Excess Conductivity Analysis of Tl1−x Y x Ba2Ca2Cu3O10−δ Superconductors

Excess conductivity analyses of resistivity data of Tl_1?x Y _x Ba₂Ca₂Cu₃O_10?δ (x=0, 0.04, 0.06, 0.08, 0.1) samples have been carried out by following Lawrence & Doniach (LD) and Maki-Thompson (MT) models. In the critical regime important superconductivity parameters have been elucidated by employing Ginzburg-Landau number N _G of Ginzburg Landau theory. Our samples have shown a decrease in the T _c (R=0) and magnitude of diamagnetism with increased Y-doping. The cell parameters and volume of the unit cell increase with doping of Y⁺³ in Tl_1?x Y _x Ba₂Ca₂Cu₃O_10?δ (x=0, 0.04, 0.06, 0.08, 0.1) which shows a decrease in the density of charge carriers in the conducting CuO₂ planes. Since the Fermi vectors of the carriers, K _F=[3π ² N/V]^1/3=[3π ² n]^1/3, their coherence length along the c-axis, ξ _c=?K _F/2mΔ, and the Fermi velocity, V _F=?K _F/m depend on density of mobile charge carriers, the doping of Y⁺³ suppresses it and hence the superconductivity parameters. We have confirmed these conjectures with the excess conductivity analyses (FIC) of our conductivity data. The FIC analysis of conductivity data has shown a decrease in the values of ξ _c, V _F, B _c(0), B _c1(0) and J _c(0) with increase doping of Y (except for the samples with x=0.04). The width of two dimensional conductivity regimes is shrunken with increased Y-doping. From these studies it is concluded that presence of Y⁺³ in the unit cell of TlBa₂Ca₂Cu₃O_10?δ impedes the flow of the mobile charge carriers to the conducting CuO₂ planes which induce suppression in the superconductivity parameters. The studies also stress the vital role of mobile charge carriers in the mechanism of high temperature superconductivity.     

Fluctuation Induced Conductivity in Hg-Doped (Cu0.5Tl0.5?x Hg x )Ba2Ca3 Cu 4O12?δ Superconductor

The fluctuation induced conductivity (FIC) analysis on resistivity data of the Hg-doped (Cu_0.5Tl_0.5−x Hg _x )Ba₂Ca₃Cu₄O_12−δ (x=0, 0.15, 0.25, 0.35) superconductor has been carried out in the light of the Aslamazov–Larken (AL) theory. The superconducting properties have been improved with Hg-doping (up to x=0.25) at Tl sites in the Cu_0.5Tl_0.5Ba₂O_4−y charge reservoir layer. These samples are also post-annealed in oxygen to improve intergrain connectivity and to optimize the carriers’ density in CuO₂ planes. The results of FIC analysis have shown three-dimensional (3D) and two-dimensional (2D) fluctuations in the order parameters. It has been observed that there is an increase in the cross-over temperature (T _o) as well as in zero resistivity critical temperature {T _c(0)} with Hg-doping. These properties have been further improved after post-annealing in oxygen, which may be due to improved inter-grain coupling and optimization of mobile carriers in CuO₂ planes. A direct correlation between T _o, T _c(0) as well as zero temperature coherence length ξ _c(0) has been observed.     

Comparison of Superconductivity Parameters of (Cu1?x Tl x )Ba2Ca4Cu5O14?δ Superconductor Synthesized at Different Temperatures

The superconductivity parameters of (Cu_1−x Tl _x )Ba₂Ca₄Cu₅O_14−δ (CuTl-1245) samples synthesized at different temperatures has been compared. Almost all the superconductivity parameters studied in this research work are suppressed with the increase of synthesis temperature beyond 890 ^○C, which may be due to defects induced by the volatility of some constituents such as thallium, oxygen deficiencies, and multiphase in the final compound. The fluctuation induced conductivity (FIC) analysis has shown a decrease in the cross-over temperature (T _o) as well as the mean-field critical temperature (T_c^mf)T_{\mathrm{c}}^{\mathrm{mf}}) and the shift of three- dimensional (3D) Aslamasov–Larkin (AL) regions to the lower temperature with the increase of synthesis temperature beyond 890 ^○C. A direct correlation between (T _o), the zero temperature coherence length {ξ _c (0)}, the interlayer coupling strength (J), mean-field critical temperature (T_c^mf)T_{\mathrm{c}}^{\mathrm{mf}}) as well as carrier concentration has also been observed.     

