Anisotropy in the resistive superconducting transition under magnetic fields in single crystal Pb2Sr2Ho0.5Ca0.5Cu3O8

Anisotropie properties of the single crystal Pb₂Sr₂Ho_0.5Ca_0.5Cu₃O₈ have been investigated by measuring the electrical resistivity in theab-plane _ab (H, ,T), which depends on the angle between theab-plane and the magnetic-field direction, in various constant fieldsH perpendicular to the current direction. All the angle-dependent values of _ab (H, ,T) at a constant temperature are scaled to be on one curve as a function of reduced field. The anisotropic parameter (m _c ^* /m _ab ^* )^1/2 is estimated as 12–13, which is larger than that of YBa₂Cu₃O₇ and much smaller than that of Bi₂Sr₂CaCu₂O₈. It has been concluded that the anisotropy does not always depend on the thickness of the blocking layer but seems to depend on the overlap of the electronic wave functions along thec-axis. Anisotropy in the pinning potential has also been discussed from the resistive tail in the temperature dependence of _ab (H,,T).     

Hc2 of MgCNi3 Determined from the Specific Heat and Resistivity Measurements

H _c2 of MgCNi₃ has been determined from the specific heat C and resistivity measurements in the same sample. The results from are nearly identical with those determined from the anomaly in C. Furthermore, utilizing the relation (H) H and the value of d/dH, the obtained value of H _c2 is the same as that by the WHH model, if the spin paramagnetic effect and the spin–orbit interaction are taken into account. The results of this comparison have strong implications on the order parameter of MgCNi₃.     

Energy Scales in the High-Tc Superconductor YBa2Cu3O6+x

The optical conductivity sum rule is used to examine the evolution of the spectral weight N() in both the normal and superconducting states of optimally and underdoped YBa₂Cu₃O_6+x along the a axis. Differences in N() above and below T _c allow the strength of the superconducting condensate _s to be determined. In the optimally-doped material, _s is fully formed at energies comparable to the full superconducting gap maximum (0.1 eV), while in the underdoped material the energy scale for convergence is considerably higher (0.6 eV). This difference is discussed in terms of normal-state properties.     

Scaling Behavior and Estimation of Activation Energy of Polycrystalline RuSr2GdCu2O8 Superconductor from AC Susceptibility Measurements

In this study, the measured curves of AC susceptibility (ACS) components, (T) and (T), of polycrystalline RuSr₂GdCu₂O₈ (Ru-1212) superconductor were scaled onto a single curve using the peak temperature of its imaginary part (T _p) as the scaling parameter for various AC field amplitudes from 0.5 to 24 G. The dependence of the AC magnetic field amplitude on T _p is scaled as: H _ac (1–T _p/T _c)^2.25. Similarly, the current density J _c, extracted from the AC field amplitude is also scaled as: J _c (1 – T _p/T _c)^2.25. The dependencies of T _p on frequency and AC field amplitude are also investigated and the time parameter t ₀ of the order of 10^–8 s is estimated from the dependence of T _p on frequency. The dependencies of activation energy on temperature, T, and the field amplitude, H _ac, are obtained from the Arrhenius-like semilog plot of frequency () and T _p. Such dependencies on temperature and field amplitude can be described by a scaling law of the form: U(H _ac,T) = U ₀[1 – T/T _p]H _ac ^–0.17.     

Anisotropy in ac losses near the irreversibility field of Bi2Sr2CaCu2O8

The ac susceptibility under a biased dc field near the irreversibility field (H _irr) of a Bi₂Sr₂CaCu₂O₈ single crystal has been measured. The frequency dependence, the ac-power dependence, and the nearly lossless character of the vs.H _dc curve forHa-axis have been roughly explained from a reversible (elastic) fluxoid motion, while those forH c-axis have been explained from a thermally assisted flux-flow (TAFF) model. The obtained parameters are discussed in relation to anisotropic flux-pinning mechanisms in the layered structure of this compound.     

