Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

Ginzburg–Landau expansion in strongly disordered attractive Anderson–Hubbard model

We have studied disordering effects on the coefficients of Ginzburg–Landau expansion in powers of superconducting order parameter in the attractive Anderson–Hubbard model within the generalized DMFT+Σ approximation. We consider the wide region of attractive potentials U from the weak coupling region, where superconductivity is described by BCS model, to the strong coupling region, where the superconducting transition is related with Bose–Einstein condensation (ВЕС) of compact Cooper pairs formed at temperatures essentially larger than the temperature of superconducting transition, and a wide range of disorder—from weak to strong, where the system is in the vicinity of Anderson transition. In the case of semielliptic bare density of states, disorder’s influence upon the coefficients A and В of the square and the fourth power of the order parameter is universal for any value of electron correlation and is related only to the general disorder widening of the bare band (generalized Anderson theorem). Such universality is absent for the gradient term expansion coefficient C. In the usual theory of “dirty” superconductors, the С coefficient drops with the growth of disorder. In the limit of strong disorder in BCS limit, the coefficient С is very sensitive to the effects of Anderson localization, which lead to its further drop with disorder growth up to the region of the Anderson insulator. In the region of BCS–ВЕС crossover and in ВЕС limit, the coefficient С and all related physical properties are weakly dependent on disorder. In particular, this leads to relatively weak disorder dependence of both penetration depth and coherence lengths, as well as of related slope of the upper critical magnetic field at superconducting transition, in the region of very strong coupling.     

Normal phase and superconducting instability in the attractive Hubbard model: a DMFT(NRG) study

We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T _c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.     

Temperature Dependence of the Upper Critical Field in Disordered Hubbard Model with Attraction

We study disorder effects upon the temperature behavior of the upper critical magnetic field in an attractive Hubbard model within the generalized DMFT+Σ approach. We consider the wide range of attraction potentials U—from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose–Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder—from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of H_c2(T), especially at low temperatures. In BEC limit and in the region of BCS–BEC crossover H_c2(T), dependence becomes practically linear. Disordering also leads to the general growth of H_c2(T). In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of the transition point and to the increase of H_c2(T) in the low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of H_c2(T) at low temperatures, so that the H_c2(T) dependence becomes concave. In BCS–BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to T _c . However, in the low temperature region H_c2 (T may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase H_c2 (T = 0) also making H_c2(T) dependence concave.     

Attractive Hubbard model: Homogeneous Ginzburg–Landau expansion and disorder

We derive a Ginzburg–Landau (GL) expansion in the disordered attractive Hubbard model within the combined Nozieres–Schmitt-Rink and DMFT+Σ approximation. Restricting ourselves to the homogeneous expansion, we analyze the disorder dependence of GL expansion coefficients for a wide range of attractive potentials U, from the weak BCS coupling region to the strong-coupling limit, where superconductivity is described by Bose–Einstein condensation (BEC) of preformed Cooper pairs. We show that for the a semielliptic “bare” density of states of the conduction band, the disorder influence on the GL coefficients A and B before quadratic and quartic terms of the order parameter, as well as on the specific heat discontinuity at the superconducting transition, is of a universal nature at any strength of the attractive interaction and is related only to the general widening of the conduction band by disorder. In general, disorder growth increases the values of the coefficients A and B, leading either to a suppression of the specific heat discontinuity (in the weak-coupling limit), or to its significant growth (in the strong-coupling region). However, this behavior actually confirms the validity of the generalized Anderson theorem, because the disorder dependence of the superconducting transition temperature T_c, is also controlled only by disorder widening of the conduction band (density of states).     

Enhanced superconductivity by correlations between two Kondo impurities

We study the interplay between magnetic correlations of two Kondo impurities and superconducting singlet pairing. Performing a Schrieffer-Wolff transformation in the zero-bandwidth limit of the two-impurity Anderson model we obtain the Hamiltonian of two magnetic impurities and we add a superconducting term to the conduction electrons. The model allows us to study the effect of the magnetic correlation between the impurities on the superconducting ground state. At zero temperature, different superconducting ground states can be obtained depending on the magnitude of magnetic coupling between S₁ and S₂. For increasing coupling, the superconducting region is enlarged showing an interesting result: in the strong coupling limit, where the impurities are in a very strong ferromagnetic correlation state, half of the conduction electrons are decoupled from the local moments of the impurities and take advantage of the superconducting pairing lowering the ground state energy. On the contrary, when the coupling between S₁and S₂ decreases, the scenario of the two independent Kondo impurities in presence of superconductivity emerges and all the conduction electrons are involved in the pair breaking physics. At finite temperature, we obtain the phase diagram and we observe a region of parameters where the re-entrance phenomenon occurs.     

