On the effect of boundary conditions on I–V characteristics of HTSC tunnel junctions

The pairing potential distribution over the thickness of superconducting CuO₂ layers in cuprate HTSCs is determined within the Ginzburg–Landau (GL) theory using the microscopic justification of this theory by Gor’kov. It is found that the pairing potential in them is significantly suppressed due to the effect of non-superconducting interlayers, which results in a decrease in the critical temperature of these superconductors. The temperature dependences of the effective energy gap and current–voltage (I–V) characteristic of tunnel junctions of the “break junction” type made of these superconductors are calculated.     

Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

A microscopic theory of superconductivity is considered in the framework of the Hubbard p-d model for the CuO₂ plane. The Dyson equation is derived in the nonintersecting diagram approximation using the projection technique for the matrix Green function of the Hubbard operator. The solution of the equation for the superconducting gap shows that interband transitions for Hubbard subbands lead to antiferromagnetic exchange pairing as in the t-J model, while intraband transitions additionally lead to spin-fluctuation pairing of the d-wave type. The calculated dependences of the superconducting transition temperature on the hole concentration and of the gap on the wave vector are in qualitative agreement with experiments.     

Influence of transport current and thermal fluctuations on the resistive properties of HTSC+CuO composites

Measurements of the temperature dependence of the electrical resistance R(T) below the superconducting transition temperature have been performed at different values of the transport current in HTSC+CuO composites modeling a network of weak S-I-S Josephson junctions (S—superconductor, I—insulator). It has been shown experimentally that the temperature dependence R(T) at different values of the transport current is adequately described by means of the mechanism of thermally activated phase slippage developed by Ambegaokar and Halperin for tunnel structures. Within the framework of this model we have numerically calculated the temperature dependence of the critical current J _c(T) as defined by various criteria. Qualitative agreement obtains between the measured and calculated temperature dependences J _c(T). Fiz. Tverd. Tela (St. Petersburg) 41, 969–974 (June 1999)     

Isotope effect in the model of strongly correlated electrons with the magnetic and phonon superconducting pairing mechanisms

Peculiarities of the temperature isotope effect in a BCS-type theory describing the exchange and phonon mechanisms of Cooper pairing in a system of strongly correlated electrons are considered. The electron-phonon interaction constant is determined from the fitting of the calculated value of the isotope-effect index to the observed value with the parameters of La_{2 − x} Sr _x CuO₄ obtained from ab initio calculations. The value of this constant indicates that the contribution from the traditional pairing mechanism to the superconducting state is of the same order of magnitude as the contribution from the magnetic mechanism.     

Effective interactions and the nature of Cooper instability of spin polarons in the 2D Kondo lattice

It has been shown that two-and three-center interactions arise in the strong-coupling regime for the 2D Kondo lattice; these interactions both induce and suppress the Cooper instability. It is important that, in contrast to the t-J* model, the three-center interactions promote the Cooper pairing and ensure the appearance of the superconducting phase with a high critical temperature T _c. The calculated concentration dependences of T _c agree well with the experimental data for the cuprate superconductors.     

HighT c superconductivity in the itinerant Ising model II. Spin triplet pairing

We study the spin triplet pairing superconducting states of the itinerant Ising model. The spin and spatial symmetries of the states are explored. We find that only a restricted set of spin symmetry states are allowed, while an infinite number of spatial symmetry states exist. The spin triplet pairing states can either be gapless or have finite energy gaps, but all spin triplet pairing states have the sameT _c .The free energies of spin triplet and spin singlet pairing states are calculated and compared.     