Magnetic field dependence of the density of states of YBa2Cu3O6.95: Implications for the vortex structure

The total specific heat of YBa₂Cu₃O_6.95 single crystals includes contributions from phonons and spin-1/2 particles, as well as electronic contributions. The electronic specific heat is described by a quadratic term T² in zero field and a linear term [(0)+(H)]T which is increased when a magnetic field H is applied perpendicular to the CuO₂ planes. In agreement with d-wave superconductivity, we find that _n/T_c and (H)_n(H/H_c2)^1/2, where _n is the coefficient of the normal-state linear term. The H^1/2 dependence of the density of states at the Fermi level was predicted by G. Volovik for lines of nodes in the gap: the quasiparticles which contribute to this density of states are close to the nodes in momentum space and are located outside the vortex core.     

Theab-plane optical conductivity of high-Tc superconductors

There is anisotropy in theab-plane optical properties of the high-temperature superconductors, both in the normal state and in the superconducting state. In both states, two components appear in the optical conductivity: a free carrier part and a midinfrared component. BelowT _c , the free carriers form the superconducting condensate. In YBa₂Cu₃O_7–, the anisotropy of the penetration depth shows that the chains contribute strongly to this superfluid. In Bi₂Sr₂CaCu₂O₈, where chains are absent, there is stillab plane anisotropy. BelowT _c a finite absorption parallelb remains at frequencies as small as 20 meV. This anisotropy could be due to anisotropy either of the superconducting gap or the midinfrared component.     

Comparative Study of Dense Bulk MgB2 Materials Prepared by Different Methods

We report on the results of a comparative investigation of highly dense bulk MgB₂ samples prepared by three methods: (i) hot deformation; (ii) high pressure sintering; and (iii) mechanical alloying of Mg and B powders with subsequent hot compaction. All types of samples were studied by AC susceptibility, DC magnetization, and resistivity measurements in magnetic fields up to ₀ H = 160 kOe. A small but distinct anisotropy of the upper critical field connected with some texture of MgB₂ grains was found for the hot deformed samples. The samples prepared by high pressure sintering as well as by mechanical alloying show improved superconducting properties, including high upper critical fields H _c2 (₀ H _c2 (0) 23 T), irreversibility fields H _irr which are strongly shifted towards higher values H _irr(T) 0.8 H _c2(T) and high critical current J _c (J _c = 10⁵ A/cm² at 20 K and 1 T).     

Frequency and temperature dependence of the millimeter wave conductivity of epitaxial YBa2Cu3O7 films

A millimeter wave spectrometer for frequencies between 100 and 350 GHz consisting of continuously tunable backward wave oscillators as sources and a quasioptical interferometer in the Mach-Zehnder configuration was used to measure the transmittivity in phase and amplitude of YBa₂Cu₃O₇ thin films on NdGaO₃ substrates. From the measured spectra we derived the real and imaginary part of the dynamic conductivity= ₁+i ₂ in the superconducting state as a function of temperature. The ₁(T) and ₂(T) values at 300 GHz were compared to corresponding values at 19 GHz determined by surface impedance measurements of the same films using a shielded dielectric resonator. Our observed frequency dependence of both ₁(T) and ₂(T) is consistent with a strong reduction of the quasiparticle scattering rate ^–1(T) with decreasing temperature belowT _c .     

