Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ_corr. It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T _c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T>T _c, superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ_corr; in particular, the range of existence for drops becomes narrower and vanishes as ξ_corr → 0, but for finite values of ξ_corr, complete self-averaging does not take place.     

Spectral density and density of states in a superconductor in an exactly solvable model of a pseudogap state

A simple, exactly solvable model of a pseudogap state induced by fluctuations of dielectric short-range order is used to study the peculiarities of the electronic spectral density and density of states of a superconductor in the model of the Fermi surface with hot patches. The problem is considered for arbitrary values of the short-range order correlation length ξ_corr. It is shown that the absence of self-averaging of the superconducting order parameter over the random field of dielectric fluctuations causes the spectral density and density of states to change significantly. The superconducting character of these quantities persists in a wide temperature range above the temperature T _c of the superconducting transition, which is uniform over the whole sample.     

“Magnetodipole” self-organization of charge carriers in high-T c superconductors and the kinetics of phase transition

A phenomenological model describing “magnetodipole” self-organization of charge carriers (the formation of so-called stripe-structures and the energy gap in the spectrum of states) was suggested to interpret the data of nonstationary nonlinear spectroscopy of high-T _c superconductors. It was shown that, after rapidly heating a superconducting sample, the kinetics of the succeeding phase transition depended on initial temperature T. At small “overheatings” T*<T<T _m x≈(1.4?1.5)T* (T _c and T*≈T _c are the temperatures of the transition to the superconducting state and the formation of stripe-structures) and the optimal level of doping, the decay of stripe-structures (and of the gap in the spectrum of states) occurred at a low rate (in times above to 10^?9 s) in spite of the virtually instantaneous disappearance of superconductivity.     

Surface electromagnetic waves at a superconductor-dielectric interface

This paper reports on the results of investigating the frequency dependence, the structure, and the polarization-and energy-related characteristics of surface electromagnetic waves propagating along a superconductor-dielectric interface. An expression for the complex permittivity of a superconductor is derived in the approximation of a two-component plasma containing “normal” and “superconducting” electrons. Basic relations are obtained in the general case at temperatures T≤T _c (where T _c is the critical temperature) and in the limiting case at T?T _c, when the contribution from normal electrons to the permittivity of the superconductor can be disregarded.     

Phase transitions and vortex structure evolution in two-level high-temperature granular superconductor YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 – δ</Subscript> under temperature and magnetic field

Temperature dependences of the resistivity ρ(T) of samples of granular high-temperature superconductor YBa₂Cu₃O_{7 – δ} are measured at various transverse external magnetic fields at 0 < H _ext < 1900 Оe in the temperature range from the upper Josephson critical temperature of “weak bonds” T _c2J to temperatures slightly exceeding the superconducting transition temperature T _c . Based on the data obtained, the behavior of the field dependences of the critical temperatures of superconducting grains and “weak bonds,” and temperature and field dependences of the magnetic contribution to the resistivity \(\left[ {\Delta \rho \left( {T,H} \right) = \rho {{\left( T \right)}_{{H_{ext}} = const}} - \rho {{\left( T \right)}_{{H_{ext}} = 0}}} \right]\). It is shown that the behavior of the magnetic contribution to the resistivity Δρ along the line of the phase transition related to the onset of the magnetic field penetration in the form of Abrikosov vortices into the subsystem of superconducting grains T _c1g (H _ext) is anomalous. The concepts on the magnetic flux redistribution between both subsystems of two-level HTSC near in the vicinity of T _c1g : the Josephson vortex decreases, and the Abrikosov vortex density increases.     

Vertex functions as a factor of enhancing electron-electron attraction in d-wave channel of the “Coulomb” superconductivity mechanism

It is shown that many-particle Coulomb correlations described by Coulomb vertex functions Γ_c in layered high-T _c superconducting metal oxide cuprates substantially enhance effective electron-electron attraction in the d-wave Cooper-pairing channel. This attraction is due to the combined action of a strong in-layer anisotropy of the quasi-two-dimensional electronic spectrum and the suppression of a screened Coulomb repulsion for small transferred momenta in small-angle charge-carrier scattering from long-wavelength charge-density fluctuations. Such a “Coulomb” mechanism of anisotropic Cooper pairing may provide high superconducting transition critical temperatures (T _c ≥100 K) for optimum-doped cuprates.     

