Pair breaking, “intrinsic”Tc, and the upper limit ofTc in the cuprates

The presence of magnetic impurities leads to a drastic decrease inT _c in the overdoped region, gaplessness, and the usual temperature dependence ofH _c2. The magnetic moments are localized on the apical oxygen site, and this allows us to explain the increase inT _c with the increase in the number of Cu-O planes in the unit cell. Applied pressure can raiseT _c above the usual value at optimum doping, toward the intrinsicT _c. The cuprates as a class of compounds have an upper limit ofT _c in the rangeT _c,upp=160–170 K.     

Upper limit ofT c 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, “intrinsic”T _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.     

Magnetic penetration depth of Tl2Ba2CuO6+δ:Tc～σ0 in the overdoped region

We report transverse-field muon-spin-rotation experiments carried out on Tl₂Ba₂CuO₆₊ . This system spans the whole overdoped regime, andT _c is reduced by excess oxygen doping, which increases the normal-state carrier concentration. In the heavily overdoped regime(0) is found to scale linearly with the superconducting critical temperatureT _c , similar to the behavior previously observed for other cuprates in the underdoped regime. However, for the overdoped region one has to explain the reduction of ₀, thus the increase of the magnetic penetration depth, in spite of an increasing normal-state carrier concentration. We discuss some possible explanations for this behavior.     

Observation of X-band SQUID signals in a High-Tc superconducting film device

A microwave superconducting magnetometer is described in which a microstrip resonator is coupled to a two-hole high-T _c thin-film SQUID device. Both the microstrip circuit and the thin-film SQUID were fabricated by photolithography techniques. The YBCO thin film was deposited on single-crystal substrate of yttria-stabilized zirconia [YSZ(100)] by an ion beam sputtering technique producing a superconducting transition measured at a critical temperature ofT _c =92 K to within T 3 K. Non linear oscillatory behavior was observed in the microstrip resonator when inductively coupled to the SQUID. This nonlinear behavior yielded a microwave device in which the reflected microwave power varied with applied DC magnetic flux.     

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.     

High Tc: Top Down or Bottom Up?

We present and discuss recent tunneling results, which shed some light on the two contradicting approaches to the high-T _c problem. The top-down approach starts from the ansatz that the anomalous properties of the cuprates in their normal state above T _c need to be understood first, before the problem of superconductivity can be tackled successfully. On the other hand, in the bottom-up approach, both high T _c and the anomalous normal-state properties come about because of the vicinity of a quantum critical point. Our new tunneling results indicate that in the superconducting state, at some critical doping, the order parameter goes from a pure d-wave on the underdoped side to a complex one on the overdoped one. This symmetry breaking lends support to the hypothesis that there does exist a quantum critical point and, therefore, favors the bottom-up approach.     

Musical, Bond Ordered Superconductors—Does a Common Phenomenological Model Hold for All High Tc Materials [Cuprates, C60, MgB2, C–S Composites etc.]?

The presence of high T _c (e.g., 117 K) in doped C₆₀ poses the question for the ultimate condition of superconductivity in this and related systems, which are devoid of complex ingredients such as magnetic transition metals. To answer this question, essential aspects of cuprate phenomenology are generalized. A quantitative and universal T _c formalism is developed from empirical rules for the cuprates. Accordingly, T _c increases linearly on doping up to a sharp peak, corresponding to an optimal charge order filling, and decreases thereafter. The hole filling degree of an optimal bond order depends on lattice pressure. Shape of the T _c-hole dependence and magnitude of T _c on the bond order model are born out by transistor doping of CaCuO₂, which is here used as a calibration. Inferences are drawn concerning the optimal bond order. Accordingly, linear local pair kernels are based on a newly postulated trijugate bond system that is mobile, while electronically frozen orders are based on tetrajugate bonding. In the superconductor, linear pair patterns are correlated into a two-dimensional bond order pattern by energies such as elasticities. This concept is here extended to materials based on other electronegative materials. Accordingly, arguments are presented that a common basis for their superconductivity lies in a novel chemical bonding state (e.g., trijugate) in a doped covalent lattice. The hallmarks of the bond order model are also born out by the curve shape of transistor doping of C₆₀. A disproportionation of pairs per molecule is proposed for optimal doping. Complex redox equilibria within laminated layers in the structure can lead to self-doping and can relieve lattice pressure in complex cuprates, MgB₂, C₆₀, or C–S composites.     

