Vortex lattice transition in D-wave superconductors

Making use of the extended Ginzburg Landau theory, which includes the fourth order derivative term, we study the vortex state in a magnetic field parallel to the $c$ axis. The vortex core structure is distorted due to this higher order term, which reveals t he fourfold symmetry. Futher, this distortion gives rise to the core interaction energy, which favo rs a square lattice tilted by $45^\circ$ from the $a$ axis. The critical field of this transition is determined. The magnetization diverges at the transition. This suggests the transition is of the fi rst order.