Thermodynamics of Gaussian fluctuations and paraconductivity in layered superconductors

A detailed theoretical analysis of the Gaussian fluctuations of the order p arameter in layered superconductors is performed within the Ginzburg-Landau (GE) theory. The available results for the Gaussian fluctuations are syste matized and a number of novel formulae for the fluctuation magnetization, n onlinear magnetic susceptibility, heat capacity and high-frequency conducti vity in layered superconductors are derived. We propose several new prescri ptions: how to determine the life-time constant of fluctuation Cooper pairs tau (0), the in-plane coherence length xi (ab)(0), the energy cutoff param eter epsilon (open scissors) = ch(2)/2m(ab)xi (2)(ab)(0), and the Ginzburg number epsilon (Gi). It is demonstrated, for example, how the spectroscopy of the life-time can be used to verify the existence of depairing mechanism s in layered cuprates. The ultraviolet regularization of the GL free energy is carried out by means of the well-known from the field theory zeta -func tion method. We further show that the archetype of the latter method has it s origin in the century of enlightenment and the novel result is that the f luctuation part of the thermodynamic variables of the layered superconducto rs can be expressed in terms of the Euler Gamma -function and its derivativ es. Universal scaling curves for the magnetic field dependence of the parac onductivity sigma (ab)(T-c,B), fluctuation magnetization M(T-c, B) and the heat capacity C(T-c, B) are found for the quasi-2D superconductors at T-c a nd further related to the form-factor of the Cooper pairs.