Transistor Doping Experiments on Superconducting CaCuO2 and C60 Interpreted on a Bond Ordering Model

The curve shape of T _c vs. holes injected by fields (transistor doping) of CaCuO₂ and C₆₀ are interpreted on a charge or bond ordering [BO] model. For CaCuO₂ both the magnitude of optimal T _c (89 K vs. a calculated 83 K) and the linear portions around a sharp T _c peak at h 0.17 = 1/6 are in accord with a universal algorithm for cuprates, in which T _c scales linearly with radical bond density to an optimal BO. These linear regions extrapolate to h = 0 and 1/3 respectively. Small trends to electronic freezing are observed at h = 1/8. A second linear region extends from h 1/12 to 1/16 with 4 times the slope of the first linear region, indicating a second mode of BO filling. A surprisingly similar behavior is observed for transistor doped C₆₀ type materials with characteristic sequence of BO dictated hole concentrations for T _c onset, rise, a linear region extrapolating to T _c = 0 at h = 0, indications for electronic freezing, a sharp peak and linear decrease thereafter. This suggests that a common phenomenology obtains for all high T _c materials, representing generally an ordering phenomenon of doped covalent radical bonds.     

Normal-State Optical Response Functions of MgB2 Superconductor

The reflectivity of superconducting MgB₂ (T _c = 39 K) has been measured on a randomly oriented thin film at room temperature over a wide-range of frequencies, 20 < 100000 cm^–1. The conductivity shows highly metallic behavior but cannot be explained with a simple Drude model alone. The electronic contribution is analyzed by a generalized Drude model. The scattering rate 1/() and the mass renormalization ratio m*()/m = 1 + () exhibit clear frequency dependence. The electron–phonon coupling strength is estimated to be 1.5 ± 0.5 while the plasma frequency _p is 2.4 eV.     

Upper Critical Field Hc2 on c Axis of Ag/Bi-2223 Polycrystal Tape

The upper critical field H _c2, based on Ginzburg–Landau theory at medial magnetic fields, can be calculated from the relationship of the magnetization intensity M(H) versus magnetic field H if M is linear with ln₀ H. For Ag/Bi-2223 tapes, the measured M(H) was found to be linear with ln₀ H. In this case, the values of H _c2(T) may in principle be determined. To do this, we will meet another problem in that the obliquity of crystal planes is not equal for different grains in tapes, and values of grain-oblique angle will appear in the calculated H _c2. Obviously, for Ag/Bi-2223 tapes is an uncertain parameter and hard to determine. To avoid the effects of , we only study the H _c2 in the c axis direction and the projections of H onto the c axis is taken as the actual applied fields. Thus, the effects of grain-oblique angle may be counteracted when measuring critical current density J, if the external magnetic fields are applied to the tape along both the parallel to and perpendicular to the c axes directions (on the narrow surfaces of the tape). On medial fields (H = 0 – 3 T), the upper critical fields H _c2(T) on c axis for the Ag/Bi-2223 tape are obtained and fitted as ₀ H _c2(T) = 830 e ^–0.07T . The average slope d[₀ H _c2(T)]/dT – 8T/K is found to be as large as that of Bi-2212. On extrapolating the relation to T = 0 K, the value of ₀ H _c2(0) 800T. The coherence length _ab is determined from H _c2(c), and _ab (0) = 0.63 nm at T = 0 K.     

Analysis of electronic structure and charge density of the high-temperature superconductor YBa2Cu3O7

Self-consistent linearized augmented plane wave (LAPW) method calculations of the band structure, density of states, Fermi surface, Coulomb potential, charge density, core-level shifts, and electron-phonon interaction are presented for Y₁Ba₂Cu₃O₇. The calculated Sommerfield parameter is 4.35 mJ(mole Cu)^–1 K^–2, roughly about a factor of 2 smaller than experimentally deduced values of the enhanced value=(1 + )₀, suggesting that the Fermi surface mass enhancement is of the order of unity. The crystal charge density is best represented by overlapping spherical ionic densities when the Cu and O ions are assigned charges of +1.62 and –1.69, respectively, corresponding to about 0.3 holes per oxygen atom. Core-level energies for the inequivalent atoms differ by as much as 0.45 eV for Cu and 0.7 eV for O, amounts which may be detectable by core-level spectroscopies. These results provide important information on the character and magnitude of ionic contributions to bonding in these materials. Within the rigid muffin-tin approximation, calculated McMillan-Hopfield parameters yield estimates for the electron-phonon strength that appear to be too small to account for the observedT _c. We point out an unusual band of oxygen-derived chain states below, but within 0.1 eV of, the Fermi level.     

