Penetration of a magnetic field into the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript> high-temperature superconductor: Magnetoresistance in weak magnetic fields

The penetration of a magnetic field into superconducting grains and weak links of YBa₂Cu₃O_7?δ ceramic high-temperature superconductors is investigated using measurements of the transverse and longitudinal magnetoresistances at T=77.3 K and 0≤H≤～500 Oe as a function of the transport current in the range ～0.01≤I/I _c ≤～0.99. The effects associated with the complete penetration of Josephson vortices into weak links of the high-temperature superconductor in magnetic fields H_c2J, the onset of penetration of Abrikosov vortices into superconducting grains in magnetic fields H_c1A, and the first-order transition from the Bragg glass phase to the vortex glass phase in fields H_BG-VG are revealed and interpreted. The I-H phase diagrams YBa₂Cu₃O_7?δ high-temperature superconductors are constructed for I ⊥ H and I ‖ H.     

Contactless method for measuring the parameters of the current-voltage characteristic of YBCO superconductors in a perpendicular magnetic field

A contactless method for determination of the parameters of the current-voltage (I—V) characteristic of hard superconductors by measuring the magnetization relaxation of the superconductor in a perpendicular magnetic field has been developed. The relaxation curves obtained for melt-textured YBCO samples are well approximated by the curves calculated within the electrodynamic model based on power-law I—V characteristics. This procedure uses only two fitting parameters: the critical current density J _c and the exponent m of the I—V characteristic.     

The c-axis fluctuation conductivity in layered superconductors in a strong electric field under a magnetic field

The effect of a high electric field on the c-axis fluctuation conductivity in layered superconductors near the superconducting transition is investigated by the time-dependent Ginzburg-Landau equation. The c-axis fluctuation conductivity is calculated in self-consistent Gaussian approximation for an arbitrarily strong electric field and a magnetic field perpendicular to the layers. Our results include all Landau levels and have refined analytical form. The results in linear response are in good agreement with the experimental data in a wide region around T _c in high T _c superconductor. We also show that high electric fields can be effectively used to suppress the c-axis fluctuation conductivity in high-temperature superconductors.     

Magnetization and Static Magnetic Susceptibility of Fine-Crystalline High-Temperature YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> Superconductors Synthesized by the Sol–Gel Method

A comparative study of the magnetization and static magnetic susceptibility of high-temperature superconductors (HTSC) YBa₂Cu₃O_y synthesized by two variants of the sol–gel method with different average sizes of crystallites 〈 D〉 ranging 0.4–2 μm has been performed in constant magnetic fields (Н ≤ 6 kOe). It has been shown that the different annealing temperatures and times, at which their crystal structure is formed, change both the average sizes of crystallites 〈D〉 and the sizes of the structural homogeneity regions 〈l〉 and, at the same time, the magnetic field penetration depth (λ) and the coherence length (ξ). As a result, such parameters as 〈D〉 ~ λ and 〈l〉 ~ ξ become comparable, leading to a change in the physical characteristics of HTSCs. It has also been shown that the superconducting transition temperature T_c determined from the measurements of magnetic characteristics in constant magnetic fields remains within values optimal for superconductivity (T_c ≈ 92 K) in the case of an optimal number (y) of oxygen atoms, which determine the levels of charge doping for a given compound.     

Thermal expansion of (Sr<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>)<Subscript>3</Subscript>Ru<Subscript>2</Subscript>O<Subscript>7</Subscript> single crystals at low temperatures

For single-crystal samples of the (Sr_1?xLa_x)₃Ru₂O₇ ruthenates, the temperature dependence of the thermal expansion coefficient α(T)) is measured in the range 4.2–80 K. The effect of magnetic fields H ≤ 3.5 T on thermal expansion is analyzed. It is found that the (Sr_1?xLa_x)₃Ru₂O₇ ruthenates exhibit an anomalous (negative) thermal expansion coefficient in the temperature range T ≤ 18 K. The position and width of the anomaly revealed in the temperature dependence of the thermal expansion coefficient α(T)) depend substantially on the magnetic field. The origin of the thermal expansion anomaly in ruthenates, the correlation of this anomaly with the stability of the crystal lattice, and the common nature of the anomalies in the thermal properties of ruthenates and high-temperature superconductors are discussed.     