Electronic structure and superconductivity of κ-(BEDT-TTF)2X salts

We have analyzed the electronic structure and superconducting properties of layered crystals based on BEDT-TTF salts (hereafter denoted as ET), in which intramolecular interaction among electrons is important. For the case of realistic κ-packing of ET-molecules in a plane of ET₂ dimers we have calculated the electron density of states. Using the calculated electronic structure, we have analyzed the symmetry of the anisotropic superconducting pairing. The critical value of the effective attraction between electrons for formation of a bound pair in an empty lattice has been estimated. The relation between the nodes of the d-type order parameter on the anisotropic Fermi surface and superconducting properties of the condensate is discussed in the Bardeen-Cooper-Schrieffer (BCS) model. The results are in agreement with the known band parameters of the normal phase and measurements of the magnetic field penetration depth, heat capacity as a function of temperature in the low-temperature range, and NMR in κ-ET₂X superconducting salts. Zh. éksp. Teor. Fiz. 113, 715–733 (February 1998)     

Contribution of superconducting grains and grain boundaries to the magnetoresistance of ceramic YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> high-temperature superconductors in weak magnetic fields

The current-voltage characteristics of granular YBa₂Cu₃O_6.95 high-temperature superconductor samples have been measured at a temperature of 77.3 K in external transverse magnetic fields H _ext with a strength of up to H _ext ≈ 500 Oe for low transport current densities (0.1 A/cm² ≤ j ≤ 0.6 A/cm²). The current-voltage characteristics obtained have been used to construct dependences of the magnetoresistance ρ on the quantities j (ρ(j) _Hext=const) and H _ext(ρ(H _ext) _{j = const}). It has been revealed that the current and field dependences of the magnetoresistance exhibit anomalies at H _ext ≥ H _c1g , where H _c1g is the lower critical field of superconducting grains. A comparative analysis of the dependences ρ(j)H _{ext = const} and ρ(H _ext) _{j = const} has made it possible to develop concepts regarding the influence of the processes of redistribution of the magnetic field between grain boundaries and superconducting grains on the transport and galvanomagnetic properties of granular high-temperature superconductors. It has been established that the field dependences of the magnetoresistance exhibit specific features associated with the beginning of penetration of Josephson vortices into grain boundaries in the magnetic field H _c1J and with the breaking of a continuous chain of Josephson junctions in the magnetic field H _c2J .     

Stationary Josephson current in junctions involving d-wave superconductors with charge density waves: the temperature dependence and deviations from the law of corresponding states

Stationary Josephson current I _c in symmetric and non-symmetric junctions involving d-wave superconductors with charge density waves (CDWs) was calculated. It was found that, if CDWs are weak or absent, there exists an approximate proportionality between I _c and the product of superconducting order parameters in the electrodes (the law of corresponding states) for several factors affecting those quantities, such as the temperature, T, or one of the parameters characterizing the combined CDW superconducting phase (the degree of the Fermi surface dielectric gapping and the ratio between the parent superconducting and CDW order parameters). Otherwise, the dependences I _c (T) were shown to deviate from those in the absence of CDWs, and the relevant corresponding-state dependences from linearity, the deviations being especially strong at certain rotation angles of crystalline electodes with respect to the junction plane. Hence, making use of specially designed experimental setups and analyzing the I _c (T) and corresponding-state dependences, the existence of CDWs in cuprates and other non-conventional superconductors can be detected.     

Multiple andreev reflections spectroscopy of superconducting LiFeAs single crystals: Anisotropy and temperature behavior of the order parameters

The superconducting state of LiFeAs single crystals with the maximum critical temperature T _c ≈ 17 K in the 111 family has been studied in detail by multiple Andreev reflections (MAR) spectroscopy implemented by the break-junction technique. The three superconducting gaps, Δ_Γ = 5.1–6.5 meV, Δ_L = 3.8–4.8 meV, and Δ_S = 0.9–1.9 meV (at T ? T _c), as well as their temperature dependences, have been directly determined in a tunneling experiment with these samples. The anisotropy degrees of the order parameters in the k space have been estimated as <8, ～12, and ～20%, respectively. Andreev spectra have been fitted within the extended Kümmel-Gunsenheimer-Nikolsky model with allowance for anisotropy. The relative electron-boson coupling constants in LiFeAs have been determined by approximating the Δ(T) dependences by the system of the two-band Moskalenko and Suhl equations. It has been shown that the densities of states in bands forming Δ_Γ and Δ_L are approximately the same, intraband pairing dominates in this case, and the interband coupling constants are related as λ_ΓL ≈ λ_LΓ ? λ_SΓ, λ_SL.     