Mechanism of carrier generation and the origin of the pseudogap and 60 K phases in YBCO

The mechanism of hole carrier generation is considered in the framework of a model assuming the formation of negative U centers (NUCs) in HTSC materials under doping. The calculated dependences of carrier concentration on the doping level and temperature are in quantitative agreement with experiment. An explanation is proposed for the pseudogap and 60 K phases in YBa₂Cu₃O_6+δ. It is assumed that a pseudogap is of superconducting origin and arises at temperature T* > T_c∞ > T_c in small nonpercolating clusters as a result of strong fluctuations in the occupancy of NUCs (T_c∞ and T_c are the superconducting transition temperatures of an infinitely large and finite NUC clusters, respectively). The T*(δ) and T_c(δ) dependences calculated for YBa₂Cu₃O_6+δ correlate with experimental dependences. In accordance with the model, the region between T*(δ) and T_c(δ) is the range of fluctuations in which finite nonpercolation clusters fluctuate between the superconducting and normal states due to NUC occupancy fluctuations.     

Effect of nuclear irradiation on the superconducting transition temperatures of A-15 materials

A mechanism for the degradation of superconducting transition temperatures T_c by high energy nuclear irradiation in A-15 materials is proposed. The radiation is supposed to produce small “disordered” regions having a very low T_c, in a matrix having the original T_c of the material. The composite system has a well defined but lower T_c due to the proximity effect of the “disordered” regions.     

Dynamical properties of superconducting nanowires

The dynamical properties of thin superconducting wires (nanowires) are studied using numerical simulations based on a one-dimensional time-dependent Ginzburg-Landau equation, which is modified by introducing an order parameter u characterizing the “purity” of the superconductor material. It is established that relatively long nanowires (with lengths much greater than the coherence length) made of a “pure” superconductor (u > 1) are characterized by two critical current density values: j _c1 and j _c2. For j < j _c1, the total current is entirely superconducting, whereas for j > j _c2, the current is purely normal. In the intermediate region of current densities, j _c1 < j < j _c2, the total current contains both superconducting and normal components (mixed state) and the nanowire exhibits the generation of high-frequency electromagnetic waves. The current-voltage characteristics are constructed and the radiation spectrum is obtained. The properties of short superconducting nanowires (with lengths on the order of the coherence length) coincide with those of the Josephson junction. In the case of an “impure” superconductor (u < 1), the nanowire is characterized by a single critical current density.     

Spin-orbit effects in carbon nanotubes – Analytical results

We report a study of the normal and superconducting state properties of the Ti _x V_1?x alloys for x = 0.4, 0.6, 0.7 and 0.8 with the help of dc magnetization, electrical resistivity and heat capacity measurements along with the electronic structure calculation. The superconducting transition temperature T _c of these alloys is higher than that of elemental Ti and is also higher than elemental V for x ≤ 0.7. The roles of electron density of states, electron-phonon coupling and spin fluctuations in the normal and superconducting state properties of these alloys have been investigated in detail. The experimentally observed value of T _c is found to be considerably lower than that estimated on the basis of electron density of states and electron-phonon coupling in the x = 0.4, 0.6 and 0.7 alloys. There is some evidence as well for the preformed Cooper pair in all these Ti-V alloys in the temperature regime well above T _c . Similar to x = 0.6 [Md. Matin, L.S. Sharath Chandra, R.K. Meena, M.K. Chattopadhyay, A.K. Sinha, M.N. Singh, S.B. Roy, Physica B 436, 20 (2014)], the normal state properties of the x = 0.4 alloy showed the signature of the presence of spin fluctuations. The difference between the experimentally observed T _c and that estimated by considering electron density of states and electron-phonon coupling in the x = 0.4, 0.6 and 0.7 alloys is attributed to the possible influence of these spin fluctuations. We show that the non-monotonous variation of T _c as a function of x in the Ti _x V_1?x alloys is due to the combined effects of the electron-phonon coupling and the spin fluctuations.     

Coulomb repulsion-induced hyperbolic pairing as a mechanism of high-T c superconductivity

The hyperbolic metric of the dispersion law (the effective mass tensor components of carriers are opposite in sign) in the vicinity of the Fermi contour in high-T _c superconducting cuprates in the case of repulsive interaction gives rise to a superconducting state characterized by the condensate of pairs with a large total momentum (hyperbolic pairing). The gain in the energy of the superconducting state over the normal state is due to the fact that a change in the kinetic energy of pairs (because of the negative light component of the effective mass) dominates over the change in the potential energy (corresponding to energy loss). The shift of the chemical potential upon the transition to the superconducting phase is substantial in this case. With increasing repulsive interaction, the superconducting gap δ_K increases and the resulting gain in energy changes to an energy loss at a certain critical value of the repulsive potential. The low temperature T _c of the superconducting transition and the large value of δ _K in this region of potential values are the reasons for the high value of the 2δ_K/T _c ratio and for the developed quantum fluctuations that are observed in underdoped cuprate superconductors.     