The magnetic field dependence of the low temperature (0.1K to 3K) residual specific heat of Pr<Subscript>2−<Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CuO<Subscript>4−δ</Subscript>

Measurements are presented of the low temperature specific heat of three polycrystalline samples of Pr_2?x Ce _x CuO₄ in magnetic fields of 0, 2 and 4 Tesla. The residual specific heat contribution in zero field seems to have a form αT ⁿ (n<1) for all of the samples, whether superconducting or non-superconducting. The behaviour in magnetic fields is similar to that reported for other high Tc superconductors where a change in exponent of the residual term occurs at some crossover temperature in magnetic fields.     

Formation of exotic states in the <Emphasis Type="Italic">s–d</Emphasis> exchange and <Emphasis Type="Italic">t–J</Emphasis> models

Different scenarios of the implementation of the two-band model in systems of strongly correlated electrons, including frustrated magnetic systems, high-temperature superconductors, and Kondo lattices, are considered. The interaction of current carriers with magnetic moments in the representations of pseudofermions or Schwinger bosons describing the spinon excitations is studied on the basis of the derived Hamiltonians of the s–d exchange and t–J models within the formalism of many-electron Hubbard X operators.     

Analytical assessment of some characteristic ratios for <Emphasis Type="Italic">s</Emphasis>-wave superconductors

We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high-temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ? T_c are discussed using the method of successive approximations. The equation for the ratio R₁, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R₂, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low-T_c superconductors. The prospect of application of the presented model in studies of high-T_c superconductors and other superconducting systems of the new generation is also discussed.     

Mechanism of the hysteretic behavior of the magnetoresistance of granular HTSCs: The universal nature of the width of the magnetoresistance hysteresis loop

The hysteretic behavior of the magnetoresistance R(H) of granular high-temperature superconductors (HTSCs) of the Y-Ba-Cu-O, Bi-Ca-Sr-Cu-O, and La-Sr-Cu-O classical systems is investigated for transport current densities lower and higher than the critical density (at H = 0). All systems exhibit universal behavior of the width of the magnetoresistance hysteresis loop: independence of transport current under identical external conditions. This means that flux trapping in HTSC grains is the main mechanism controlling the hysteretic behavior of the magnetoresistance of granular HTSCs, while pinning of Josephson vortices in the intragranular medium makes no appreciable contribution to the formation of magnetoresistance hysteresis (when transport current flows through the sample). Experimental data on relaxation of residual resistance after the action of a magnetic field also confirm this conclusion.     

Schwarzian derivative as a proof of the chaotic behaviour

In recent years, a sufficient condition for determining chaotic behaviours of the non-linear systems has been characterized by the negative Schwarzian derivative (Hac?bekiro?lu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame of reference, which is known as a nonlinear dynamical system that displays some macroscopic quantum effects. In our previous works, two quantum chaotic transition points of the critical transition temperature, T _c, and paramagnetic Meissner transition temperature, T _PME, have been phenomenologically predicted for the mercury-based high-temperature superconductors (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009); Aslan et al, J. Phys.: Conf. Ser. 153, 012002 (2009); Çataltepe, Superconductor (Sciyo Company, India, 2010)). The T _c, at which the one-dimensional global gauge symmetry is spontaneously broken, refers to the second-order phase transition, whereas the T _PME, at which time reversal symmetry is broken, indicates the change in the direction of orbital current in the system (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009)). In this context, the chaotic behaviour of the mercury-based high-temperature superconductors has been investigated by means of the Schwarzian derivative of the magnetic moment versus temperature. In all calculations, the Schwarzian derivatives have been found to be negative at both T _c and T _PME which are in agreement with the chaotic behaviour of the system.     