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.     

Interplay of superconductivity and magnetism in presence of inter sub-lattice effect in cuprates

In the present communication, we report a model Hamiltonian to study the interplay between the two long range orders of anti-ferromagnetism (AFM) and superconductivity (SC) in cuprate superconductors in presence of the intersite pairing effect. The BCS type but non-phonon pairing mechanism is considered among the electrons of two equivalent ‘Cu’ sites. The pairing among the electrons of two nearest neighbour non-equivalent ‘Cu’ sites is included in the Hamiltonian and its effect on the interplay of SC and AFM is investigated. The Hamiltonian is solved by the Green’s function method and the corresponding gap equations are calculated and solved selfconsistently. The influence of model parameters like AFM coupling (λ), SC couling (λ ₁) and the coupling (λ ₂) for intersite superconducting interactions on the gaps (SC and AFM) are studied numerically and the results are reported.     

Inelastic resonance tunneling in S-Sm-S tunnel structures

Inelastic resonance tunneling through junctions with an amorphous interlayer and superconducting electrodes is studied. The form of the current-voltage characteristic I(V) at low temperature and the temperature dependence of the conductance G(0) at low bias are calculated and are found to be much different from the analogous dependences of structures with normal electrodes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 159–163 (25 January 1997)     

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     

Raman scattering in YBa2Cu3O7 single crystals: Anisotropy in normal and superconductivity states

Precise temperature and polarization dependences of Raman spectra have been investigated for fully oxygenated twin-free YBa₂Cu₃O₇ single crystals. We have found a striking superconductivity-induced x−y anisotropy in the temperature behavior of the 340 cm⁻¹ line: the magnitudes of the softening and broadening are quite different in the xx-and yy-polarizations. This anisotropy suggests a contribution of the CuO-chain superconductivity with a pairing symmetry different from that for the CuO₂ plane, or indicates that the superconducting gap amplitudes are different in the k _x and k _y directions. The d+s gap symmetry is the only realistic symmetry in the case of Δ_x≠Δ_y. Fiz. Tverd. Tela (St. Petersburg) 40, 403–412 (March 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Mechanisms of dissipation in a Josephson medium based on a high-temperature superconductor in a magnetic field

This paper reports on the results of an investigation into the influence of magnetic fields (0–60 kOe) on the temperature dependences of the electrical resistance R(T) of the Y_3/4Lu_1/4Ba₂Cu₃O₇ + CuO composites. The structure of these composites is considered to be a network of tunnel-type Josephson junctions in which a nonsuperconducting component (CuO) forms boundaries (barriers) between high-temperature superconducting crystallites. The temperature dependence R(T) of the composites has two steps characteristic of granular superconductors: (i) an abrupt change in the electrical resistance at the critical temperature of high-temperature superconducting crystallites and (ii) a smooth transition to the superconducting state under the influence of the boundaries between the crystallites. The experimental dependences R(T) are analyzed within the Ambegaokar-Halperin model of thermal fluctuations in Josephson junctions and the flux creep model. An increase in the magnetic field leads to a crossover from the Ambegaokar-Halperin mechanism to the flux creep mechanism. The temperature dependences R(T) in the range of weak magnetic fields (from 0 to 10² Oe) are adequately described by the relationship following from the Ambegaokar-Halperin model. In the range of strong magnetic fields (from 10³ to 6 × 10⁴ Oe), the dissipation obeys the Arrhenius law R ～ exp(?U(H)/T)], which is characteristic of the flux creep model with a temperature-independent pinning energy U(H). The effective Josephson coupling energies and the pinning energies corresponding to the Ambegaokar-Halperin and flux creep mechanisms are determined.     

