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 .     

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.     

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.     

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.     

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 .     

Microwave surface resistance of epitaxial YBa2Cu3O7 thin films at 18.7 GHz measured by a dielectric resonator technique

We used a dielectric resonator technique for highly sensitive measurements of the temperature dependence of the microwave surface resistanceR _s of 1×1 cm² superconducting films at 18.7 GHz. It consists of a sapphire disc positioned on the film under investigation within a copper cavity which is acting as a radiation shield. In the TE₀₁ oscillation mode the highly reproducible quality factor of about 10⁵ results in a sensitivity of ±50 forR _s measurements. The temperature dependence ofR _s can be measured up to values as high as 1 . We have investigated several YBa₂Cu₃O₇ thin films prepared by high oxygen pressure d.c. sputtering on LaAlO₃ and NdGaO₃. Our best films exhibit a pronounced nonlinear behavior of the d.c. resistivity(T) with(300K)/(100K) values of about 3.7. Those films show, besides the initial fall-off just belowT _c , a further strong decrease ofR _s at low temperatures. This was observed both at 18.7 GHz and 87 GHz, as measured by a conventional cavity end plate replacement technique. ForTT_c/2 these films exhibit an exp (–T _c/T) dependence ofR _s with-values around 0.4. These observations may be explained by a superconducting energy gap with 2/kT _c0.8 for charge carriers localized in the CuO chains for YBa₂Cu₃O₇.     

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).     

Effect of sample density on magnetic penetration depth in YBaCuO ceramic superconductors

We have measured magnetic penetration depth(0) of high-T _c YBCO samples of different density by the cavity resonant frequency shift method at 10, 16.65, and 22.3 GHz microwave frequencies. The value of(0) at 10 GHz is found to decrease from 5850 Å to 2550 Å as the density of the sample increases from 4.4 to 5.3 g/cm³. The results of the frequency response of the penetration depth show a fairly constant value of(0) for all the three samples in the frequency range 10–22.3 GHz. The wide variation observed in the value of(0) for different density samples has been explained in terms of varying Josephson coupling strength in these ceramics.     

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.     

Mean polarizabilities and second optical and density virial coefficients of CH3OH and CCl2F2 between 300 and 355 K

Mean dipole polarizabilities ₀(, T) as well as second optical (or refractive index) virial coefficients b _R(, T) and second density virial coefficients B(T) of gaseous CH₃OH and CCl₂F₂ have been determined by precise measurements of the refractive index n(, T, p) [543 nm 633 nm, 300 K T 355 K, p<0.25 bar (CH₃OH) and p<3 bar (CCl₂F₂)]. ₀ critically compared with the few data in literature. The b _R of these gases was measured for the first time with the cyclic-expansion method. The values of ¦B¦ and b _R=3160(25) cm³ · mol^–1 measured for CH₃OH are considerably greater than the values calculated by Buckingham's statistical-mechanical expressions for a Stockmayer interaction potential. This difference is discussed by assuming dimerization via H bonds, with result H ₂ ⁰ –(28 ... 33) kJ · mol^–1 and S ₂ ⁰ –(116 133) J · mol^–1 · K^–1 for the dimerization enthalpy and entropy for standard conditions, respectively. On the other hand, Buckingham's formulae can be used with success to estimate b _R and B of CCl₂F₂.Dedicated to Prof. Dr. F. Kohler on the occasion of his 65th birthday     

Parallel-plate resonator of variable spacer thickness for accurate measurements of surface impedance of high-Tc superconductive films

Measurements of microwave surface impedance of high-T _c films at gigahertz frequencies and nitrogen temperature are performed. A simple technique employing a parallel-plate resonator with liquid nitrogen as a dielectric spaces is suggested. The use of a precise mechanical device provides smooth changing of distance between films from 200m down to zero. Coupling to the resonator is accomplished by means of two small antennas-half-wave vibrators for frequency 10 GHz. The method for determining resistivity and magnetic field penetration depth was based on the analysis of spacer thickness dependences of the resonator quality factor and frequency. YBa₂Cu₃O₇ films produced by a laser deposition technique on CaNdAlO₄ substrates withT _c =91 K andj _c =10⁷ A/cm² and on NdGaO₃ substrates withT _c =91 K andj _c =10⁶ A/cm² are examined, and the valuesR _s =0.6 m,=348 nm atf=8.97 GHz andR _s =0.5 m,=250 nm atf=10.12 GHz, respectively, are obtained at 77 K.     