Der Einfluß von Spinfluktuationen auf die Sprungtemperatur eines Zweibandsupraleiters

The superconducting transition temperatureT _c of a two band superconductor in the presence of magnetic and nonmagnetic impurities as well as exchange fields is calculated using a new (8 × 8)-matrix formalism for the electron Green's function. In particular we investigate the influence of spin correlations onT _c near a magnetic phase transition. It is shown that in the strong interband phonon coupling limit the system behaves essentially as a one band superconductor. In the weak coupling limit we find typical deviations from one band theories.     

Enhancements of the superconducting transition temperature within the two-band model

The two-band model as introduced by Suhl, Matthias and Walker [Phys. Rev. Lett. 3, 552 (1959)] accounts for multiple energy bands in the vicinity of the Fermi energy which could contribute to electron pairing in superconducting systems. Here, extensions of this model are investigated wherein the effects of coupled superconducting order parameters with different symmetries and the presence of strong electron-lattice coupling on the superconducting transition temperature T_c are studied . Substantial enhancements of T_c are obtained from both effects.Received: 2 July 2003, Published online: 2 April 2004PACS: 74.20.-z Theories and models of superconducting state     

Effect of pressure on transition temperature of Rb3C60 fullerides

Electronic structure parameters play a significant role in fullerides leading to a superconducting state. Relevant electronic parameter as renormalized Coulomb repulsive parameter μ* and the attractive electron-phonon coupling strength λ are obtained within the dielectric function formalism for random phase approximation. As a first step, the superconducting transition temperature is deduced within the framework of McMillan approximation and strong coupling results using the widely spread phonon spectrum. In view of the importance of Coulomb screening for doped fullerides, the influence of pressure and volume on T _c are estimated to be within the range of experimental values. The isotope and dopant effects are also discussed. It is noticed that the high-T _c , the huge pressure effect, negative pressure derivative of T _c and positive volume derivative of T _c in alkali intercalated fullerides are dictated by the properties of Coulomb and on-ball-C₆₀ high energy intramolecular modes.     

Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper we find and present on diagrams in the coordinates of η=2t₁/t₀ (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters hatching out during the phase transition from the normal to the superconducting phase. The diagrams are obtained for an anisotropic two-dimensional superconducting system with a relatively wide partially-filled conduction band. We study a tight-binding model with an attractive nearest neighbor interaction with the amplitude V₁, and the on-site interaction (with the amplitude V₀) taken either as repulsive or attractive. The problem of the coexistence of the s-, p- and d-wave order parameters is addressed and solved for chosen values of the ratio V₀/V₁. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are localized on diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the BCS-type approximation.     

Competition mechanism between singlet and triplet superconductivity in the tight-binding model with anisotropic attractive potential

Based upon the tight-binding formalism a model of a high-T_c superconductor with isotropic and anisotropic attractive interactions is considered analytically. Symmetry facets of the group C_4v are included within a method of successive transformations of the reciprocal space. Complete sets of basis functions of C_4v irreducible representations are given. Plausible spin-singlet and spin-triplet superconducting states are classified with regard to the chosen basis functions. It is displayed that pairing interaction coefficients and the dispersion relation, which can be characterized by the parameter η= 2t₁/t₀, have a diverse and mutually competing influence on the value of the transition temperature. It is also shown that in the case of a nearly half-filled conduction band and an anisotropic pairing interaction the spin-singlet d-wave symmetry superconducting state is realized for small values of the parameter η, whereas in the opposite limit, for sufficiently large values, the spin-triplet p-wave symmetry superconducting state has to be formed. This result cannot be obtained within the Van Hove scenario or BCS-type approaches, where the p-wave symmetry superconducting state absolutely dominates. The specific heat jump and the isotope shift as functions of the parameter η are assessed and discussed for the d-wave symmetry singlet and the p-wave symmetry triplet states.     

