Abstract:
We argue based on theoretical considerations and analysis of experimental data that quasiparticle excitations near the nodes determine the low temperature properties in the superconducting state of cuprates. Quantum effects of phase fluctuations are shown to be quantitatively important, but thermal effects are small for $T \ll T_c$. An anisotropic superfluid Fermi liquid phenomenology is presented for the effect of quasiparticle interactions on the temperature and doping dependence of the low $T$ penetration depth.

Abstract:
Electron irradiation has been used to introduce point defects in a controlled way in the CuO2 planes of underdoped and optimally doped YBCO. This technique allows us to perform very accurate measurements of Tc and of the residual resistivity in a wide range of defect contents xd down to Tc=0. The Tc decrease does not follow the variation expected from pair breaking theories. The evolutions of Tc and of the transition width with xd emphasize the importance of phase fluctuations, at least for the highly damaged regime. These results open new questions about the evolution of the defect induced Tc depression over the phase diagram of the cuprates

Abstract:
It is shown that an account for combined effect of both nonmagnetic and magnetic scatterers on Tc and/or an assumption about a non-pure d-wave order parameter allows for a quantitative explanation of the experimental data on the electron irradiation-induced suppression of superconductivity in Y-123 single crystals within the AG-like pair breaking theory, without resorting to phase fluctuations effects.

Abstract:
Experiments on the irradiation-induced suppression of the critical temperature in high-Tc superconductors are analyzed within the mean-field Abrikosov-Gor'kov-like approach. It is shown that the experimental data for YBa2Cu3O7 single crystals can be quantitatively explained by the pair breaking effects under the assumption of the combined effect of potential and spin-flip scattering on the critical temperature and with account for a non-pure d-wave superconducting order parameter.

Abstract:
In certain materials with strong electron correlations a quantum phase transition (QPT) at zero temperature can occur, in the proximity of which a quantum critical state of matter has been anticipated. This possibility has recently attracted much attention because the response of such a state of matter is expected to follow universal patterns defined by the quantum mechanical nature of the fluctuations. Forementioned universality manifests itself through power-law behaviours of the response functions. Candidates are found both in heavy fermion systems and in the cuprate high Tc superconductors. Although there are indications for quantum criticality in the cuprate superconductors, the reality and the physical nature of such a QPT are still under debate. Here we identify a universal behaviour of the phase angle of the frequency dependent conductivity that is characteristic of the quantum critical region. We demonstrate that the experimentally measured phase angle agrees precisely with the exponent of the optical conductivity. This points towards a QPT in the cuprates close to optimal doping, although of an unconventional kind.

Abstract:
We show that an array of Josephson coupled Cooper paired planes can never have long range phase coherence at any finite temperature due to an infrared divergence of phase fluctuations. The phase correlations decay in a slow enough manner providing enough local phase coherence as to make possible the nucleation of vortices. The planes then acquire Kosterlitz-Thouless topological order with its intrinsic rigidity and concomitant superfluidity. We thus conclude that the high temperature superconducting cuprates are topologically ordered superconductors rather than phase ordered superconductors. For low enough superfluid densities, as in the underdoped cuprates, the transition temperature, Tc, will be proportional to the superfluid density corresponding to vortex-antivortex unbinding, and not to disappearance of the Cooper pairing amplitude. Above Tc, but below the BCS pairing temperature Tp, we will have a dephased Cooper pair fluid that is a vortex-antivortex liquid. The AC and DC conductivities measured in this region are those corresponding to flux flow. Furthermore there will be vortices above Tc which will lead to Nernst vortexlike response and there will be a measurable depairing field H_c2 above Tc as evidenced by recent experiments.

Abstract:
Phase fluctuations of the superconducting order parameter play a larger role in the cuprates than in conventional BCS superconductors because of the low superfluid density of a doped insulator. In this paper, we analyze an XY model of classical phase fluctuations in the high temperature superconductors using a low-temperature expansion and Monte Carlo simulations. In agreement with experiment, the value of the superfluid density at temperature T=0 is a quite robust predictor of Tc, and the evolution of the superfluid density with T, including its T-linear behavior at low temperature, is insensitive to microscopic details.

Abstract:
Within the phase fluctuation picture for the pseudogap state of a high-$T_{c}$ superconductor, we incorporate the phase fluctuations generated by the classical XY model with the Bogoliubov-de Gennes formalism utilizing a field-theoretical method. This picture delineates the inhomogeneous characteristics of local order parameters observed in high-$T_{c}$ superconductors above $T_{c}$. We also compute the local density of states near a non-magnetic impurity with a strong scattering potential. The resonance peak smoothly evolves as temperature increases through $T_{c}$ without showing any sudden broadening, which is consistent with recent experimental findings.

Abstract:
We explore a BCS Bose Einstein crossover scenario for $0 \leq T \leq T_c$ and its implications for the superfluid density and specific heat. The low lying excitations consist of nodal (fermionic) quasi-particles as well as excited (bosonic) pair states. Semi-quantitative comparison with cuprate data is reasonable, with no compelling indications for Landau parameter effects.

Abstract:
Electronic Raman scattering from high- and low-energy excitations was studied as a function of temperature, extent of hole doping, and energy of the incident photons in Bi_2Sr_2CaCu_2O_{8 \pm \delta} superconductors. For underdoped superconductors, short range antiferromagnetic (AF) correlations were found to persist with hole doping, and doped single holes were found to be incoherent in the AF environment. Above the superconducting (SC) transition temperature T_c, the system exhibits a sharp Raman resonance of B_{1g} symmetry and energy of 75 meV and a pseudogap for electron-hole excitations below 75 meV, a manifestation of a partially coherent state forming from doped incoherent quasi particles. The occupancy of the coherent state increases with cooling until phase ordering at T_c produces a global SC state.