Anisotropic superconductivity in extendedt-Jmodels

Anisotropic superconductivity in layered ${\mathrm{CuO}}_2$ structures is theoretically examined by using extended t-J models. It is predicted that in multilayered structures the second transition can occur in superconducting states. The transition is between superconducting states belonging to different representations with respect to a symmetry operation of exchanging layers. Therefore, the transition is reduced to a sharp crossover when the layers are nearly equivalent. It is probable that above the crossover temperature the gap vanishes along lines on the Fermi surface in the three-dimensional Brillouin zone. However, around the crossover temperature the gap can start to open everywhere on the Fermi surface in multilayered structures distorted from tetragonal symmetry. The results can explain both the temperature dependences of the nuclear-magnetic relaxation time and the penetration depth in high-${\mathit{T}}_{\mathit{c}}$ superconductors, which appear to be inconsistent with each other.