Electronic Inhomogeneity and Possible Pseudogap Behavior of Spin Susceptibility in the Electron-Doped Superconductor Sr0.93La0.07CuO2: 63Cu NMR Study

The magnetic susceptibility, NMR spectra, nuclear spin-lattice relaxation rate (T ₁ ^–1) and the echo-decay rate (T ₂ ^–1) of ⁶³Cu were measured for the electron-doped infinite-layer superconductor Sr_0.93La_0.07CuO₂/T _c ^onset = 42.4 K). The results obtained revealed a clear tendency toward frustrated phase separation in this nominally underdoped high-T _c material. Above T _c the ⁶³Cu Knight shift is found to decrease upon cooling giving an evidence for a pseudogap-like decrease of the spin susceptibility. It is shown that unusual anisotropy of the ⁶³Cu Knight shift in the electron-doped CuO₂ layer can be understood as a compensation effect between the isotropic hyperfine coupling, mediated by the 4s Fermi-contact and 3d core-polarization exchange interactions, and the anisotropic on-site spin-dipolar hyperfine interaction of the Cu nuclei with the itinerant carriers, whose states near the Fermi energy have a sizeable admixture of Cu(4p_z) and/or Cu(3d_z ²) orbitals.     

Single-crystal growth and anisotropic electrical properties of (La1?xCax)2CaCu2O6

Large single crystals of (La_1–x Ca _x )₂CaCu₂O₆ were synthesized by the travelling solvent floating zone (TSFZ) technique. The dimension of the grown boules was typically 4 mm×30 mm long with thec-axis perpendicular to the growth direction. After oxygen loading at 1080°C in 400 atm of O₂, they became superconductive with a sharp transition at around 50 K. The resistivity was metallic both along thec-axis and within theab-plane, with an anisotropy ratio of ²( _c/ _ab ) 50 which is almost independent of temperature. Details of the crystal growth, heat treatment procedures, and the results of electrical and magnetic property measurements are presented.     

Surface resistance of large-area Tl2Ba2CaCu2O8 thin films at microwave and millimeter wave frequencies measured by three noncavity techniques

The surface resistanceR _s of Tl₂Ba₂CaCu₂O₈ films fabricated on LaAlO₃ wafers up to 3 inches (7.6 cm) in diameter through a post-deposition anneal process was measured over the frequency range 5.55–94.1 GHz by the following techniques: 5.55 and 27.5 GHz high-temperature superconductor (HTS)-sapphire resonators, 10 GHz parallel plate resonator, and 94.1 GHz scanning confocal resonator.R _s was found to exhibit a quadratic dependence on frequencyf at 77 K:R _s f ^2.0±0.1. The highest-quality films yieldR _s =145±15 at 10 GHz and 77 K. Scanning confocal resonator mapping ofR _s across a 2-inch (5.1 cm) diameter wafer yielded a base value forR _s of 16±1 m at 77 K and 94.1 GHz (equivalent to 180±10 at 10 GHz) and good uniformity inR _s across the wafer. HTS-sapphire resonator measurements ofR _s for fifteen 1.2 cm square parts cut from a 3-inch diameter wafer yieldedR _s values scaled to 10 GHz of 196±10 at 80 K. Similar values were measured for Tl₂Ba₂CaCu₂O₈ films prepared on both sides of a 2-inch diameter wafer.Rs values at 10 GHz and 80 K of 147–214 were maintained over the course of 40 independent and successive deposition runs and corresponding anneals under nominally identical film fabrication conditions. Surface resistance at 5.55 GHz remained below 80 for maximum rf magnetic fields up to 85 Oe at 4.2 K and 7 Oe at 80 K, respectively. Results are compared with predictions of the two-fluid model. The relative advantages and disadvantages of the different techniques for measuring surface resistance are discussed.     

