Thermal Fluctuations in d-wave Layered Superconductors

We study the thermal fluctuations of anisotropic order parameters (OP) in layered superconductors. In particular, for copper oxides and a d-wave OP, we present some experimental consequences of fluctuations in the direction normal to the layers. It is shown that the c-axis penetration depth $\lambda_c$ can have a "disorder-like" quadratic temperature dependence at low temperature. The fluctuations are analyzed in the framework of a Lawrence-Doniach model with an isotropic Fermi surface. Anisotropies pin the orientation of the OP to the crystallographic axes of the lattice. Then we study an extended t-J model that fits Fermi suface data of bilayers $YBCO$ and $BSCCO$. This leads to a d-wave OP with two possible orientations and, including the thermal fluctuations, yields the announced temperature dependence of $\lambda_c$. Furthermore a reservoir layer is introduced. It implies a finite density of states at the Fermi energy which is successfully compared to conductance and specific heat measurements.