Resistive transitions in Nb/Cu0.41Ni0.59/Nb trilayers

The superconducting phase transition in Nb/Cu_0.41Ni_0.59/Nb trilayers, with superconducting (S) Nb and ferromagnetic (F) Cu_0.41Ni_0.59, has been experimentally studied as a function of the F-layer thickness by measuring the temperature dependence of the electrical resistance R(T). It is shown that the shape and the width of the R(T) curves depends on the Cu_0.41Ni_0.59 thickness, in particular in the regime where π is the coupling between the S layers, which can be expected. To explain the data, we developed a qualitative model which makes the interconnection between the superconducting phase transition and the 0 to π transition in SFS structures are more evident. The text was submitted by the authors in English.     

Strong coupling superconductivity and prominent superconducting fluctuations in the new superconductor Bi4O4S3

Electric transport and scanning tunneling spectrum(STS)have been investigated on polycrystalline samples of the new superconductor Bi4O4S3.A weak insulating behavior in the resistive curve has been induced in the normal state when the superconductivity is suppressed by applying a magnetic field.Interestingly,a kink appears on the temperature dependence of resistivity near 4 K at all high magnetic fields above 1 T when the bulk superconductivity is completely suppressed.This kink associated with the upper critical field as well as the wide range of excess conductance at low fields and high temperatures is explained as the possible evidence of strong superconducting fluctuation.From the tunneling spectra,a superconducting gap of about 3 meV is frequently observed yielding a ratio of 2Δ/kB TC~16.6.This value is much larger than the one predicted by the BCS theory in the weak coupling regime(2Δ/kB TC~3.53),which suggests the strong coupling superconductivity in the present system.Furthermore,the gapped feature persists on the spectra until 14 K in the STS measurement,which suggests a prominent fluctuation region of superconductivity.Such a superconducting fluctuation can survive at very high magnetic fields,which are far beyond the critical fields for bulk superconductivity as inferred both from electric transport and tunneling measurements.     

Effects of strong coupling on pairing fluctuations in layered superconductors

The influence of short inelastic lifetimes due to strong coupling of fermionic quasiparticles to bosons on superconducting fluctuation effects aboveT _c is calculated. Considering a strong-coupling model for a layered superconducting metal, it is shown that pairing fluctuation corrections to the spin-lattice relaxation rate in weak coupling and very strong coupling are qualitatively different if the pairing fluctuation spectrum has s-wave symmetry. For weak coupling the corrections are positive, whereas for very strong coupling γ = 2? d ω α² F(ω)/ω > 2 the corrections are negative. In contrast, the Pauli spin susceptibility is insensitive to strong-coupling corrections.     

Superconductivity and normal state resistivity of Ba0.6K0.4BiO3: an optical phonon approach

We discuss the nature of the pairing mechanism and the physical properties associated with the normal as well as the superconducting state of cubic perovskites Ba_0.6K_0.4BiO₃using the strong coupling theory. An interaction potential which includes the Coulomb, electron–optical phonon and electron–plasmon interactions is developed to elucidate the superconducting state. A model dielectric function is constructed with these interactions fulfilling thef-sum rule. The screening parameter (μ^* = 0.26) infers the poor screening of charge carriers. The electron–optical phonon strength (λ) estimated as 0.98 is consistent with an attractive electron–electron interaction and supports the moderate to strong coupling theory. The superconducting transition temperature of Ba_0.6K_0.4BiO₃is then estimated as 32 K. Ziman's formula of resistivity is employed to analyse and compare this with the temperature-dependent resistivity of a single crystal. The estimated contribution from the electron–optical phonon together with the residual resistivity clearly infers a difference when a comparison is made with experimental data. The subtracted data infer a quadratic temperature dependence in the temperature domain (30 ≤ T ≤ 200 K). The quadratic temperature dependence of ρ [ = ρ_exp − (ρ₀ + ρ_e–ph)] is understood in terms of 3D electron–electron inelastic scattering. The presence of these el–el and el–ph interactions allows a coherent interpretation of the physical properties. Analysis reveals that a moderate to strong coupling exists in the Ba_0.6K_0.4BiO₃system and the coupling of electrons with the high-energy optical phonons of the oxygen breathing mode will be a reason for superconductivity. The implications of the above analysis are discussed.     