Metastable phases in YBCO films created by short-term annealings

The effect of short-term low-temperature annealing in air and in vacuum on the properties of HTSC films of YBCO is studied. It is shown that, under certain conditions of preparation of initial samples, a transition from the HTSC phase with the superconducting transition temperature T_c=90 K to a phase with T_c=60 K occurs without a noticeable change in the oxygen content. It is found that, as a result of short-term annealings, a transition from the HTSC phase with T_c=60 K to the phase with T_c=90 K can occur only through the vacuum annealing stage, which converts the sample into the superconducting state. Short-term annealings lead to multiple reversible “switching” of the films from one phase to another. The obtained results are of practical interest, since the proposed method can be used to quickly obtain superconducting YBCO films in various phase states. It is shown, in addition, that the annealing procedure makes it possible not only to increase the oxygen concentration but also to produce a structural rearrangement of a YBCO film.     

Stripes, electron fractionalization, and ARPES

Although structurally the high temperature superconductors are quasi-two-dimensional, there is both theoretical and experimental evidence of a substantial range of temperatures in which ‘stripe’ correlations make the electronic structure locally quasi-one-dimensional. We consider an array of Josephson coupled, spin gapped one dimensional electron gases as a model of the high temperature superconductors. For temperatures above T_c, this system exhibits electron fractionalization, yielding a single particle spectral response which is sharp as a function of momentum, but broad as a function of energy. For temperatures below the spin gap but above T_c, there are enhanced one-dimensional superconducting fluctuations and pseudogap phenomena. Pair tunneling induces a crossover to three-dimensional physics as T_c is approached. Below T_c, solitons are confined in multiplets with quantum numbers which are simply related to the electron, and a coherent piece of the single particle spectral function appears. The weight of this coherent piece vanishes in the neighborhood of T_c in proportion to a positive power of the interchain superfluid density. This behavior is highly reminiscent of recent ARPES measurements on the high temperature superconductors.     

Fluctuations in superconductors belowT c

Thermal fluctuations of the order parameter in the superconducting state are investigated, particularly near the transition temperature, using the time dependent Ginzburg-Landau theory. These fluctuations give rise to a contribution of the dynamical conductivity, which strongly increases as the temperature is raised towardsT _c , in contrast to the temperature dependence of the electromagnetic response due to the static order parameter. At the transition temperature this contribution joins continuously to the extra response (conductivity, susceptibility) which has been calculated and observed in the temperature region aboveT _c , where it represents the onset of superconductivity in the normal state. Particularly the dynamical conductivity due to fluctuations is calculated and discussed for bulk material, thin films and thin wires belowT _c . The temperature and frequency dependence should be observable in microwave experiments.     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

Spin resonance of Gd in LaOs2

Spin resonance has been observed in the normal and superconducting state of Gd in the C-15 superconductor LaOs₂. The electron-impurity relaxation rate allows the prediction of the Abrikosov-Gorkov depression of T_c. A field dependent “g-shift” is observed in the superconducting state.     

Magnetic susceptibility of fine crystalline high-temperature YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.93</Subscript> superconductors. The role of nanoscale structural disordering

Static magnetic susceptibility χ(T) in the normal state (T_c ≤ T ≤ 400 K) and specific heat C(T) near temperature T_c of the transition to the superconducting state are experimentally studied for a series of fine crystalline samples of high-temperature YBa₂Cu₃O_y superconductor, having y and T_c close to optimal but differing in the degree of nanoscale structural disordering. It is shown that under the influence of structural disordering, there is enhancement of anomalous pseudogap behavior of the studied characteristics and a significant increase in the width of the pseudogap.     

Superconducting properties of tin embedded in nanometer-sized pores of glass

The electrical resistance of tin embedded from a melt in porous glasses with an average pore diameter of ??7 nm has been investigated at low temperatures in magnetic fields up to 2 T. The temperatures of the transition to the superconducting state for nanocrystalline tin have been determined in magnetic fields of 0, 0.3, 0.5, 1.0, 1.5, and 2.0 T. It has been found that the temperature and magnetic-field dependences of the electrical resistance of the nanocomposite under investigation exhibit two transitions to the superconducting state. The nature of the double superconducting transitions has been discussed. The H _c -T _c phase diagram has been constructed using the entire set of data on the magnetic-field and temperature dependences of the electrical resistance of nanostructured tin. This phase diagram indicates that the upper critical magnetic field H _c2(0) for nanostructured tin is almost two orders of magnitude higher than the corresponding field for bulk tin.     

Quantum decay of supercurrent in thin superconducting wires

Quantum fluctuations cause a decay of the supercurrent in thin superconducting wires making them resistive even at very low temperatures. We derive a microscopic effective action formalism that goes beyond the usual TDGL approach and study quantum fluctuations of the superconducting order parameter at all temperatures belowT _C . We calculate the quantum phase slip rate in thin superconducting wires, demonstrate the importance of dissipation in a quantum phase slip process, and evaluate the resistanceR(T) of the wire. In very thin wires the effect is well observable, even at zero temperature.     

The vortex-like excitations detected by Nernst signals in high-T c superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.