Phase transition between d-wave and anisotropic s-wave gaps in high-temperature oxides superconductors

We numerically study models for superconductivity with two interactions: V^> due to antiferromagnetic. (AF) fluctuations and V^< due to phonons, in a weak coupling approach to the high-temperature superconductivity. The nature of the two interactions is considerably different: V^> is positive and sharply peaked at (±π,±π) while V^< is negative and peaked at (0, 0) due to weak phonon screening. The superconductivity is mainly induced by V^<. The positive interaction V^> (AF) is not effective in superconductivity, but important to give d-wave superconductivity. The gap order parameter △(k) is constant (s-wave) at an extremely overdoped region and it becomes anisotropic as doping is reduced. Then there exists a first-order phase transition between anisotropic s-wave and d-wave gaps as doping is reduced further. These results are qualitatively in agreement with preceding works; they should be modified in the strongly underdoped region by the presence of antiferromagnetic pseudogap due to the fluctuations.