A realistic microscopic theory for the high-Tc cuprates

The electronic structure of the high-T_c cuprates is worked out by decomposing the orbitals around the Fermi level into large-U and small-U components. The large-U orbitals are treated by the slave-fermion method, the small-U orbitals by a mean-field approach, and the hybridization between them is then worked out. It turns out that hopping energy binds the spin and the charge of the large-U orbitals. The state so obtained is either antiferromagnetic, or paramagnetic with antiferromagnetic fluctuations and with violation of parity. Two types of charge carriers are predicted: (i) spinless polarons with a very small bandwidth, explaining the anomalous thermoelectric power, the mid-infrared peak, lattice anomalies, etc.; (ii) anomalous carriers of both charge and spin, explaining marginal-Fermi-liquid behavior and deviations from it, anomalous relaxation time, the systematic behavior of the resistivity, the Hall constant, the Hall angle, etc.     

A Critical Examination of the Spin Dynamics in High-Tc Cuprates

A critical examination of the spin dynamics in high-T _c cuprates is made in the light of recent inelastic neutron scattering results obtained by different groups. The neutron data show that incommensurate magnetic peaks in YBCO belong to the same excitation as the resonance peak observed at (/a, /a). Being observed only in the superconducting state, the incommensurability is rather difficult to reconcile with a stripe picture. We also discuss the link between the resonance peak spectral weight and the superconducting condensation energy.     

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.     

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.     

Low-Field microwave measurements of YBa2Cu3O7?x near the superconducting transition temperature

Novel microwave absorption and dispersion measurements have been performed on well-characterized single-crystal platelets of the high-T _c superconductor YBa₂Cu₃O_7–x . The results are explained in terms of the rapid variation of the penetration depth near and belowT _c . Since EPR measurements are very sensitive to small changes in absorption and dispersion, this technique should be very useful in the understanding of the transition temperature region in both new and old superconducting materials.     

Spontaneous nuclear ferromagnetic ordering of in nuclei in AuIn2 Part I. Nuclear specific heat and nuclear susceptibility

We have measured the nuclear specific heat C_n and nuclear susceptibility _n of In nuclei (I=9/2, =5.5 _n) in the cubic intermetallic compound AuIn₂ (Korringa constant =0.11 Ksec) in the normal conducting state at 30K10mK and 2mTB115 mT. Our data show a positive nuclear Weiss temperature =+ 43 K and that the In nuclei undergo a nuclear ferromagnetic transition at T_c=35 K. The In nuclei experience an internal field of about 10 mT (obtained from C_n at T>T_c ). The nuclear ordering temperature T_c and the internal field increase with applied magnetic field. From the data we deduce exchange constants for the investigated system. The critical entropy reduction S(T_c)/S_max=8.6% and critical enthalpy E=0.28 RT_c are in reasonable agreement with the measured ordering temperature T_c,applying the Heisenberg model for a simple cubic I=9/2 spin system. The nuclear spin relaxation time calculated from the real and imaginary parts of _n is 10 msec at T>50 K, but drops to <1msec at T_c.This is the first observation of a spontaneous nuclear magnetic ordering transition in a not-hyperfine-enhanced metal at thermal equilibrium, i.e. at T _nuclear =T _electron .     

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.     

How “Musical” Are High-Tc Superconductors and What Can Empirical Rules Tell About Their Origin?

It is shown that parameters such as optimal T _c for cuprate superconductors or details of their doping curves can be organized on phenomenological rules. Accordingly, T _c in a range between a kink and the optimum scale linearly with the number of effective holes h _e, according to T _e = h _e T _c ^e, with T _c ^e = 600 K. Effective holes are composed of the difference between holes in the Cu—O bonds in the CuO₂ planes, h _p, and holes in the Cu—O bonds with the c axis or apical O, h _e, according to h _e = h _p– h_c = fh _p. The deleterious effect of the apical O manifests itself in three levels, depending on the basic modes of its coordination of the CuO₂ planes in zero, one, or two sheets (according to factor f = 1, 2/3, ¹/₂). The values of h _p at T _c optimum tend to rational fractions, ranging from 1/6 to 1/3, and are determined by lattice pressure. This musical or harmonic T _c matrix, originating from two structurally determined factors, groups optimal T _c into families. Knight shift data, establishing h _p, bear out the general assumptions. Some flexibility in the range within families is observed. This flexibility indicates the operation of more complex influences from structural detail, such as the varying distance of Cu to the apical O. The existence of ranges within optimal T _c families indicate a somewhat tunable rather than a strict musical T _c-level scheme with measured intervals. The details of the doping curves are similarly organized. These phenomenological rules suggest the operation of bond ordering effects. Arguments for the actual nature of the bond orderings are presented in terms of local pairs of doped bonds in trijugate positions. These quantitative concepts can be expanded to other characteristic features in the doping curves of cuprates and other high-T _c materials such as C or B containing systems, providing a universal frame for explaining high-T _c superconductivity in bond ordering terms.     