Synthesis and Excess Conductivity Analyses of Ce-Doped Tl1−x Ce x Ba2Ca2Cu3O10−δ Superconductors

The role of mobile carriers density supplied by TlBa ₂ O _4?δ charge reservoir layer is investigated by doping Ce in TlBa ₂Ca ₂Cu ₃ O _10?δ superconductors. The T _c(onset) and T _c(R= 0) versus Ce contents have shown almost a parabolic-shaped phase diagram which is interpreted in terms of hole’s doping. The magnetic measurements showed that magnitude of diamagnetism is gradually suppressed with Ce doping at Tl site. Fourier transform infrared (FTIR) revealed that the phonon modes associated with apical oxygen atoms type Cu(2)–O _A –Tl are softened, whereas the planar oxygen modes are hardened with the doping of Ce the unit cell. In the excess conductivity, analyses of conductivity data of Tl _1?x Ce _x Ba ₂Ca ₂Cu ₃ O _10?δ samples have shown a suppression of T _{c m f} (K) and the width of 2D conductivity regimes, whereas the coherence length along the c-axis ξ _c(0) and the interlayer coupling J are enhanced with the doping of Ce ⁺⁴ in the charge reservoir. The increase in ξ _c(0) is interpreted in the form of homogenization of the carrier’s density of carriers the CuO ₂ planes. The process of homogenization is accomplished with the reduction of density of carriers in the outer CuO ₂ that consequently promotes increase in the phase relaxation time, τ _? , of the carriers, their Fermi velocity, and the energy required to break apart the Cooper pairs.     

The Effect of Cadmium Substitution on the Superconducting Properties of Tl1−x Cd x Ba2Ca2Cu3O9−δ Compound

In order to study how Cd substitution for Tl changes, the superconducting properties of Tl_1?x Cd _x Ba₂Ca₂Cu₃O_9?δ compound with x=0, 0.1, 0.2 and 0.3. We have prepared samples with Cd in place of Tl by the solid state reaction method. It has been found that the increase of the Cd concentrations of all samples produced increases the transition temperature from 113 to 123 K and changes the mass density ρ _m, C/a and volume fraction V _Ph(1223).. XRD shows that the partial substitution of Tl with Cd is helpful to form the superconducting 1223 phase (TlBa₂Ca₂Cu₃O_9?δ ). It has been shown that samples mainly contain tetragonal phase 1223 with a few additional mixed 1212 and 1201 phases.     

Temperature and Frequency Dependent Dielectric Properties of Cu0.5Tl0.5Ba2Ca3(Cu4−y Cd y )O12−δ Bulk Superconductor

The temperature and frequency dependent dielectric properties of polycrystalline Cd-doped Cu_0.5Tl_0.5Ba₂Ca₃(Cu_4?y Cd _y )O_12?δ (y=0,0.25,0.5,0.75) bulk superconductor samples are investigated. The zero resistivity critical temperature {T _c(R=0)} has decreased and normal state resistivity has increased with the increase of Cd-doping in Cu_0.5Tl_0.5Ba₂Ca₃(Cu_4?y Cd _y )O_12?δ samples. The dielectric properties such as dielectric constants (ε′,ε″), dielectric loss tangent (tanδ) and ac-conductivity (σ _ac ) are investigated by measuring the capacitance (C) and conductance (G) in the frequency range of 10 KHz to 10 MHz at different temperature from 80 K to 300 K. The negative capacitance (NC) is observed in all Cu_0.5Tl_0.5Ba₂Ca₃(Cu_4?y Cd _y )O_12?δ samples. The large values of NC observed at lower frequencies and temperatures may be due to reduced thermal vibrations and enhanced polarizability of the material. The effect of Cd-doping on bulk properties, dc-resistivity (ρ) and ac-electrical conductivity (σ _ac ) of these superconductor samples are investigated. The polarization in Cu_0.5Tl_0.5Ba₂Ca₃(Cu_4?y Cd _y )O_12?δ samples is most likely arising from the displacement of charges in CuO₂/CdO₂ planes relative to the static charges at Ba²⁺, Tl³⁺, and Cu²⁺ sites in Cu_0.5Tl_0.5Ba₂O_4?δ charge reservoir layers by external applied field.     

Microwave Surface Impedance of Nd-rich Nd 1+x Ba 2−x Cu 3 O 7−δ Thin Films

Surface impedance measurements on highly c-axis epitaxial Nd _1+x Ba _2–x Cu ₃ O ₇ (x=0, 0.09 and 0.12) films grown by d.c. magnetron sputtering on LaAlO ₃ substrates are presented. It is found that the zero temperature London penetration depth correlates well with the critical temperature of the films and with the corresponding number of carriers. The low temperature penetration depth follows a linear T law for optimally doped Nd123 sample and a T ² law in Nd-rich samples. In the case of the heavily underdoped samples (T _c < 60K) the T ² law extends to temperatures higher than T _c/2. The possible role of the Nd/Ba ions substitution on the penetration depth and surface resistance is discussed.     

