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 λc 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 Y BCO and BSCCO. This leads to a d-wave OP with two possible orientations and, including the thermal fluctuations, yields the announced temperature dependence of λc. 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
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