Paramagnetism of copper–oxygen chains in high-temperature YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6 + δ</Subscript> superconductors

Experimental evidence for the existence of chain paramagnetic Curie-type contributions to the temperature dependence of static magnetic susceptibility χ(T) in the normal (nonsuperconducting) state is obtained for a series of pure YBa₂Cu₃O_{6 + δ} high temperature superconductors with different oxygen contents (0.6 < δ ≤ 1). It is shown that the chain contribution is obvious on χ(T) curves only in the T < 150K range of temperatures, grows along with the number of oxygen vacancies in Cu1–O4 chains, and depends on the ordering of these vacancies.     

Enhancement of pseudogap anomalies induced by nanoscale structural inhomogeneity in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.93</Subscript> high-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductor

The magnetization M(H) in the superconducting state, dc magnetic susceptibility χ(T) in the normal state, and specific heat C(T) near the superconducting transition temperature T _c have been measured for a series of fine-crystalline YBa₂Cu₃O _y samples having nearly optimum values of y = 6.93 ± 0.3 and T _c = (91.5 ± 0.5) K. The samples differ only in the degree of nanoscale structural inhomogeneity. The characteristic parameters of superconductors (the London penetration depth and the Ginzburg–Landau parameter) and the thermodynamic critical field H _c are determined by the analysis of the magnetization curves M(H). It is found that the increase in the degree of nanoscale structural inhomogeneity leads to an increase in the characteristic parameters of superconductors and a decrease in H _c(T) and the jump of the specific heat ΔC/T _c. It is shown that the changes in the physical characteristics are caused by the suppression of the density of states near the Fermi level. The pseudogap is estimated by analyzing χ(T). It is found that the nanoscale structural inhomogeneity significantly enhances and probably even creates the pseudogap regime in the optimally doped high-T _c superconductors.     

Manifestation of pseudogap features in structurally inhomogeneous optimally doped HTSC YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.92</Subscript>

Magnetization M(H,T) in magnetic fields H up to 90 kOe and at temperatures 2 K ≤ T < T _c (where Tc is the superconducting transition temperature), along with magnetic susceptibility χ(T) in the normal state T _c < T < 400 K for optimally oxygen-doped samples of YBa₂Cu₃O_6.92 with varying degrees of defects in the crystal structure, are studied to determine the influence of structural inhomogeneity on the electron systems characteristics of cuprate superconductors. It is shown that the existence of structural inhomogeneity of samples leads to the manifestation of peculiarities appropriate to pseudogap regime in their properties.     

Magnetic capacitance of the Gd<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Bi<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>FeO<Subscript>3</Subscript> thin films

The capacitance, inductance, and dissipation factor of the Gd _x Bi_1–x FeO₃ films were measured in the temperature range of 100 K < T < 800 K in magnetic fields of up to 8 kOe at frequencies of 0.1–100 kHz. The magnetic susceptibility maxima in the low-temperature region and dependences of the relaxation time and inductance on prehistory of the films cooled in zero and nonzero magnetic fields are established. The giant increase in magnetic capacitance in the external bias electric field is found. The results obtained are explained by the domain structure transformation in external electric and magnetic fields.     

Temperature and purity dependence of the nuclear-spin relaxation rate in the gapless region of type-II superconductors

The volume average of the nuclear-spin relaxation rate in type-II superconductors,R _s, is calculated for magnetic fields slightly below the upper critical field and all mean free paths,l, and temperatures. It is found to be expressible solely in terms of the volume average of the density of states,\(\bar N(\omega )\), where the latter quantity has been determined recently byNeumann for alll. The derivation is based onHelfand andWerthamer's eigen-value equation for the order parameter,Δ. The deviation of\(\bar R_s \) from the relaxation rate in the normal state,R _n, is proportional to the quantity\([|\overline {\Delta |^2 } /\Delta _{BCS}^2 (T)]R_n \) (the bar denotes the spatial average). The proportionality factor is found to decrease monotonously as the temperature decreases and/orl increases. This behavior is closely related to the fact that\(\bar N(\omega )\) shows no gap for the excitation energiesω and decreases asl increases, in particular at energiesω close to zero (ω=0 corresponds to the Fermi energy).     

