Solutions of Eliashberg equations for an electron-phonon coupling with a cutoff

In this paper we discuss the Eliashberg equations for the case of an electron-phonon coupling with an energy cutoff. This cutoff is imposed either for the energy difference by means of a strip function, or for both energies, with a Cooper-like expression. The strip function cutoff requires explicit calculation of not only the frequency renormalization functionZ but also the energy renormalizationX. The physical origin of such cutoffs might lie in the very strong electron-electron interaction which seems typical for highT _c superconductivity. If such cutoffs are admitted, the hypothesis thatT _c is caused at least in part by a strong electron-phonon interaction can be reconsidered. We find that the combination of strong coupling and low-energy cutoff could produce highT _c with only small isotope effect and with little damping or pulling of the phonon modes. Correlation with other physical properties, such as specific heat, is reexamined in view to estimate the coupling constant . Some objections to the model using strong electron phonon interaction are removed and better agreement with observed properties is obtained     

The ground state and the thermodynamics of an extended BCS model of superconductivity

The thermodynamics of an extended BCS model of superconductivity is investigated. A physical system is described by a Hamiltonian containing the BCS interaction and an attractive four-fermion interaction. The four-fermion potential is caused by attractions between Cooper pairs mediated by the phonon field. The weakness of this potential allows the use of perturbation theory. The perturbation expansion was restricted to the first order because in the ground state the second order terms are not larger than 0.5 percent of first order correction for parameters used for calculations. The BCS Hamiltonian is an unperturbed one. The ground state and the thermal properties are examined. As a result the jump in the specific heat is higher than that in the BCS case. Moreover, the squared critical field is larger than the corresponding one in the BCS theory. Additionally, we show connections with the Bogolyubov's mean field approach used earlier in order to investigate general physical consequences of the model.     

Investigate the effect of anisotropic order parameter on the specific heat of anisotropic two-band superconductors

The effect of anisotropic order parameter on the specific heat of anisotropic two-band superconductors in BCS weak-coupling limit is investigated. An analytical specific heat jump and the numerical specific heat are shown by using anisotropic order parameters, and the electron–phonon interaction and non-electron–phonon interaction. The two models of anisotropic order parameters are used for numerical calculation that we find little effect on the numerical results. The specific heat jump of MgB₂, Lu₂Fe₃Si₅ and Nb₃Sn superconductors can fit well with both of them. By comparing the experimental data with overall range of temperature, the best fit is Nb₃Sn, MgB₂, and Lu₂Fe₃Si₅ superconductors.     

Universal scaling in BCS superconductivity in three dimensions in non-s waves

The solutions of a renormalized BCS equation are studied in three space dimensions in s, p and d waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length and a large critical temperature, , appropriate for some high- materials. The BCS gap, , and specific heat as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below in p and d waves. Received: 18 July 1997 / Revised: 8 September 1997 / Accepted: 29 September 1997     

Third-order phase transition and superconductivity in thin films

We have found a new mean field solution in the BCS theory of superconductivity. This unconventional solution indicates the existence of superconducting phase transitions of third order in thin films, or in bulk matter with a layered structure. The critical temperature increases with decreasing thickness of the layer, and does not exhibit the isotope effect. The electronic specific heat is a continuous function of temperature with a discontinuity in its derivative.     

Interaction and localization effects in two-dimensional film of superconductor at T > Tc

The magnetic field and temperature dependence of the resistance of thin Al films have been investigated at T > T_c (T_c - superconducting transition temperature). The results are explained on the basis of localization and electron-electron interaction theory in two-dimensional disordered systems. The temperature dependence of inelastic scattering time and interaction constant for such films is found.     

Quantum HeisenbergS=1/2 spin glass with ferromagnetic coupling and random Dzyaloshinskii-Moriya interactions

By means of the generalized static replica symmetric spin glass theory, a quantum HeisenbergS=1/2 spin glass model with the infinite-ranged random Dzyaloshinskii-Moriya (DM) interaction and ferromagnetic coupling is investigated. The dependence of entropy, specific heat, susceptibility and the corresponding order parameters on temperature is studied numerically for different ferromagnetic interactions and fixed anisotropy. Two spin glass phases has been found including transverse and mixed spin glass phases. It has been shown that the local susceptibility exhibits double-cusp features for different ferromagnetic coupling (J ₀). Phase transition poins are found in the specific heat-temperature plane at various ferromagnetic coupling values. Additionally, the dependence of the spontaneous moment on temperature is calculated.     