典型颗粒超导体YBa2Cu3O7/V2O5中临界电流随温度变化的特性

通过制备（ＹＢａ₂Ｃｕ₃Ｏ₇）_1-x（Ｖ₂Ｏ₅）_x（０≤ｘ≤０．１５）复合材料，获得了一系列典型的弱连接的颗粒超导体，其中以ｄＲ／ｄＴ－Ｔ关系中呈现出双峰转变为主要特征。第一峰代表晶粒的超导转变，第二峰代表颗粒系统超导长程序的形成。对于具有双峰转变的样品，其临界电流密度一致地符合ｉ_c～（１－ｔ）^ｎ，ｎ＝１．６．这一行为与三维Ｊｏｓｅｐｈｓｏｎ结网络系统的渗流行为相一致；对于不具有双峰转变的系统，临界电流密度随温度的变化尽管也可以用ｊ_c～（１－ｔ）^ｎ描述，但是幂指数ｎ明显地大于１．６，且随样品的不同而离散地分布。本文还对产生这种离散的原因进行探索和分析。 关键词：     

Studies of chemical diffusion in La1-X SrXCoO3-δ

Recent investigations of superconductivity in carbon nanotubes have shown that a single-wall zig-zag nanotube can become superconducting at around 15?K. Theoretical studies of superconductivity in nanotubes using the traditional phonon exchange model, however, give a superconducting transition temperature T _c less than 1?K. To explain the observed higher critical temperature we explore the possibility of the plasmon exchange mechanism for superconductivity in nanotubes. We first calculate the effective interaction between electrons in a nanotube mediated by plasmon exchange and show that this interaction can become attractive. Using this attractive interaction in the modified Eliashberg theory for strong coupling superconductors, we then calculate the critical temperature T _c in a single-wall nanotube. Our theoretical results can explain the observed T _c in a single-wall nanotube. In particular, we find that T _c is sensitively dependent on the dielectric constant of the medium, the effective mass of the electrons and the radius of the nanotube. We then consider superconductivity in a bundle of single-wall nanotubes and find that bundling of nanotubes does not change the critical temperature significantly. Going beyond carbon nanotubes we show that in a metallic hollow nanowire T _c has some sort of oscillatory behaviour as a function of the surface number density of electrons.     

Mott-Hubbard transition in a magnetic field

We study the density of states (DOS) as a function of the interaction U in the half-filled simplified Hubbard model in a magnetic field. This model is considered on the Bethe lattice in the limit of high dimensions. We show that the DOS can be calculated exactly, and that many of its properties have an astonishingly simple form. In particular, the DOS can be investigated explicitly in the limits of weak and strong coupling and near the metal-insulator transition. E.g., we find an explicit result for the critical value U_c, at which the metal-insulator transition occurs, as a function of the magnetization. The relation between the magnetization and the magnetic field is calculated numerically. An important result is that the metal-insulator transition, occurring in the model with B = 0, is continuously connected to the metal-insulator transition in the subspace of single spin flips.     

Role of anisotropy of the coupling constant in a superconductor model with singularities near the Fermi surface

The role of anisotropy of the coupling constant in the influence of nonmagnetic impurities on the behavior of the superconducting transition temperature T _c is investigated in the high-temperature superconductor (HTSC) model, where high values of T _c result from an increase in the density of states near the Fermi surface. It is shown that this model is more sensitive to impurities than the BCS model; Anderson compensation does not occur in the HTSC model, even for identical distributions of the densities of states in the superconducting and impurity channels, and the impurity contributions are no longer linear with respect to the impurity concentration in the vicinity of T _c. Anisotropy of the superconducting gap Δ and the possibility of its disappearance at certain points on the Fermi surface due to various types of pairing are manifested in the stability of the superconducting phase against the influence of impurities. Fiz. Tverd. Tela (St. Petersburg) 39, 1940–1942 (November 1997)