Growth of (Cu0.5Tl0.5?x Hg x )Ba2Ca3Cu4O12?δ Superconductor with Optimal Carrier Density in CuO2 Planes and Fluctuation-Induced Conductivity

The growth of (Cu_0.5Tl_0.5?x Hg _x )Ba₂Ca₃Cu₄O_12??? (x=0, 0.25) superconductor with optimal carrier density in CuO₂ planes has been made possible by partial substitution of Hg at Tl sites in (Cu_0.5Tl_0.5)Ba₂O_4??? charge reservoir layer of (Cu_0.5Tl_0.5)Ba₂Ca₃Cu₄O_12??? superconductor. The fluctuation-induced conductivity (FIC) analysis has been carried out on resistivity vs. temperature curves by using Aslamazov?CLarkin (AL) theory and the results have shown three-dimensional (3D) and two-dimensional (2D) fluctuations in order parameters. The microscopic parameters deduced from FIC analysis such as crossover temperature (T _o ), zero temperature c-axis coherence {?? _c (0)} and the interlayer coupling strength?(J) have been improved with Hg substitution. Also, 3D region has been shifted to higher temperature with Hg substitution. In order to verify the optimal carrier density in CuO₂ planes with Hg substitution, the post-annealing experiments have been carried out on these samples in nitrogen and air. These post-annealing experiments have caused under-doping of carriers from the optimal level resulting into a decrease in T _c (R=0) as well as the magnitude of diamagnetism.     

Fabrication of Micro-pipes of YBa2Cu3O7−δ Superconductor

Synthesis of micro-pipes of YBa₂Cu₃O_7−δ superconductor has been carried out for the first time by using chemical method. The shape, size and length of these micro-pipes depends upon dimensions of growth matrix and structure of geometry, i.e., circular, square, rectangular and hexagonal, etc., which could be uniformly coated with superconductor. The onset temperature of diamagnetism of the material is found to be 93 K, which is not shifted to lower values by the application of DC magnetic field; this is most likely due to large surface area provided by micro-pipes to the shielding currents. These micro-pipes behave as pinning centers, hence they can be used for the fabrication of devices that are capable of working in high magnetic fields.      

Microwave Measurements of Overdoped Y0.9Ca0.1Ba2Cu3O7−δ Thin Films

In the present report we show, for the first time, that a complex order parameter is not just a surface effect, but a bulk property in overdoped Y_0.9Ca_0.1Ba₂Cu₃O_7– thin films. The penetration depth change versus temperature is very well fitted to a complex order parameter of the form d_x ^{2-y 2} + id _xy , where = 14.5 meV and = 2meV. This result contrasts our previous results for optimally doped YBCO thin films where a power law for the penetration depth, versus temperature was reported, corresponding to a d_x ^{2-y 2}-wave order parameter. The penetration depth behavior is accompanied by a rapid reduction of the scattering rate at low temperatures, in contrast with a flattening of this quantity for the optimally doped YBCO films.     

Distribution of Induction, Electric Field, and Current Density, in Thin YBa2Cu3O7−x Films Carrying Transport Current

An array of miniature Hall sensors has been utilized to measure the spatial distribution and time evolution of the local induction in a thin YBa ₂ Cu ₃ O _7–x film at the remanent state, before and after the application of a dc transport current. As a result of transport current the induction peak is shifted from the center of the sample, indicating an inhomogeneous current distribution. Transport current markedly changes the spatial distribution of the electric field and the relaxation rate, creating a dynamic neutral line where the electric field is maximum, and the relaxation rate is zero.     

Effect of MgO Nano-oxide Additions on the Superconductivity and Dielectric Properties of Cu0.25Tl0.75Ba2Ca3Cu4O12?δ Superconducting Phase

The effect of MgO nano-oxide on both superconducting and dielectric properties of polycrystalline (Cu_0.25Tl_0.75)-1234 was studied. The MgO-content varied from x=0.0 up to 1.0 wt% of the sample’s total mass. The volume fraction of the prepared samples (x=0.0, 0.2, 0.6 and 1.0 wt%) was estimated from the room-temperature X-ray powder diffraction patterns. The superconducting transition temperature T _c, calculated from resistivity data, increased from 122 to 136 K as x increased from 0.0 to 0.8 wt% and then it decreased to 117 K for x=1.0 wt%. Also, the dielectric properties of all samples were measured in the frequency range from 100 Hz to 4 MHz at different temperatures from 113 to 300 K. The real part of dielectric constant ε′ was strongly dependent on both temperature and frequency for all x values. The imaginary part of dielectric constant ε″ and loss factor tan δ showed dispersion which shift toward lower frequencies with decreasing temperature. The ac conductivity σ _ac was derived from the admittance and sample dimensions in the same frequency range. It followed the power law σ _ac(ω)∼ω ^−γ with γ≈0.8.     