Theory of superconductivity. 3. 2D conduction bands for high Tc. Bose-Einstein condensation transition of the third order

A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V ₁₁,V ₂₂,V ₁₂) among and between electron (1) and hole (2) Cooper pairs are differentiated, and identifying electrons (holes) with positive (negative) masses as those Bloch electrons moving on the empty (filled) side of the Fermi surface. The supercondensate is shown to be composed of equal numbers of electron and hole ground (zero-momentum) Cooper pairs with charges ±2e and different masses. This picture of a neutral supercondensate naturally explains the London rigidity and the meta-stability of the supercurrent ring. It is proposed that for a compound conductor the supercondensate is formed between electron and hole Fermi energy sheets with the aid of optical phonons having momenta greater than the minimum distance (momentum) between the two sheets. The proposed model can account for the relatively short coherence lengths observed for the compound superconductors including intermetallic compound, organic, and cuprous superconductors. In particular, the model can explain why these compounds are type II superconductors in contrast with type I elemental superconductors whose condensate is mediated by acoustic phonons. A cuprous superconductor has 2D conduction bands due to its layered perovskite lattice structure. Excited (nonzero momentum) Cooper pairs (bound by the exchange of optical phonons) aboveT _c are shown to move like free bosons with the energy-momentum relation=1/2v_Fq. They undergo a Bose-Einstein condensation atT _c = 0.977v _F k _b ^–1 n ^1/2, wheren is the number density of the Cooper pairs. The relatively high value ofT _c (100 K) arises from the fact that the densityn is high:n ^1/2–1 10⁷ cm^–1. The phase transition is of the third order, and the heat capacity has a reversed lambda ()-like peak atT _c .     

Vortex Lattice Melting in YBa2Cu4O8 with H∥ab

We report c-axis resistivity measurements in the mixed state of YBa₂Cu₄O₈ with the magnetic field applied parallel to the a-, b-, and c-axes. For all orientations of the magnetic field, a kink is observed in the resistive transition, associated with the first-order melting of an anisotropic three-dimensional vortex lattice. Whereas the melting lines for Hb and Hc obey the expected relation H _m = H ₀(1 – T/T _c ) ⁿ with n = 1.5, H _m (T) for Ha follows a different temperature dependence with a lower exponent. This result is consistent with a suppression of the melting line due to a reduction in the dimensionality of YBa₂Cu₄O₈ in this field geometry, as observed in normal-state magnetoresistance measurements.     

Upper limit ofTc for the copper oxides

The value of the critical temperature of the cuprates correlates with the doping level and is affected by the interplay of two competing factors: (1) the increase in carrier concentration, and (2) the pair-breaking effect of magnetic impurities. An analysis of the temperature dependence of the critical field leads to the conclusion that magnetic impurities are present even in a sample with the maximum observed value ofT _c.A new parameter, intrinsicT _c (T _cintr), which is its value in the absence of magnetic impurities, is introduced. The maximum value ofT _cintr, which corresponds to the maximum doping level, appears to be similar for different cuprates and to be equal to 160–170 K. This is the upper limit ofT _c in the cuprates.     

Mean polarizabilities and second and third virial coefficients of the gases C2H4, C2H6, and SF6

Mean polarizabilities ₀(₀, T) as well as second and third virial coefficients B(T) and C(T) of the equation of state of the gases C₂H₄, C₂H₆, and SF₆ have been determined from refractive index measurements with a Michelson interferometer for wavelength ₀=632.99 nm in the overall ranges 250 KT 340 K and 0p3 MPa of temperature T and pressure p. Some negative C(T) values at low temperatures have been obtained. The C(T) data could be fitted satisfactorily to the simple three-parameter function C(T)= a(T–T ₀) exp[ –b(T–T ₀)], with the maximum near the critical temperature T _c. A possible correlation between C(T) and the vapor pressure p _v(T) is discussed.