Local approximation oscillatory differential method for the analysis of physical processes at the interface between vortex and Meissner regions in superconductors

A “differential” method for local diagnostics of superconductors has been developed. Regular steps with identical heights through certain intervals of an external field have been revealed on the magnetic-field dependences of the trapped magnetic flux density B _tr(H ₀) and the effective demagnetizing factor n _eff (H ₀) of bulk and film YBCO samples. It has been shown that the sample in high magnetic fields “decays” stepwise into subcrystallites and nanocrystallites whose size is much smaller than the depth of penetration of the magnetic field λ.     

A brief review on <Emphasis Type="Italic">μ</Emphasis>SR studies of unconventional Fe- and Cr-based superconductors

Muon spin relaxation/rotation (μSR) is a vital technique for probing the superconducting gap structure, pairing symmetry and time reversal symmetry breaking, enabling an understanding of the mechanisms behind the unconventional superconductivity of cuprates and Fe-based high-temperature superconductors, which remain a puzzle. Very recently double layered Fe-based super- conductors having quasi-2D crystal structures and Cr-based superconductors with a quasi-1D structure have drawn considerable attention. Here we present a brief review of the characteristics of a few selected Fe- and Cr-based superconducting materials and highlight some of the major outstanding problems, with an emphasis on the superconducting pairing symmetries of these materials. We focus on μSR studies of the newly discovered superconductors ACa₂Fe₄As₄F₂ (A = K, Rb, and Cs), ThFeAsN, and A₂Cr₃As₃ (A = K, Cs), which were used to determine the superconducting gap structures, the presence of spin fluctuations, and to search for time reversal symmetry breaking in the superconducting states. We also briefly discuss the results of μSR investigations of the superconductivity in hole and electron doped BaFe₂As₂.     

Paramagnetische Relaxation und Phonon-Engpaß im Terbium-Äthylsulfat

The magneto-optical Faraday effect was used to study the spin-lattice relaxation in in the terbium ethyl sulfate. The effective spin-lattice relaxation timeT _eff was measured in the temperature range 1,4≦T≦3,5 °K and for magnetic fields of 1000, 1500 and 2000 Oe.T _eff depends on the initial disturbance of the thermal equilibrium between the spin-system and the lattice. There has been identified a phonon bottleneck in the terbium ethyl sulfate.     

Phase transitions in a MgB<Subscript>2</Subscript> granular BCS superconductor in weak magnetic fields

The character of temperature dependences of the electric conductivity of MgB₂ granular BCS superconductors at temperatures of ~35–45 K in external magnetic fields H _ext of up to ~2 kOe is studied. An increase in the superconducting transition width ΔT _c with an increase in Hext is found. The presence of a system of weak links in MgB₂-based granular superconductors is established. On the basis of experimental data, MgB₂ granular superconductor is assigned to two-level superconducting systems and the H–T phase diagram is constructed.     

Quantum interference effects induced by multiple magnetic impurities on a triangular lattice f-wave superconductor

The effects of multi-impurity quantum interference on triangular lattice f-wave superconductors are studied by self-consistently solving Bogoliubov-de Gennes equations within the t?t′?J?V model. An overall phase diagram is presented, which shows that f-wave superconductivity dominates near 0.3 doping. Rich phenomena are induced by quantum interference effects, such as periodic modulations in charge orders, pyramid frustum structures, and a magnetic moment reverse transition, which are qualitatively different from the single-impurity case. We also examine the local density of states to show how localized quasiparticle states are created at or near the impurity sites, which can be directly measured by scanning tunneling microscopy experiments.