamical Mean-Field Theory Approach

Density of states, dynamic (optical) conductivity and phase diagram of strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT+\Sigma approximation). Strong correlations are accounted by DMFT, while disorder is taken into account via the appropriate generalization of self-consistent theory of localization. The DMFT effective single impurity problem is solved by numerical renormalization group (NRG) and we consider the three-dimensional system with semi-elliptic density of states. Correlated metal, Mott insulator and correlated Anderson insulator phases are identified via the evolution of density of states and dynamic conductivity, demonstrating both Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of complete zero-temperature phase diagram of Anderson-Hubbard model. Rather unusual is the possibility of disorder induced Mott insulator to metal transition.Comment: 15 pages, 16 figure

Weak Pseudogap Behavior in the Underdoped Cuprate Superconductors

We report on an exact solution of the nearly antiferromagnetic Fermi liquid spin fermion model in the limit \pi T << \omega_{sf}, which demonstrates that the broad high energy features found in ARPES measurements of the spectral density of the underdoped cuprate superconductors are determined by strong antiferromagnetic (AF) correlations and precursor effects of an SDW state. We show that the onset temperature, T^{cr}, of weak pseudo-gap (pseudoscaling) behavior is determined by the strength, \xi, of the AF correlations, and obtain the generic changes in low frequency magnetic behavior seen in NMR experiments with \xi(T^{cr}) \approx 2, confirming the Barzykin and Pines crossover criterion.Comment: REVTEX, 4 pages, 3 EPS figure

Two-dimensional Anderson-Hubbard model in DMFT+Sigma approximation

Density of states, dynamic (optical) conductivity and phase diagram of paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean-field theory (DMFT+Sigma approximation). Strong correlations are accounted by DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular "bare" density of states (DOS). The DMFT effective single impurity problem is solved by numerical renormalization group (NRG). Phases of "correlated metal", Mott insulator and correlated Anderson insulator are identified from the evolution of density of states, optical conductivity and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of the finite size, allowing us to construct the complete zero-temperature phase diagram of paramagnetic Anderson-Hubbard model. Localization length in our approximation is practically independent of the strength of Hubbard correlations. However, the divergence of localization length in finite size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.Comment: 10 pages, 10 figures, improve phase diagra

Localization effects in radiationally disordered high-temperature superconductors: Theoretical interpretation

Theoretical interpretation of recent experiments on radiationally disordered high-temperature superconductors is presented, based on the concepts of mutual interplay of Anderson localization and superconductivity. Microscopic derivation of Ginzburg-Landau coefficients for the quasi-two-dimensional system in the vicinity of localization transition is given in the framework of the self-consistent theory of localization. The 'minimal metallic conductivity' for the quasi-two-dimensional case is enhanced due to a small overlap of electronic states on the nearest neighbor conducting planes. This leads to a stronger influence of localization effects than in ordinary (three-dimensional) superconductors. From this point of view even the initial samples of high-temperature superconductors are already very close to Anderson transition. Anomalies of H(c2) are also analyzed, explaining the upward curvature of H(c2)(T) and apparent independence of dH(c2)/dT (T = T(sub c)) on the degree of disorder as due to localization effects. Researchers discuss the possible reasons of fast T(sub c) degradation due to the enhanced Coulomb effects caused by the disorder induced decrease of localization length. The appearance and growth of localized magnetic moments is also discussed. The disorder dependence of localization length calculated from the experimental data on conductivity correlates reasonably with the theoretical criterion for suppression of superconductivity in the system with localized electronic states

Scaling near the upper critical dimensionality in the localization theory

The phenomenon of upper critical dimensionality d_c2 has been studied from the viewpoint of the scaling concepts. The Thouless number g(L) is not the only essential variable in scale transformations, because there is the second parameter connected with the off-diagonal disorder. The investigation of the resulting two-parameter scaling has revealed two scenarios, and the switching from one to another scenario determines the upper critical dimensionality. The first scenario corresponds to the conventional one-parameter scaling and is characterized by the parameter g(L) invariant under scale transformations when the system is at the critical point. In the second scenario, the Thouless number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation of the Wegner relation s=\nu(d-2) between the critical exponents for conductivity (s) and for localization radius (\nu), which takes the form s=\nu(d_c2-2). The resulting formulas for g(L) are in agreement with the symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous version of Mott's argument concerning localization due topological disorder has been proposed.Comment: PDF, 7 pages, 6 figure

Electronic structure of Pr_{2-x}Ce_xCuO_4 studied via ARPES and LDA+DMFT+\Sigma_k

The electron-doped Pr(2-x)Ce(x)CuO(4) (PCCO) compound in the pseudogap regime (x~0.15) was investigated using angle-resolved photoemission spectroscopy (ARPES) and the generalized dynamical mean-field theory (DMFT) with the k-dependent self-energy (LDA+DMFT+\Sigma_k). Model parameters (hopping integral values and local Coulomb interaction strength) for the effective one-band Hubbard model were calculated by the local density approximation (LDA) with numerical renormalization group method (NRG) employed as an "impurity solver" in DMFT computations. An "external" k-dependent self-energy \Sigma_k was used to describe interaction of correlated conducting electrons with short-range antiferromagnetic (AFM) pseudogap fluctuations. Both experimental and theoretical spectral functions and Fermi surfaces (FS) were obtained and compared demonstrating good semiquantitative agreement. For both experiment and theory normal state spectra of nearly optimally doped PCCO show clear evidence for a pseudogap state with AFM-like nature. Namely, folding of quasiparticle bands as well as presence of the "hot spots" and "Fermi arcs" were observed.Comment: 4 pages, 4 figures, as accepted to PRB Rapid Communications. Title is changed by Editor

Finite-size scaling from self-consistent theory of localization

Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good agreement with numerical results: it signifies the absence of essential contradictions with the Vollhardt and Woelfle theory on the level of raw data. The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of the correlation length, are explained by the fact that dependence L+L_0 with L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu} with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived; it demonstrates incorrectness of the conventional treatment of data for d=4 and d=5, but establishes the constructive procedure for such a treatment. Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with high precision data by Kramer et a