Static and Dynamical Anisotropy Effects in Mixed State of D - Wave Superconductors

We describe effects of anisotropy caused by the crystal lattice in d-wave superconductors with s-wave mixing using the effective free energy approach. Only the d-wave order parameter field d is introduced, while the effect of the s wave mixing as well as other effects breaking the rotational symmetry down to the fourfold symmetry of the crystal are represented by a single four (covariant) derivative term: ηd(Πy −Πx)d. The single vortex solution in a phenomenologically interesting range of parameters is almost identical to the two order parameters approach. We analytically consider the most general oblique lattice and orientation, but find that only rectangular body centered lattices are realized. A critical value ηc at which a phase transition from the rectangular lattice to the square lattice takes place. The influence on the phase transition line is discussed. The formalism is extended to the time dependent [email protected] [email protected] [email protected] [email protected]