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.     

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.     

Temperature-dependent collective pinning exponent in Bi2Sr2Ca2Cu3O10+x tapes and bulk samples with preferential crystallite orientation

The low-voltage-level current-voltage characteristics of Bi₂Sr₂Ca₂Cu₃O_10+x tapes and bulk samples with preferential crystallite orientation were measured in applied magnetic fields both parallel and perpendicular to the samples' surfaces. The data were interpreted within the framework of the collective pinning model. The collective pinning exponent changes from 1 to 0.5 (close toT _c), while in the case of unoriented samples it is constant (and equal to the theoretical value 1/2) as shown in an earlier paper. We suggest that this temperature dependence of is due to the change of the dimensionality of the intragranular vortices.     

Large-Area YBa2Cu3O7 ? x Films on Sapphire with Excellent Microwave Power Handling Capability

Crack-free thick YBa₂Cu₃O_{7 – x} films are prepared on CeO₂ buffered r-cut sapphire (2 inch in diameter) with thickness up to 700 nm, smooth surfaces (peak-to-valley roughness <10 nm), high critical currents (J _C > 2 MA/cm² at 77 K and 0 T), and low microwave surface resistances (R _s(77K) .4m and R _s(4.2K) .110 at 19.15GHz) comparable to the best values reported in the literature for YBCO films on structurally better matched substrates. These thick YBCO films were able to handle high microwave power corresponding to magnetic field amplitudes (B _HF) up to 54, 37, and 17.4 mT at 4.2, 50, and 77 K, respectively, which for the lower temperatures were limited by the available power of the 25-W HF amplifier. The high-power performance, which to our knowledge belongs to the best reported so far for unpatterned YBa₂Cu₃O_{7 – x} films, was achieved without any degradation of the samples despite frequent thermal cycling.     

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.     

Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region

A parametric crossover model is adapted to represent the thermodynamic properties of pure D₂O in the extended critical region. The crossover equation of state for D₂O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D₂O + H₂O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D₂O and for the D₂O + H₂O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T _c(x)T1.5T _c(x) and densities 0.35_c(x)1.65_c(x).     

Preparation of Tl-HTS-Films for Microwave Application

This paper presents the preparation of Tl₂Ba₂Ca₂Cu₃O_x thin films on 2 LaAlO₃-substrates for microwave applications and some aspects of phase formation. We found barium cuprate but no calcium cuprate as an intermediate phase before Tl₂O is incorporated into the film. Steps necessary for the formation of Tl₂Ba₂Ca₂Cu₃O_x-films with c-axis orientation are outlined. Our highest quality film exhibits a surface resistance of R_s = 6.5 m at 87 GHz and 77K .     

A New Method for the Estimation of Hc2 Anisotropy in Polycrystalline MgB2 Samples

By using isothermal magnetization measurements in polycrystalline MgB₂ samples, we estimate the H ^c _c2 in the interval [0, T _c]. By combining these measurements to the estimated H ^ab _c2 from the onset of the diamagnetic transition in isofield and isothermal magnetic measurements, an estimation of the anisotropy parameter can be achieved. The H ^c _c2 values coming from high quality polycrystalline samples agrees nicely to those obtained on single crystals. Our results show a temperature variation of the (T ) = H ^ab _c2/H^c2 with (T _c) 3.     

Magnetic Phase Diagram of Ca1?xMnxO

Alternating current susceptibility and direct current magnetization have been studied for polycrystalline Ca_1–x Mn _x O. On increasing the Mn content, magnetic ordering changes from spin glass behavior for 0.25 x 0.4 to antiferromagnetic order. The paramagnetic/antiferromagnetic transition is of second order for 0.5 x 0.65 and of first order for x 0.7. For low Mn concentrations, the high-temperature alternating current susceptibility can be described by a diluted Heisenberg magnet model developed for diluted magnetic semiconductors.