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 ${\zeta }_1$ and ${\zeta }_2$, respectively. The Gaussian fluctuation free energy is diagonalized, yielding N distinct $T_c$ values. Just above the highest $T_c$, the fluctuations are usually dominated by the three-dimensional (3D) regime of a single cellular OP. In the 2D regime further above $T_c$, more of the OP’s contribute to the fluctuations, their relative contributions depending upon the ${\zeta }_1$ and ${\zeta }_2$ values. The temperature (T) and angular (θ) dependence of the resulting fluctuation magnetization M(θ,T) is calculated.