Abstract:
A universal and self-consistent set of equations is developed utilizing the principle empirical parameters of Superconductivity which are the coherent condensation temperature, the Debye temperature, the coherent condensation energy gap at critical temperature equals zero degrees Kelvin and the electron phonon coupling constant. Empirical data from both crystalline elements and amorphous compounds is shown to produce the same self consistent relationships which are critical temperature equals Debye energy/2 exp(-2/electron phonon coupling constant), coherent condensation temperature equals the Debye energy exp (-2/electron phonon coupling constant) and the ratio of coherent condensation temperature/critical temperature equals 2.0 i.e. coherent condensation temperature equals coherent energy gap and is found to be constant for all superconductors. We also find that electron phonon coupling constant is related exponentially related to the zero point energy where the zero point energy equals the Debye energy/2 and is the zero point energy of a quantum mechanical oscillator. These relationships are derived exclusively from electron phonon mediated superconductor data and are also shown to encompass cuprate superconductors with ease. [Abridged]

Abstract:
We have measured thermoelectric power (TEP) as a function of hole concentration per CuO2 layer, Ppl, in Y1-xCaxBa2Cu3O6 (Ppl = x/2) with no oxygen in the Cu-O chain layer. The room-temperature TEP as a function of Ppl, S290(Ppl), of Y1-xCaxBa2Cu3O6 behaves identically to that of La2-zSrzCuO4 (Ppl = z). We argue that S290(Ppl) represents a measure of the intrinsic equilibrium electronic states of doped holes and, therefore, can be used as a common scale for the carrier concentrations of layered cuprates. We shows that the Ppl determined by this new universal scale is consistent with both hole concentration microscopically determined by NQR and the hole concentration macroscopically determined by the Cu valency. We find two characteristic scaling temperatures, TS* and TS2*, in the TEP vs. temperature curves that change systematically with doping. Based on the universal scale, we uncover a universal phase diagram in which almost all the experimentally determined pseudogap temperatures as a function of Ppl fall on two common curves; upper pseudogap temperature defined by the TS* versus Ppl curve and lower pseudogap temperature defined by the TS2* versus Ppl curve. We find that while pseudogaps are intrinsic properties of doped holes of a single CuO2 layer for all high-Tc cuprates, Tc depends on the number of layers, therefore the inter-layer coupling, in each individual system.

Abstract:
We have recently used inelastic neutron scattering to measure the magnetic excitation spectrum of La(1.875)Ba(0.125)CuO(4) up to 200 meV. This particular cuprate is of interest because it exhibits static charge and spin stripe order. The observed spectrum is remarkably similar to that found in superconducting YBa(2)Cu(3)O(6+x) and La(2-x)Sr(x)CuO(4); the main differences are associated with the spin gap. We suggest that essentially all observed features of the magnetic scattering from cuprate superconductors can be described by a universal magnetic excitation spectrum multiplied by a spin gap function with a material-dependent spin-gap energy.

Abstract:
We consider the effect of non-magnetic impurities on the onset temperature $T^*$ for the $d-$wave pairing in spin-fluctuation scenario for the cuprates. We analyze intermediate coupling regime when the magnetic correlation length $\xi/a >1$ and the dimensionless coupling $u$ is O(1). In the clean limit, $T^* \approx 0.02 v_f/a$ in this parameter range, and weakly depends on $\xi$ and $u$. We found numerically that this universal pairing scale is also quite robust with respect to impurities: the scattering rate $\Gamma_{cr}$ needed to bring $T^*$ down to zero is about 4 times larger than in weak coupling, in good quantitative agreement with experiments. We provide analytical reasoning for this result.

Abstract:
The disclosure of spinon superconductivity and superconductivity mediated by spin-waves in hole-doped Bi2212 cuprate raises the question about the origin of the superconductivity in other cuprates and specially in an electron-doped NCCO cuprate.

Abstract:
Superconductivity in the cuprates emerges from an enigmatic metallic state. There remain profound open questions regarding the universality of observed phenomena and the character of precursor fluctuations above the superconducting (SC) transition temperature (T_c). For single-CuO_2-layer La_{2-x}Sr_xCuO_4 (LSCO) and Bi_2(Sr,La)_2CuO_{6+\delta} (Bi2201), some experiments seem to indicate an onset of SC fluctuations at very high temperatures (2-3 times T_c^{max}, the T_c value at optimal hole concentration p), whereas other measurements suggest that fluctuations are confined to the immediate vicinity of T_c(p). Here we use torque magnetization to resolve this conundrum by systematically studying LSCO, Bi2201 and HgBa_2CuO_{4+\delta} (Hg1201). The latter is a more ideal single-layer compound, featuring high structural symmetry, minimal disorder, and T_c^{max} = 97 K, a value more than twice those of LSCO and Bi2201. We find in all three cases that SC diamagnetism vanishes in an unusual exponential fashion above T_c, and at a rapid rate that is universal. Furthermore, the high characteristic fluctuation temperatures of LSCO and Bi2201 closely track T_c(p) of Hg1201. These observations suggest that, rather than being indicative of SC diamagnetism, the fluctuations at high temperatures in the low-T_c^{max} compounds are associated with a competing order. This picture is further supported by an analysis of available results for double-layer cuprates.

Abstract:
The origin of the universal optical conductivity form sigma(omega) ~ (1-e^(omega/T))/omega established in numerical model studies of doped antiferromagnets and consistent with experiments on cuprates near optimal doping is discussed. It is shown that such a behaviour appears quite generally when the single-particle excitations are overdamped and their relaxation follows the marginal Fermi liquid concept. Relation to recent ARPES experiments is also discussed.

Abstract:
We developed an experimental method for measuring the intrinsic susceptibility \chi of powder of cuprate superconductors in the zero field limit using a DC-magnetometer. The method is tested with lead spheres. Using this method we determine \chi for a number of cuprate families as a function of doping. A universal linear (and not proportionality) relation between Tc and \chi is found. We suggest possible explanations for this phenomenon.

Abstract:
We report on a study of the influence of defects introduced in the CuO$_{2}$ planes of cuprates in a wide range of hole dopings n. T$_{c}$ and electrical resistivity $\rho (T)$ measurements have been performed on electron irradiated YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ and Tl$_{2}$Ba$_{2}$CuO$_{6+x}$ single crystals. A universal scaling between the decrease in T$_{c}$ and $\UNICODE[m]{0x394}\rho_{2D}\UNICODE[m]{0xd7}n$, where $\UNICODE[m]{0x394}\rho _{2D}$ is the increase of the 2D-resistance induced by the defects, is found for all the samples investigated here. This demonstrates that n is the relevant parameter to describe the transport properties all over the phase diagram, in contradiction with a recent suggestion of a change in the number of carriers from n to 1-n at the optimal doping. Moreover, the analysis of our data suggests that strong scattering persists on the overdoped side.

Abstract:
The polarization dependence of magnetic excitations in the quasi one-dimensional antiferromagnet BaCu2Si2O7 is studied as a function of momentum and energy transfer. The results of inelastic neutron scattering measurements are directly compared to semi-analytical calculations based on the chain-Mean Field and Random Phase approximations. A quantitative agreement between theoretically calculated and experimentally measured dynamic structure factors of transverse spin fluctuations is obtained. In contrast, substantial discrepancies are found for longitudinal polarization. This behavior is attributed to intrinsic limitations of the RPA that ignores correlation effects.