The Effect of Simultaneous Substitution of Strontium at the Barium site of Tl0.6Pb0.4Ba2−x Sr x Ca2Cu3O9−δ Superconductors

High temperature superconductors, namely Tl_0.6⋅ Pb_0.4Ba_2−x Sr _x Ca₂Cu₃O_9−δ , have successfully been prepared by the solid state reaction method. The substitutions for this compound were taken as x=0.0, 0.10, 0.20, 0.30, 0.40 and 0.50. The optimum calcination was at 1073 K and for sintering was within 1128–1133 K. Electrical resistivity, using the four-probe technique, was used to find the transition temperature T _c. The highest T _c(offset) was 113 K for Tl_0.6Pb_0.4Ba_1.5Sr_0.5Ca₂Cu₃O_8.76. All samples were prepared by using O₂ flow. X-ray diffraction (XRD) analysis have shown a pseudotetragonal structure with an increase of the c-axis lattice constant for the samples which were doped with Sr as compared to those which have no Sr content.     

Activation Energy of Bi2Sr2Ca1−x Er x Cu2O8+d Epitaxial Thin Films

The scaling behavior of the effective activation energy U(T, H) of epitaxial oriented Bi₂Sr₂Ca_1–x Er _x Cu₂O_8+d thin films with 0x0.10 has been studied as function of temperature and magnetic field. It has been found that the activation energy scales as U(H, T)=U ₀(1–t)^m H ⁿ with exponent m=1.20±0.03 and n=–1/2. The field and temperature dependence of the activation energy, as well as its overall magnitude, is consistent with a model in which U(T, H) arises from plastic deformations of viscous flux liquid above the vortex-glass transition temperature.     

The Energy Gap in the (Hg1−x Sn x )Ba2Ca2Cu3O8+y Superconductor

The experimental data show that the increase of tin in the (Hg_1?x Sn _x )Ba₂Ca₂Cu₃O_8+y superconductor results in a visible increase in the pseudogap temperature (T ^?) with a slight decrease in the value of the critical temperature (T _C). Based on the above results, the dependence of the average amplitude of the energy gap on the temperature (G(T)) has been determined for x∈〈0,0.25〉. On this basis, it has been found that the dimensionless ratio R _G ≡G(0)/k _B T _C increases with the increasing tin content from the value of 3.48 to the value of 4.88. Next, for x=0.25 and T∈〈0,T ^?〉, the dependence of the energy gap on the wave vector has been calculated in the surrounding of the Fermi level. It has been shown that in the anti-nodal region the energy gap is very weakly dependent on the temperature. On the other hand, in the nodal region its values strongly decrease together with the increasing temperature.     

Magneto-resistance and Excess Conductivity Studies of Tl(Ba2−y Mg y )Ca 2 Cu 3 O 10−δ Samples

The flux pinning characteristics of T l(B a _2?y M g _y )C a ₂ C u ₃ O _10?δ(0.0≤y≤ 1.5) samples have been studied under the influence of various dc magnetic fields in the light of thermally activated flux flow model. It was observed form the magneto resistivity measurements that the activation energy U has been increased in the sample with Mg incorporation of y=0.5, however, it is decreased in the samples with higher Mg doping. This shows that lower Mg doping concentration promotes enhancement, whereas its higher concentration suppresses the flux pinning characteristics of Tl(Ba _2?yMg _y )Ca ₂Cu ₃ O _10?δ (0.0 ≤y≤1.5) samples. The excess conductivity analysis of Tl(Ba _2?yMg _y )Ca ₂Cu ₃ O _10?δ (0.0 ≤ y ≤ 1.5) samples has shown that the coherence length along the c-axis ξ _c(0), the interlayer coupling J, the phase relaxation time of the carriers τ _? , and the Fermi velocity v _F of the carriers are suppressed with Mg doping. However, the values of B _c0(T), B _c1(T), and J _c(0) are enhanced which complement the magnetoresistivity analysis. These results showed that the flux pinning characteristics are enhanced for lower doping concentration of Mg at the charge reservoir layer sites.     

Bond Angle Study of Self-compensating Y1−x Ca x Ba2−x La x Cu3O z System

Single-phase samples of a self-compensating Y_1?x Ca _x Ba_2?x La _x Cu₃O _z system were synthesized through a solid-state reaction method with x<0.4. The structure of all samples were characterized by X-ray diffraction and refined by the Rietveld method. Superconducting properties have been investigated by the DC magnetization measurement. The critical temperature (T _c ) decreases evidently with the increment of x although the carrier concentration remains constant in the samples for different doping level. Careful study of the chemical bonds in the crystalline lattice demonstrates that the T _c is closely correlated to four pairs of bond angles in the unit cell. The analysis indicates that crystalline structure is one of the important factors to high-T _c superconductivity, and its influence is independent of the carrier concentration.