A microscopic model for the intrinsic Josephson tunneling in high- superconductors

A quantitative analysis of a microscopic model for the intrinsic Josephson effect in high-temperature superconductors based on interlayer tunneling is presented both within a mean-field BCS evaluation and a numerically essentially exact Quantum Monte-Carlo study. The pairing correlations in the CuO₂-planes are modelled by a 2D Hubbard model with attractive interaction, a model which accounts well for some of the observed features such as the short planar coherence length. The stack of Hubbard planes is arranged on a torus, which is threaded by a magnetic flux. The current perpendicular to the planes is calculated as a function of applied flux (i.e. the phase), and - after careful elimination of finite-size effects due to single-particle tunneling - found to display a sinusoidal field dependence in accordance with interlayer Josephson tunneling. Studies of the temperature dependence of the supercurrent reveal at best a mild elevation of the Josephson transition temperature compared to the planar Kosterlitz-Thouless temperature. These and other results on the dependence of the model parameters are compared with a standard BCS evaluation. Received: 24 February 1998 / Revised: 28 April 1998 / Accepted: 23 June 1998     

Double phase transition in highT c superconductors

Experiments have revealed that some samples of high-T _c ceramic superconductors possess a double peak structure in the specific heat. We shall show that within a BCS formalism it is possible to explain this double peak as a pure superconduction phenomenon. An important feature of the model is the onsite pairing interaction term which turns out to determine the difference between the two peaks.     

Superconductivity in weakly correlated electron systems

We study the influence of the short-ranged Hubbard correlation U between the conduction electrons on the Cooper pair formation in normal (s-wave) superconductors. The Coulomb correlation is considered within the standard second order perturbation theory, which becomes exact in the weak coupling limit but goes beyond the simple Hartree-Fock treatment by yielding a finite lifetime of the quasiparticles at finite temperature. An attractive pairing interaction V, which may be mediated by the standard electron-phonon mechanism, is considered between nearest neighbor sites. A critical value for the attractive interaction is required to obtain a superconducting state. For finite temperature a gapless superconductivity is obtained due to the finite lifetime of the quasiparticles, i.e. the Coulomb correlation has a pair-breaking influence. The energy gap and depend very sensitively on U, V and band filling n and develop a maximum away from half filling as function of n. The ratio varies with n, being higher than the BCS value near half filling and reaching the BCS value for lower n. Received 17 February 1999     

Some parameters of superconductors with an extreme singularity in the density of state: (s+d) model

We study some parameters of superconductors with δ-function type singularities in the electronic density of states (DOS), exhibiting (s+d)-wave symmetry of the order parameter. Starting with a pure s-wave pairing potential V_s, the critical temperature T_c at first slightly increases with increasing the d-wave interaction potential V_d, being determined by this interaction only for stronger V_d values. The ratio R=2|Δ(0)|/k_BT_c of the mean value of the zero temperature energy gap |Δ(0)| to T_c increases with increasing V_d, reaching a maximum which depends on the mixing interaction term. The maximum values of R are comparable with very high values obtained in some gap measurements. The jump in the specific heat at critical temperature is by a factor 2.4 higher for the extreme singularity of pure s-wave symmetry, as compared with the BCS theory with constant DOS. Such higher values of the jump are in agreement with the experimentally observed values, as well as with the calculations determined by extended saddle points in the electronic bands. By switching the d-wave channel, the value of the jump decreases. The results show the usefulness of calculations with δ-type singularities as a limiting case of very strong singularities in the DOS.     

Superconductivity in amorphous thin films of tin–copper

The properties of the superconducting state in the amorphous Sn_1?xCu_x thin films were characterized. The concentration of copper changes in the range from 0.08 to 0.41. The calculations were conducted in the framework of the strong-coupling formalism, wherein the Eliashberg functions determined in the tunnel experiment were used. The value of the Coulomb pseudopotential equal to 0.1 was adopted. It will be shown that the critical temperature (T_C) decreases from 7 to 3.9 K. The ratio, R_Δ = 2Δ(0)/k_BT_C, differs from the BCS value: R_Δ ∈ <4.4, 3.95>, where Δ(0) represents the order parameter. Similarly behave the ratios: R_C = ΔC(T_C)/C^N(T_C) ∈ <2.2, 1.75> and R_H = T_CC^N(T_C)/H²_C(0) ∈ <0.141, 0.154>. The parameter ΔC(T_C) is the specific heat jump, C^N(T_C) denotes the specific heat of the normal state and H_C(0) is the thermodynamic critical field.     

Another approach to mechanism of ferromagnetic superconductor UGe2

We study the ferromagnetic superconductor of UGe₂ applying our previous model [Phys. Rev. B 61 (2000), 4289] for the high transition temperature superconductivity (HTSC). The Coulomb interaction for triplet electron pairs is reduced by a difference of the exchange interaction. In the case of UGe₂ including other heavy fermion superconductors, coexistence of triplet superconductivity and ferromagnetism is possible in the case of our scheme. We also investigate the pressure-dependence of Curie temperature, T_c and superconducting temperature, T_sc.     

