We consider a model of high-T_c superconductors with an anisotropic boson-mediated pairing mechanism corresponding to the nearest-neighbor interactions, and the one-particle dispersion relation characterized by 2D Fermi surface nesting. Based upon the tight-binding or t-J approaches with half-filling we show that the effective pairing potential coefficients and the dispersion relation, which can be characterized by the parameterη=2t_1/t_0, have a diverse and mutually competing influence on the values of transition temperatures. The spin-singlet d-wave symmetry superconducting state is realized for small values ofη, whereas for sufficiently large values, the spin-triplet p-wave symmetry superconducting state should be formed. The specific heat jump and the isotope shift, as functions of the parameter η, are evaluated for the d- and p-wave symmetry.
Electromagnetic response of cuprate superconductors is studied within the model of kinetic energy driven d-wave superconductivity by analyzing the Meissner effect. The kernel of the linear response function is found and employed to calculate the magnetic field penetration depth and the superfluid density of cuprate superconductors within the specular reflection model for a purely transverse vector potential. It is shown that the magnetic field penetration depth and the superfluid density depend linearly on temperature, except for a strong deviation from the linear characteristics at extremely low temperatures, which is attributed to nonlocal effects. The zero-temperature superfluid density is found to decrease linearly with decreasing doping concentration in the underdoped regime. The problem of gauge invariance in the theoretical description of the electromagnetic response is addressed, and an approximation which does not violate local charge conservation is proposed.
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