Spin Gap Effects on Bulk R1+xba2?x Cu3O7?δ (R=Eu or Nd and 0≤x≤0.4)

Spin gap effects on the underdoping states of the bulk system of R_1+x Ba_2–x Cu₃O_7– (R = Eu or Nd and 0 x 0.4) were investigated through transport property measurements. The underdoping states were achieved by, alternatively substituting R³⁺ for Ba²⁺ ions in the system rather than adjusting the oxygen deficiency. The excess R³⁺ ions were to occupy the Ba sites of the crystalline lattice as revealed from Rietveld analysis for powder X-ray diffraction. The underdoped materials were observed to first undergo spin pairing transition in the temperature range well above T _c, and come across with superconducting transition at T _c. The increasing feature observed for spin gap temperature and the decreasing one for T _c, as the concentration of holes decreases, are in qualitatively good agreement with theoretical predictions from the mean-field RVB model.     

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.     

Comparison of Superconductivity and Structure for Lanthanum Replacing for Barium and Copper in YBa2Cu3Od

X-ray diffraction studies and the resistivity measurements are used to characterize the structure and the superconductivity of the nominal composition of YBa₂Cu_{3 – x} La _x O _d (YBCLO) cuprates with x 0.30. There was a BaCuO₂ impurity phase detected with x 0.10. The structure of the main phase (123) has the orthorhombic form with Pmmm symmetry in the whole doping range. With increasing content of lanthanum, x, the lattice constants increase for x < 0.04, and decrease for x 0.04. Rietveld refinements for X-ray diffraction show that the dopant of lanthanum substitutes for copper in the lower doping level, and replaces for both barium and copper in the high doping level. The zero-resistance temperature T _c0 first increases with the increase of the content of lanthanum in YBCLO as x 0.04 and then decreases with x as x 0.04. We compared the results with those of La-doped YBa_{2 – z} La _z Cu₃O _y cuprates. The different relationship in superconductivity dependence of lanthanum content may result from the strains due to the different occupancy of lanthanum in the unit cell of YBa₂Cu₃O _d .     

d-Hole localization and the suppression of superconductivity in YBa2(Cu1-xZnx)3O7?y

The temperature and Zn concentration dependence of the electrical resistivity, specific heat, magnetic susceptibility, and electron paramagnetic resonance (EPR) spectra of YBa₂(Cu_1–x Zn _x )₃O_7–y withy0.1 has been measured forx0.16. In addition, the temperature and field dependence of the magnetization has been measured for 2<T<300K and 0<H<9.0T, along with the temperature and quasihydrostatic pressure dependence of the electrical resistivity for selected samples for 0<P<13 GPa. The substitution of Zn for Cu in YBa₂Cu₃O_7–y causes a rapid and nearly linear depression of the superconducting transition temperature,T _c , withT _c going to 0 K forx 0.10. YBa₂(Cu_1–x Zn _x )₃O_7–y retains the YBa₂Cu₃O_7-y orthorhombic structure forx0.16 for both the superconducting and nonsuperconducting samples. Initially, the unit cell volume increases nearly linearly with Zn content; however, an abrupt change occurs in the vicinityx=0.8–0.10. Forx<0.10, the temperature dependence of the electrical resistivity,(T), is metallic-like (d/dT>0) and increases gradually with increasing Zn content. However, forx 0.10,(T) becomes semiconductor-like, with a very rapid increase of the resistivity with increasingx. The electrical resistivity, magnetic susceptibility, EPR spectra, and specific heat all indicate that thed-holes associated with the Cu ions become localized in the nonsuperconducting phase,x>-0.10.