Role of surface Cooper pair interactions on critical temperature of ultra thin film superconductors

The superconductivity mechanism of Pb thin film on a Si substrate in the weak interaction regime is investigated. A discrete Fermi surface is constructed depend on the film thickness and electron density and crystallographic orientation. We consider two types of Cooper pair interactions, Cooper pair interaction at thin film surfaces and Cooper pair in the thin film volume. We have chosen the surface Cooper pair interaction, of ultra thin films superconductor proportional to the inverse of thin film thickness, while the volume Cooper pair interaction has been considered as a constant. By these assumptions, we have found oscillation feature of critical temperature Tc and energy gap Δ in terms of thin film thickness similar to the experimental results for Pb/Si(111) thin film superconductor. However, by increasing number of Pb layers, the thin film Tc goes to bulk Tc. In contrast to the previous claimed constant value for the Δb(T=0)/kBTc in bulk, we have found oscillation of this parameter in terms of thin film thickness similar to the Tc oscillation.     

Low temperature electrical conductivity and magnetoconductivity of Fe39Ni39Mo4Si6B12 and Co58Ni10Fe5Si11B16 metallic glass alloys

A detailed study on the weak localization phenomenon vis-a-vis electron-electron interaction effects in magnetic metallic glasses has been carried out. We measured the electrical conductivity and magnetoconductivity within the temperature range 1.8≤T≤300K. A maximum on the conductivity versus temperature curve exists atT=T _m. The conductivity was observed to follow aT ^1/2 law forT<T _m andT ² law forT>T _m. Magnetoconductivity data of these alloys indicate the prominence of electron-electron interaction at low temperatures. The authors have determined the inelastic scattering field and spin-orbit scattering field from the magnetoconductivity data. The inelastic scattering field obeys aT ^p law (p=2) at low temperatures.     

Nonextensive quantum method for itinerant-electron ferromagnetism: Factorization approach

Magnetic and thermodynamical properties of itinerant-electron (metallic) ferromagnets described by the Hubbard model have been discussed with the use of the generalized Fermi-Dirac (GFD) distribution for nonextensive quantum systems. We have derived the GFD distribution within the superstatistics, which is equivalent to that obtained by the maximum-entropy method to the Tsallis entropy with the factorization approximation. By using the Hartree-Fock approximation to the electron-electron interaction in the Hubbard model, we have calculated magnetic moment, energy, specific heat and Curie-Weiss-type spin susceptibility, as functions of the temperature and entropic index q expressing the degree of the nonextensivity: q=1.0 corresponds to the Boltzmann-Gibbs statistics. It has been shown that by increasing the nonextensivity of |q−1|, the temperature dependence of magnetic moment becomes more significant and the low-temperature electronic specific heat is very much increased. This is attributed to enlarged Stoner excitations in the GFD distribution, which is elucidated by an analysis with the use of the generalized Sommerfeld expansion. We discuss the difference and similarity between the effects of the nonextensivity on metallic and insulating ferromagnets.     

Theory of high temperature superconductivity in YBa2Cu3O7_δ

A theory of high temperature superconductivity in YBa₂Cu₃O₇__δ compound has been developed on the basis of the momentum pairing of electrons through the relativistic Darwin interaction. The transport behaviour of electrons is explained in terms of a mechanism of correlated electron transfer arising from the electron-phonon coupling. A model Hamiltonian has been developed to describe the superconducting properties of the system. This gives an energy gap which is higher than the BCS value. Attempts have been made to explain the absence of isotope effect, the linear dependence of specific heat, the presence of larger temperature-independent paramagnetism in the normal phase and the softening of some of the optic phonon modes observed in this system.     

Electronic state on the surface in the strongly correlated electron systems

In order to clarify the tunneling spectroscopy in high-T_c cuprates, we study electronic state of the surface in the strongly correlated electron systems. First, we obtain Green's function of strongly correlated normal bulk system using the fluctuation exchange (FLEX) approximation. Next, we insert infinite potential into the bulk system and obtain Green's function of surface. We find that the density of states (DOS) in strongly correlated bulk systems are different from that on the surface, and the difference decreases as the magnitude of Coulomb interaction (U) increases.     

d-Wave superconductivity via buckling-like phonon mode

We follow the classic strong-coupling theory of superconductivity through electron-phonon interaction with a buckling-like phonon mode. We find a nonzero d-wave order parameter in the sense of the Eliashberg theory. We derive a zero temperature gap Δ(0,π) at the gap edge versus the electron-phonon coupling strength g² relation. We find that large enough value for Δ(0,π) as compared to those of high-T_c superconductors cannot be realized in the electron-buckling-like-phonon coupling on the CuO₂ planes.     

BCS theory of driven superconductivity

We study the impact of a time-dependent external driving of the lattice phonons in a minimal model of a BCS superconductor. Upon evaluating the driving-induced vertex corrections of the phonon-mediated electron-electron interaction, we show that parametric phonon driving can be used to elevate the critical temperature T_c, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of T_c. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify T_c. Our results hold universally for the large class of normal BCS superconductors.