Theoretical analysis of tunneling experiments in the MgB<Subscript>2</Subscript> system

A detailed theoretical analysis of the experimental data obtained earlier in the studies of the tunneling spectra in the MgB₂ two-band superconducting system has been performed. It is shown that most these data are well described in the generalized two-band Bardeen-Cooper-Schrieffer theory with the constants of the intraband electron-phonon interaction that reasonably coincide with the ab initio calculation results. It is shown that the existence of specific collective excitation in this system induced by oscillations of the relative phase of two superconducting condensates (the Leggett mode) indicates the overestimation of the constants of the interband electron-phonon interaction in the ab initio calculations. The dependences of the superconducting gaps and the Leggett mode frequency on the temperature and the disorder degree in the Mg_{1 − x} Al _x B₂ system have been thoroughly studied.     

The order parameter for the superconducting phases of UPt3

I review the principal theories that have been proposed for the superconducting phases of UPt₃. The detailed H-T phase diagram places constraints on any theory for the multiple superconducting phases. Much attention has been given to the Ginzberg-Landau region of the phase diagram where the phase boundaries of three phases appear to meet at a tetracritical point. It has been argued that the existence of a tetracritical point for all field orientations eliminates the two-dimensional (2D) orbital representations coupled to a symmetry-breaking field (SBF) as a viable theory of these phases and favours either a theory based on two primary order parameters belonging to different irreducible representations that are accidentally degenerate, as described by Chen and Garg 1993, or a spin-triplet, orbital one-dimensional representation with non spin-orbit coupling in the pairing channel, as described by Machida and Ozaki 1991. I comment on the limitations of the models proposed so far for the superconducting phases of UPt₃. I also find that a theory in which the order parameter belongs to an orbital 2D representation coupled to a SBF is a viable model for the phases of UPt₃, based on the existing body of experimental data. Specifically, I show that the existing phase diagram (including an apparent tetracritical point for all field orientations), the anisotropy of the upper critical field over the full temperature range, the correlation between superconductivity and basal plane antiferromagnetism and the low-temperature power laws in the transport and thermodynamic properties can be explained qualitatively, and in many respects quantitatively, by an odd-parity E_2u order parameter with a pair spin projection of zero along the ?c axis. The coupling of an antiferromagnetic moment to the superconducting order parameter acts as a SBF which is responsible for the apparent tetracritical point, in addition to the zero-field double transition. The new results presented here for the E_2u representation are based on an analysis of the material parameters calculated within the Bardeen-Cooper-Schrieffer theory for the 2D representations, and a refinement of the SBF model given by Hess et al. (1989). I also discuss possible experiments to test the symmetry of the order parameter.     

Spin-dependent tunneling in junctions containing metals with charge density waves in a magnetic field

The dependences of the differential tunneling conductance G on the voltage V across a junction in an external magnetic field H are calculated for two types of junctions involving normal or superconducting metals with charge density waves (CDWs). Junctions of the first type are asymmetric CDW metal (CDWM)-insulator-ferromagnet junctions. The results of calculations for these junctions demonstrate that there occurs splitting between the components of the conductance G(V) corresponding to the tunneling of electrons with spins aligned with the magnetic field H and opposite to it, as is the case with junctions containing a superconducting electrode instead of the CDWM electrode. Junctions of the second type are junctions between two normal or superconducting CDWM electrodes. For junctions with at least one normal CDWM electrode and H ≠ 0, the conductance G(V) also exhibits spin splitting. The form of the conductance G(V) for tunnel junctions of both types depends on the phase of the order parameter of the charge density waves.     

On the mechanism of dissipation in the internal Josephson effect in layered superconductors at low temperatures

The current-voltage characteristics (IVCs) of a layered superconductor with singlet d pairing at low temperatures are calculated in the internal Josephson effect (IJE) regime. Coherent electron tunneling between layers is assumed. A finite resistance of the superconductor in the resistive state arises because of quasiparticle transitions through the superconducting gap near nodes. Because of charge effects the interaction of the Josephson junctions formed by the layers does not lead to substantial differences in the shapes of different branches of the IVCs. The model describes the basic qualitative features of the effect in high-temperature superconductors for voltages which are low compared with the amplitude of the superconducting gap. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 516–521 (25 October 1999)