Phenomenological model of the copper oxide superconductors

We propose a phenomenological model for the copper oxide superconductors in which one complex s-wave order parameter (OP) is associated with each of the N conducting layers per unit cell, with N-1 equal spacings d and one different spacing d'; the c axis repeat distance s=d'+(N-1)d. The layers are coupled by Josephson-like tunneling, with parameters ζ1 and ζ2, respectively. The Gaussian fluctuation free energy is diagonalized, yielding N distinct Tc values. Just above the highest Tc, the fluctuations are usually dominated by the three-dimensional (3D) regime of a single cellular OP. In the 2D regime further above Tc, more of the OP's contribute to the fluctuations, their relative contributions depending upon the ζ1 and ζ2 values. The temperature (T) and angular (θ) dependence of the resulting fluctuation magnetization M(θ,T) is calculated